Synthesis of the system of automatic curing by the method of logarithmic frequency characteristics. Synthesis of linear sau by the frequency method

Logarithmic method frequency characteristics vikoristovuetsya vyznachennya frequentnyh transfer functions koriguvalnyh pristroїv, nablizhayut dynamіchnі pokazaniki to bazhanim. The most efficient method is used for the synthesis of systems with linear or digital devices, which can be corrected, but in such systems, the frequency characteristics of the lines do not fall into the amplitude of the input signals. Synthesis of ACS by the method of logarithmic frequency characteristics, including the following operations:

At the first stage, behind the transfer function of the fixed part of the ACS, there will be a logarithmic frequency response. It is best to do the selection of asymptotic frequency indicators.

At another stage, there will be a logarithmic frequency response of the self-propelled guns, as if it would satisfy the set drivers. Depending on the type of the bazhanoy LACHH, it is carried out, depending on the recognition of the system, the hour of the transitional process, re-regulation and pardon coefficients. In this case, typical frequency characteristics for systems with a different order of astatism often vary. When prompted by the bazhanoї LACHH, it is necessary to remember that the type of amplitude characteristic basically determines the nature of the transitional processes and there is no need to introduce a phase frequency response. Remains true in times of minimal-phase systems, for which the presence of zeros and poles is characteristic, rotting near the right plane. When choosing a large logarithmic amplitude and phase characteristics, it is important that the rest provide the necessary margin of stability at the frequency of the system. For this vicorist, there are special nomograms, the type of which is shown in fig. one.

Figure 16‑1 Curves for selection of resistance margin by amplitude (a) and phase (b) fallow by magnitude of overshoot

The most significant indications of the ACS in dynamic modes are reached when the amplitude characteristic of the abscissa axis changes with a flicker of -20 dB/dec.

Figure 16‑2 Designation of PKU characteristics

At the rest of the stage, equalizing the frequency characteristics of the uncorrected system and the main frequency characteristics, the frequency power of the corrective device is determined. With varying linear correction methods, the logarithmic frequency response of the post-correction adjustment (PKU) can be found in the LAFH of an uncorrected system with the LAFH ACS, tobto

Otzhe

It should be noted that from the transfer function of the successive koringuval attachment it is easy to assign the transfer function of the lances of the lancet of a direct or reverse link, for the help of which, correction of the dynamic indicators of the ACS is needed.

The next stage is the designation of the method of implementation, the scheme and the parameters of the building.

The rest stage of the synthesis will add a correction - a re-adjustment of the ACS, which will help inspire the schedules of the transitional processes for the system with the selected add-on, which is corrected. At what stage do you have to win the koshtiv counting technique that modeling software complexes VinSim, WorkBench, CircuitMaker, MathCAD.

Under the synthesis, it is necessary to understand, create, design, adjust the optimal system of all parameters. Therefore, designers, creators of ATS are engaged in synthesis. When operating already existing systems, for example, they are serially released, it may be less about upgrading the parameters when the system exits from the necessary modes for other reasons.

Synthesis Methods

1. When creating ACS of the necessary recognition, we must first of all know that it won’t perform its functions of control and regulation from the given accuracy, the warehouse of the elemental base (pidsilyuvachi, regulators, conversion, motors, sensors, etc.) that is optimal for technical and economic indications is small. ), so that it would provide for the necessary tightness, swiftness, and momentary disruption, it would be simple, supple, handy in operation and economical.

At this stage of nutrition, the dynamics are less likely to hurt the rough approach, for example - do not choose the elements of the svіdomo inconsistency, with the great fast hours, resonantly thin.

2. Power supply for static characteristics, accuracy of command processing and high technical and economic indicators for technological processes and the economies of the central ones, and for the most important ones. To that, unimportant to those without good quality dynamic modes of ACS will not be accepted into operation, the synthesis of the її structure for ensuring the necessary modes will be carried out at another stage, if functional diagram, the storage of elements and the parameters of the system are installed in front. Pojdnati skіlki-nebud effectively insulting etapi not vdaєtsya.

For the whole group, the first stage of the ACS was designed to sound a rich contour structure with a folding transfer function, the analysis of which gives unsatisfactory results from the quality of the transitional processes. To that її it is necessary to ask for the bazhanih characteristics and scoring.

Synthesis of ACS of the required capacity

Synthesis of the system is due to be carried out by changing the structure for satisfaction necessary assistance. Characteristics of the system, yakі vіdpovіdat vimogam, called bazhanimi characteristics, vіdmіnu vіd nayavnyh, yakі mаyut vihіdna suboptimal system.

The basis for the bazhanyh characteristics is the necessary indications of the system: stability, speed code, accuracy and other. The shards of the largest width have logarithmic frequency characteristics, then we can look at the synthesis of ACS for the LAFC and LPFC.

1. Pobudov's basic characteristics are based on the mid-frequency section, which characterizes the stability, swidcode, and the form of the transitional process of the system. The position of yoga is determined by the frequency in relation to s. (Fig.1.8.1).

The frequency depends on the required hour of the transitional process tpp and the allowable overshoot:

Fig.2.

• 2. Through the point c, draw the mid-frequency asymptote of the bajan indications with a gain of 20 dB/dec (Fig. 1.8.1.).
• 3. We know the low-frequency warehouse іz 2.

Sounds ask the quality of the system for the speed Dsk and quicker Dsk.

We know the frequency

Peretin tsієї asymptotics of the mid-frequency intermediary її zlіva at the frequency that happens.

4. I will choose frequency 3 so that 3/ 2 = 0.75 or lg 3-lg 2 = 0.7 dec, which will ensure your mind's strength.

My mind has insurance coverage:

it is also possible to tweak for substitution of the mid-frequency asymptote.

If there is no clear space for obvious sight, then choose 2 and 3 minds (Fig. 1.8.1, b)

L2=(616)dBLc(c)=-(616)dB(1.8.4)

The improvement of the plot 3 - 2 is not sufficient.

5. We know the low-frequency warehouse 1. For the quality factor of the speed, the strength coefficient

Dsk = Ksk. (1.8.5)

We add Ksk on the frequency axis, we draw the asymptote with a 20 dB/dec through the th point and finish on the transition with another asymptote. The cross point is a low-frequency warehouse z 1.

6. Revisited for safety margin by phase

the phase at the frequency is not guilty of revisiting - with a guarantee of 45.

7. Revisiting the minds of missing the bazhana LACHH to the fenced zone (Fig. 1.8.1, a).

i LK = 20lgKsk, (1.8.7)

de Ksk \u003d - the coefficient of the strength of the open-circuit system, or the quality factor for the speed.

Let's just bring some results to the task of the synthesis of ACS and the so-called authors.

Before the first results in the development of tasks for the synthesis of ACS, the hyperbole of I.A. Vishnegradsky (1832-1895), for the help of which the area of ​​resistance and the area of ​​non-resistance of the ACS are designated, the behavior of which is described by the DC of the third order. Hyperbol I.A. Vyshnegradsky, the aim of the stabilization of the ACS was straightened out in the form “in-out”; it allows you to see the area of ​​aperiodic and colative transitional processes. Іz the result of I.A. Vishnegradsky, the task of modal management is closely related, formalized by N.M. Rosenbrock, that analytical version of the task for the scalar vipadka, proponed by Yu. Ackerman.

1940 rock V.S. Kulebakin of formulations pidhid, which can be called the principle of two-stage synthesis of regulators (principle of two-stage correction). The difference lies in the fact that at the first stage the reference operator of the closed system is selected (for stationary systems - the reference transfer function (PF) We(s)), and at the other stage - the block diagram of the controller parameters, as well as the other element, which may be tighter , which ensures the necessary security code.

As for the class of stationary linear ACS, then there are the results of choosing the reference transmission functions of the systems, which satisfies the technical capabilities with certain typical correlative signals, if they were taken away on the robots of V.A. Bodner, B.M. Petrova, V.V. Solodovnikova, G.S. Pospelova, T.M. Sokolova, S.P. Strelkova, A.A. Feldbaum.

When the task of the synthesis of ACS, scalable to the point of falling processes, an important role is played by the importance of the dynamic characteristics of the optimal (reference) system. The work of N. Vinera, L. Zade and J. Ragazzini, V.V. Solodovnikova, V.S. Pugachova, P.S. Matveeva, K.A. Pupkova, V.I. Kukhtenko.

In the frequency method, developed by V.V. Solodovnikov and widely expanded in engineering practice, research is carried out using the standard logarithmic amplitude frequency characteristics, for which the reports of nomograms indicative of the quality of the control processes. For the help of these nomograms, you can induce the reference amplitude frequency response (implementation of the 1st stage) of the system that is being synthesized, determine the transfer function, know the frequency characteristics and the transfer function of the corrigative device.

Ya.Z. Tsipkіnim looked at the designation of the reference characteristics of the closed ACS for vipadkіv, if the indicators of capacity were taken to be the integral quadratic input energy of the control.

Theoretical foundations, which are the basis for the task of synthesis, were introduced in the works of E.P. Popova and V.A. Bezsekersky.

A wide range of approaches to the achievement of the task of motivating the MM of the reference system, for example, with different Butterworth filters, was reviewed by A.A. Pervozvansky.

V.S. Kulebakinim bulo proponated method for the synthesis of systems automatic keruvannya, which are described by linear differential equations of the other and third orders, which are satisfied with some technical capabilities. Based on the selected reference transfer function, you can know the parameters real systems. This method of synthesis is called by the method of standard coefficients. The peculiarity of this method is characteristic in the fact that the parameters are calculated when the system of equalities is perfected, taking away the way of adjusting the coefficients for different operators of the reference and real transfer functions of the control system.

The main shortcomings of the method of standard coefficients for the synthesis task are often the inconsistency of the system equal, which serves as the designation of the parameters of the system.

V.A. Bodner showed that when the turn-around parallel corrigible outbuildings are turned on by the singing rank, the system becomes untied.

Іstotnі results, directing on the task of designing the parameters of the elements that enter the control system and ensure the accuracy of the reference MM and MM of the design system, otrimani V.V. Solodovnikov, V.G. Segalinim, Gullemin, T.M. Sokolovim, V.R. Evans, V.A. Bodner, V.S. Kulebakinim, E.G. Uderman and in.

To improve the engineering tasks, methods for the synthesis of ACS were developed for such productions:

• 1. Synthesis after setting the expansion of the poles of the image of the processes (transfer functions), as well as with the variation of the D-distribution of the area of ​​the coefficients of the image standard (or the area of ​​the parameters in the system).
• 2. Synthesis after setting the expansion of the poles and zeros of the transfer function, including the root locus method.
• 3. Synthesis for integral estimates.
• 4. Synthesis by the method of similarity of amplitude-phase and speech frequency characteristics.

Methods for the synthesis of the expansion of the poles in the transfer function are considered on the robots of G.N. Mikilsky, V.K. Popova, T.M. Sokolova, Z.Sh. Bloch, Yu.I. Neimark and in.

The method of synthesis for the given (mutual) expansion of the poles and zeros of the transfer function can provide all indications of the quality of the transitional process. Vin at robots S.P. Strelkova, E.P. Popova, Traxela et al.

Cream of that root methods proponed by K.F. Teodorchik, G.A. Bendrikov, G.V. Rimsky, Gullemin.

Method, razrobleniy N.T. Kuzovkov, allowing you to link the main indicators of the quality of the control process with the values ​​of the dominant poles and zeros of the synthesized system, as well as to insert the links of these poles and zeros with the parameter that varies.

For the purpose of defining a part of the parameters of victorization, there are also integral estimates of the strength of the transitional process, which are developed on the robots of L.I. Mandelstam, B.V. Bulgakov, V.S. Kulebakina, A.A. Feldbaum, A.A. Krasovsky and in.

System parameters are changed after minimization of functionality

de V - Vipadku has a quadratic form.

Integral I without integrating the differential equations of the system.

Synthesis of lines for the amplitude-phase characteristics of the adjusted and uncorrected proponation systems in robots A.V. Fatyeva.

A.V. Basharin divided graphic method synthesis of non-linear control systems, which can also be applied to systems with changing parameters.

N.M. Sokolov studied a wide range of tasks for the synthesis of linearized automatic control systems, at its main respect was attached to the methods of designating reference transfer functions. Approach to the development of problems for the synthesis of regulators, bringing them to the algorithm for calculating the parameters of the coercive lances with the variation of linear differential operators in a class of systems with changing parameters A.V. Solodovim.

p align="justify"> The turning points of system dynamics are one of the most important divisions in analytical mechanics, the essence of which lies in the fact that after the given description of the model of a dynamic system, it is necessary to know the system of forces that generates such forces from the tasks of power. L.M. Boychuk, O.O. Zhevnin, K.S. Kolesnikov, A.P. Krishchenko, V.I. Toloknov, B.M. Petrov, P.D. Krutko, E.P. Popov, G.Є. Pukhov, K.D. Zhuk, A.V. Timofeev and in.

As a result of the continuance of minds, strangulation (steaming) poured in the storm on the behavior of the object of management O.S. Vostrikov used to formulate the principle of localization as a structural way to encourage algorithms for managing dynamic objects, the essence of such a field in the organization in the system of management of a special swidkoi subsystem, delocalize the storm, influencing such behavior of the object of parrying. The method for the synthesis of ACS, as a way to ensure the formation of tasks showing signs of the quality of transitional processes for the minds of uncontrollable storms with the improvement of the old age at the same time with a great coefficient of strength in the law of the reversals, was proponated by the robots of A.S. Vostrikov and took away the development of the method of localization. In addition, as a fundamental methodical basis for the synthesis of non-linear control systems, the principle of localization is a structural support for a design control system, which is used in the molding of a special swidkoy subsystem for suppressing the injection of signal and parametric flares. Structural representation of systems that please given principle, allowing you to see the contour - the “contour of localization”, in your control system, to be the main rank of accomplishment of two tasks: designing a reference alignment and stabilizing smooth processes at the contour of localization. The principle of localization is satisfied different types systems, zokrema, systems with coercive regimes, systems with great coefficients in the law of the free link, and also a number adaptive systems and systems close to power to adaptive.

In this hour, you can see a few of the most directly related to the theory of synthesis of control systems, which allow you to secure the formation of the necessary indications in the form of transitional processes according to the external changes, as well as their invariance in terms of changing the characteristics of the disease.

An important direct approach is the theory of the synthesis of systems with a changeable structure and, zocrema, control systems with the organization of external modes in the wake of change, given by the expanse of the objects of the object. The foundations of which were directly seen on the robots of E.A. Barbashina, E.I. Gerashchenko, S.M. Gerashchenko, S.V. Emelyanova, B.M. Petrova, V.I. Utkina and took away the development of the robots of the rich successors. Tsey directly develops intensively and in the given hour.

Systems with a variable structure (UPS), introduced into the theory and practice of automatic control by S.V. Emelyanov, know the great theoretical development of that practical zastosuvannya. The main idea of ​​encouraging the UPS is to organize several structures of the regulator and change them in the process of managing the object in such a way that the world's largest winner will win the positive power of the skin structures and eliminate new disruptions of the system, possibly taking no power over the structure of the regulator. With this, the whole system can be taken away like a new power.

The solution of the problem of compensation for looking at functional static rows was considered by G. Van-Tries. We also prompted the algorithms for assigning compensating nuclei for the direct lance and the lance for the reverse link.

K.A. Pupkovim, A.S. Yushchenko and V.I. Kapalinim systematically and from the same methodological positions presented the theory of non-linear systems; the method for the synthesis of regulators in the class of non-linear systems, the behavior of which is described by the functional series of Volterra, has been developed. The class of systems іz vipadkovyh parameters was done on the robots of E.A. Fedosova and G.G. Sebryakov, and the development of the theory of sensitivity - in the works of R.M. Yusupov.

Apparatus of rich multi-pulse transitional functions (IPF), PF, frequency characteristics, as well as rich Laplace and Fur'e integral transformations, allowing O.M. Kiselov, B.L. Shmulyan, Yu.S. Popkov and N.P. Petrov to develop constructive algorithms for identification and optimization of non-linear stochastic systems, including the synthesis of regulators. Ya.Z. Tsipkinim and Yu.S. Popkov reviewed the methods for the synthesis of regulators in the class of discrete systems.

A.S. Shatalovim, V.V. Barkovsky, V.M. Zakharov examined a wide range of nutritional problems in the synthesis of automatic control systems, the results of which are shown in their robots. Apparatus for turning heads of the dynamics of ceramic systems vikoristano P.D. Krutko for the synthesis of the operator of the reverse link, as well as for the completion of other tasks.

I.A. Orurk looked at the task of synthesis in an offensive setting: the parameters of the controller are assigned in such a rank that:

• 1) dvoryuvavsya transitional process hе(t), which is brought up to the coordinate x(t), in the case of windstorms; in case of admissible bending, the curve he (t) is to blame for extreme values, speed and hour of overrunning the transitional process;
• 2) the tasks of the stability levels and the volume of the system were taken care of. Constructive algorithms for the synthesis of regulators for a wide class of systems from various devices for mathematical programming of proponing I.О. Diduk, A.S. Orurkom, A.S. Konovalovim, L.A. Osipov.

V.V. Solodovnikov, V.V. Semenovim and O.M. Dmitriyev developed the spectral methods and the design of ACS, which allow constructive algorithms for the synthesis of regulators, V.S. Medvedevim and Yu.M. Let's take a look at the algorithms for scaling the reference PFs in case of ripple inflows, as well as the methods for synthesizing attachments, which are corrected, with varying logarithmic frequency characteristics, for setting the power values ​​of the matrix of the control system for linear objects for the quadratic criterion of capacity.

V.I. Sivtsovim and N.A. Chulinim otrimani results, allow virishuvati zavdannya automated synthesis of control systems with the improvement of the frequency method; V.A. Karabanovim, Yu.I. Borodinim and A.B. Іonisіanom reviewed the work of zavdannya zagalnennya frequency method on the class of non-stationary systems. At the robots O.D. Teryaeva, F.A. Mikhailova, V.P. Bulekova et al. reviewed the problem of synthesis of non-stationary systems.

Of paramount importance is the problem of the synthesis of regulators in rich systems. In robots, which consider the problem of decoupling the problems of synthesizing regulators while vikonnі vіdomih vomog, otrimano vіdpovіdnі razvіznosti razviznosti (R. Brockett, M. Mesarovich). V.V. Solodovnikova, V.F. Biryukovim, N.B. Filimonov reviewed the results, the creation of a task for the synthesis of regulators in the class of rich systems; them to proponate the criterion of quality, which adequately reflects the dynamic behavior of rich systems; to formulate mind, for which tasks of synthesis can be decoupled. The results were reviewed by A.G. Oleksandrovim. Bagatma the authors (B. Anderson, R. Scott and others) reviewed the pidkhid, which is based on the “model performance” of the synthesized system and the Bazhan model. The robots of B. Moore, L. Silverman, W. Wonem, A. Morse and others have gone all the way to help the vastness of the station. The “geometric pidhіd” is celebrated by W. Wonem and D. Person.

One of the problems associated with the synthesis of regulators in a class of rich systems is the problem of "decoupling" channels. In line with the vision of this problem, there are the works of E. Gilbert, S. Wang, E. Devison, V. Volovich, G. Bengston and others.

Nutrition for the synthesis of regulators in rich systems from the stagnation of various approaches was found in the robots of E.M. Smagina, X. Rosenbrock, M. Yavdan, A.G. Aleksandrova, R.I. Ivanovsky, A.G. Taranova.

S. Kant and T. Kalat discussed the “problem of minimal design”. Nutrition, connected with diagonal dominance, vyvchali O.S. Sobolevim, X. Rosenbrock, D. Haukins.

Let us consider the nutritional problems and the synthesis of rich systems is dedicated to the work of M.V. Meyerova, B.G. Ilyasov. Diyalnist E.A. Fedosova looked at promising methods and designing rich dynamic systems.

The current period of the development of the theory of management is characterized by the formulation of such a task, which will protect the inaccuracy of our knowledge about the objects of management and the storms that are blowing on them. The task of synthesizing the regulator and estimating it will be due to the correction of non-insignificance in the model of the object and the characteristics of the inputs, which are one of the central ones in modern control theory. This importance has been brought to our attention, which is practical in any engineering manager of the design of self-propelled guns, there is a lack of insignificance in the model of the object and the knowledge of the class of inputs.

The solution to the problems of the theory of automatic control, which signifies the progress of science about the control of the remaining decades, is dedicated to the book of I.V. Miroshnik, V.O. Nikiforova and A.L. Fradkova, B.R. Andrievsky and A.L. Fradkova, S.V. Emelyanova and S.K. Korovina, V.M. Afanasiev, V.B. Kolmanovsky and V.R. Nosov.

The monograph by V. D. Yurkevich is devoted to the problems of synthesis of non-stop and discrete ACS in the minds of inconsistent information about the development of uncontrolled drilling with changing parameters of the control object.

New approaches in the monograph by V.A. Podchukaevim, de otrimano razvyazannya problems of synthesis in explicit visual (in analytical form) without any iterative chi per-sound procedures.

The results, which characterize the current stage of the development of important directly in the theory of automatic healing, were reviewed by E.A. Fedosovim, G.G. Sebryakov, S.V. Emelyanovim, S.K. Korovinim, A.G. Butkovsky, S.D. Zemlyakov, I.Є. Kozakovim, P.D. Krutko, V.Yu. Butkovsky, A.S. Yushchenko, I.B. Yadikinim and others.

It should be noted that the assistants, who have left for the rest of the fates, start, as a rule, with less than the other side of the modern theory. Deyaku information can be taken from articles and looking at Russian language, but only a mosaic picture of the subject. At the book B.T. Polyak and P.S. Shcherbakov "Robust stability and management" gives a systematic summary of the modern theory of management.

In the rest of the decade, a number of monographs and articles were published that dealt with such problems as the development of the theory of systems of geometric methods, the theory of catastrophes and the theory of chaos, adaptive and robust control, the class of intelligent systems and neurocomputers and others.

The concept of bifurcation is introduced, the main definitions are considered, the class of operators is assigned the points of bifurcation, that is. points, which have a new, non-trivial development of a new, non-trivial alignment. It is also shown that the chaotic behavior of dynamic systems is characterized by a high sensitivity to the minds of the cob and the impossibility of transferring behavior at a great interval.

The deeds of the position of robust management have been reviewed. The designer is often not in his order new information about models of objects, that is. remain to avenge the insignificance and, in such a rank, to mow the space of information exchange, for example, when designing new technological processes, objects of new technology and others. Classical theories of control are based on allowances, that all the characteristics of the ceramic process are far behind and that it is possible to overcome the law of control, given in an explicit form, then in the minds of the non-insignificance of the task of safety, the necessary quality of control is ensured by the safety of the control method.

When designing automatic control systems, the power of adaptation is often victorious, if an insufficient level of a priori information is replaced by a processing for advanced algorithms of streaming information. Systems that are able to have the power of adaptation (that allow the short term of their design, improvement and testing) are called adaptive.

With the improvement of what has been said, it is possible to put the nutritional solution of the problem of optimization in the minds of incomprehensible a priori information (adaptive optimal control).

The development of the theory of automatic control without improving the physical processes that occur in the design system can lead to complete insanity in setting the highest practical goals. To this, great respect is attached to the development and development of numerical methods for the follow-up and synthesis to complete folding automatic systems with the method of giving a statement about really victorious algorithms and so understandable, like correctness, stability and rationality of counting schemes.

Correction tasks affect the improved accuracy of the systems, both in the modes that have been established, and in the transitional ones. It’s to blame, if you change the pardon of the control in typical modes, to bring such values ​​of the coefficient of strength of the opened ACS to the point of need, if there are no special entrances (installation of supplementary lanoks - corrigible attachments), the system will not work.

There are three types of main corrigative outbuildings (Fig.6.1): the last one (W k1 (p)), the one that looks like a male turning link (W k2 (p)) and the parallel one (W k3 (p)).

6.1. Structural diagrams building outbuildings.

The method of correction for the help of the last corrections is simple in rozrahunka and is easily technically implemented. That is why wines are widely known, especially during the correction of systems, which vikoristovuyutsya electric lancers with a non-modulated signal. It is recommended to stop the last adjustments in the systems, preventing parametrization from drifting. Otherwise, it will be necessary to adjust the parameters in the correction.
Correction of keruvannya systems behind the help of a parallel corrigible attachment is effective, if high-frequency shunting of inertial bars is necessary. In this way, they are shaping up the folding laws of management with the introduction of similar ones and integrations in response to the signal of a pardon for usa nedolіkami.
Correction by mistev (local) svorotniy zv'yazkom vikoristovuetsya in automatic control systems most often. The aim of the correction is to correct as a mass reversal link, to slightly weaken the influx of non-linear characteristics of the lanoks, as they enter the mass circuit, and to induce a decrease in the fallow of the parameters of the adjustment of the regulators to the drift of the parameters of the annexes.
Vicoristannya tієї chi іnshoyї mind koriguvalnyh outbuildings, tobto. last lanok, parallel lanok or return calls, Depends on the reliability of technical implementation. In this way, the transfer function of the open-loop system is to blame, but only one and the other, with different inclusions of the trimming straps:

The formula (6.1) is introduced, which allows to change one type of correction to another, in order to choose the most simple implementations.

Department of Remote and Correspondence

Synthesis of the system - ce directing rozrahunok, the method of which is: - pobudova rational structure of the system; znakhodzhennya optimal values ​​parametrіv okremih lanok. With a multiplier possible solution At the same time, it is necessary to formulate the technical support to the system. And in order to understand the overlays on the self-propelled guns of the first boundary lines, it is necessary to choose the optimization criteria - static and dynamic accuracy, speed code, reliability, energy efficiency, price too little.
In engineering synthesis, the following tasks are set: the achievement of the necessary accuracy; ensuring the singing nature of transitional processes. In this case, the synthesis is brought to the point of choosing the type of parameters of the correct parameters, as it is necessary to add to the permanent part of the system in order to ensure the indicators of the quality are not higher for the tasks.
The greatest expansion of engineering practice has taken away the frequency method of synthesis with additional logarithmic frequency characteristics.
The process of synthesizing the control system includes the next steps:
- Pobudov LACH L 0 (ω) exit system W 0 (ω)
- pobudova low-frequency part of the bazhan LACHH on the basis of high accuracy (astatism);
- prompting the mid-frequency station of the bazhanoy LACHH, which ensures the task of re-adjustment and the hour of regulation t p ACS;
- uzgodzhennya low-mid-frequency dilyanka bazhano ї l.a.g. for washing away the simplest coriguval outbuilding;
- clarification of the high-frequency part of the Bazhan L.A.G. on the basis of the necessary safety margin;
- depending on the type of the parametr_v of the successive corrigative adjustment L ku (ω) = L W (ω) - L 0 (ω), because W W (p) \u003d W k ​​(p) * W 0 (p);
- technical implementation of building outbuildings. In times of need, a change to an equivalent parallel lane or OS is carried out;
- perevirochny rozrahunok and pobudova transitional process.
Pobudova Bazhanoi L.A.G. vrozdrib.
Low-frequency part of the Bazhan L.A.G. It is formed from the understanding of the necessary accuracy of the robotic control system in the mode that it has risen, so you understand that the pardon of the system Δ(), that it has risen, is not guilty of overestimating the given value Δ() ≤Δ s.
Molding of the fenced low-frequency area for the bazhano l.a.g. maybe different ways. For example, when a sinusoidal signal is applied to the input, it is necessary to ensure the following valid indications: m - the maximum amplitude of the pardon; v m - maximum stiffness of the stiffness; m - maximum speed increase. Previously, it was shown that the amplitude of the pardon when a harmonic signal is created m = g m / W(jω k) , then. depends on the module of the transfer function of the open-circuit ACS and the amplitude of the input injection g m . In order for the pardon of the ACS to not exceed Δ z, Bazhana L.A.Kh. must pass no lower than the control point Ak with coordinates: ω=ω k, L(ω k)= 20lg|W(jω k)| = 20lgm/Δm.
Vіdomi spіvvіdnoshennia:
g(t) = g m sin(ω k t); g "(t) \u003d g m (ω k t); g "" (t) \u003d -g m ω k 2 sin (ω k t);
vm = gmk; ε m = g m ω k 2; g m = v m 2 / ε m; ω k = ε m / v m. (6.2)
The harrowed area, which gives the system a 1st order astatism and ensures the robot with the necessary flexibility in the amplitude of the rate, speed and speed of the rate, is shown in Fig. 6.2.

6.2. The area of ​​the Bazhanoi l.a.g. has been fenced.

Quality factor for speed K ν = v m / Δ m , quality factor for acceleration K ε = ε m / Δ m . In times, it is necessary to provide only a static pardon of the regulation when the signal g(t)=g 0 =const is applied to the input, then the low-frequency station of the bazhano LA.A.H. mother is guilty of sickness 0 dB / Dec and pass on the level 20lgK tr, de K tr (necessary coefficient of strengthening of the open ACS)

Δ s ()=ε st \u003d g 0 / (1+ K tr), stars K tr ≥ -1.

If it is necessary to ensure the speed from the given accuracy in the injection g(t)=νt at ν=const, then the quick pardon ε sk () =ν/K tr. Zvіdsi know K tr =ν/ε ck i to carry out the low-frequency part of the bazhan ї LAH with nahily -20 dB / dec through the quality factor for swidkistyu K ν = K tr =ν/ε ck or the point with coordinates: ω=1 s -1, L( 1) = 20lgk tr dB.
As it was shown earlier, the mid-frequency plot of the Bazhano L.A.G. ensuring the main indicators of the capacity of the transitional process - overshooting σ and the hour of regulation t p. the mother is to blame for sickness -20 dB / dec and change all frequencies at a frequency of ω avg, as it is due to the nomogram of V.V. Solodovnikov (Fig. 6.3). It is recommended to check the order of the astatism of the design system and choose ω according to the relevant nomogram.

6.3. Nomograms of the quality of Solodovnikov:
a - for astatic self-propelled guns of the 1st order; b - for static ACS

So, for example, for σ m \u003d 35% і t p \u003d 0.6 s, crusting with a nomogram (Fig. 6.3, a) for an astatic system of the 1st order, it is taken t p \u003d 4.33 π / ω cf abo ω cf \u003d 21.7 s - one .
After ω cf =21.7 s -1, it is necessary to draw a straight line with -20 dB / dec, and the width of the mid-frequency plot is determined by the mind and the safety of the necessary stability margin behind the module and phase. Vіdomі vіznі come up to vstanovlennâ stockіv stіykostі. It is necessary to remember that the frequency of sight is higher in the system, because there is a greater awareness of the fact that in the case of rozrahunka, there will be a loss of small, late hours of the adjuncts of self-propelled guns. Therefore, it is recommended for those with increased ω av to increase the stability margin by phase and module. So, for two types of self-propelled guns, it is recommended to use the one shown in the table. With high powers to the point of transient processes, for example,

20%<σ m <24%; ,

25%<σ m <45%; ,

the following average resistance indicators are recommended: φ zap =30°, H m =12 dB, -H m =10 dB.
Fig. 6.4 shows the view of the medium-frequency plot of the bazhanoj l.a.h., the width of which is the necessary safety margin.

6.4. Mid-frequency part of the Bazhan L.A.G.

If so, the midrange and low frequencies are obtained by using straight lines with -40 or -60 dB/dec.
Nakhil of the high-frequency dilyanka of the Bazhanoy l.a.g. it is recommended to leave the equal arrogance of the high-frequency plot of the l.a.g. In this way, the corygous attachment will be more protected. The weather is the average of the high-frequency plots of the Bazhano L.A.H. it is also carried out with the improvement of a simple coriguval outbuilding and, moreover, the provision of the necessary reserves of stability.
The transfer function of the Bazhan open-loop system W W L f (?). Then the phase frequency response of the open-loop automatic control system and the transitional characteristic of the closed-loop system will be assessed, and the indicators of the quality of the design system will be assessed. As if the stench is satisfied with the necessary values, prompting the bazhanoi l.a.h. it is important to finish, otherwise it is necessary to close the LCHH. To reduce the overshoot, expand the mid-frequency section of the bazhano l.a.g. (Greater value ±H m). To improve the swidcode of the system, it is necessary to increase the frequency of the call.
To determine the parameters of the last shortening, it is necessary to add:
a) look at the bazhanoi l.a.g. L L 0, then. know l.a.g. minimum-phase coriguval outbuilding L ku;
b) looks like L.A.H. I will add a successive short-form appendix L to write a transfer function and a short-term literature to select a specific scheme and implementation.
In Fig.6.5, the butt of the assignment of the transfer function of the successive corrigible attachment is shown.

6.5. LAH roztashovanoy L 0 bagzhany L w open system
and the last koriguvalny add-on L ku

After a graphical vision, we will take the transfer function of the corrigative outbuilding

Parallel koriguyuchy attachment or koriguyuchiy pristriya in the case of a mastseous whirlpool can be taken away by a pererahunk according to the formula (6.1).
For the omitted transfer function W ku (p) it is necessary to design a real corrective attachment, which can be implemented in hardware or software. In different hardware implementations, it is necessary to choose the scheme and parameters of the corrigative lanka. In the literature there are tables of typical corrigative outbuildings like passive, and active, like in a standing, and changing stream. In that case, as it is victorious for the management of ACS EOM, then the software implementation is shorter.

© V.M. Bakaev, Vologda 2004. Development of the electronic version: M.A. Gladishev, I.A. Churaniv.
Vologda State Technical University.
Department of Distance and Correspondence Education

The great expansion of the system was created, inspired by the principle of easy regulation, which is explained in Fig. 6.6. The system transfers n control circuits with its own controllers W pi (p), and the output signal of the controller of the external circuit is given to the values ​​of the internal circuit, that is. the work of the skin inner contour is ordered to the outer contour.

6.6. Structural diagram of the automatic control system for sub-order regulation

Two main advantages determine the operation of easy regulation systems.
1. Simplicity of rozrahunka that nalashtuvannya. Adjustment in the process of adjustment is carried out from the internal circuit. The skin circuit includes a regulator, for the parameters and structure of which the standard characteristics appear. Moreover, the skin contour is compensated for most of the time.
2. The stability of the exchange of boundary values ​​of the intermediate coordinates of the system. It is within the reach of the exchanger to the main values ​​of the output signal of the external circuit controller.
At the same time, according to the principle of encouraging a system of easy regulation, it is obvious that the code of the skin outer contour will be lower than the code of the outer inner contour. Definitely, even in the first circuit, the frequency of the sight of l. warehouse 1/2T μ , de 2T μ - the sum of small non-compensated late hours, then wind up for the daytime at the outer contour of the lower legs with small late hours, the frequency of this l.a.h. will be 1/4T μ etc. Therefore, systems for easy regulation are rarely available from more than three circuits.
Let's take a typical circuit in Fig. 6.7 and adjust it to modular (MO) and symmetrical (CO) optimum.

6.7. Diagram of a typical circuit

In the scheme of Fig.6.7, it is marked: T μ - the sum of small late hours;
T pro - great post_yna hour, scho p_dlyagaє compensation; K ε і K O - apparently the coefficient of block strength with small constant hours and control objects. Next, set the type of lanka, the next hour to compensate, deposit and the type of regulator W p (p). Vіn can be P, I, PІ and PID. How butt is taken PI - regulator:

.

For modular optimum vibero parameters:

Then the transfer function of the open-loop circuit looked like:

Logarithmic frequency responses, which reflect the transfer function W(p), are shown in Fig. 6.8, a.

6.8. LFC i h(t) with modular adjustment

With a stepwise control input, the output value first reaches the set value in an hour 4.7Тμ, the overshoot becomes 4.3%, and the phase margin is 63 ° (Fig. 6.8, b). The transfer function of the closed ACS can be seen

In order to reveal the characteristic alignment of a closed ACS yak T 2 p 2 +2ξTr+1=0, then the damping coefficient at the modular optimum may be the value . At that very hour it is clear that the hour of regulation lies in the great Lenten hour T o. The system is subject to first-order astatism. When adjusting the system to a symmetrical optimum, select the parameters of the PI - controller in the following order:

Then the transfer function of the open-loop circuit can be seen

Vidpovidnі їy logarithmіchnі frequency characteristics and graph of the transient process are presented in Fig.6.9.

6.9. LFC and h(t) when adjusted to the symmetrical optimum

The hour of the first reach is set to 3.1T μ, the maximum overshoot reaches 43%, the phase margin is -37°. ACS nabuvay astatism of a different order. If it is important that the lanka with the largest steady hour is aperiodic of the 1st order, then with the PI - regulator at T o = 4T μ the transitional processes are similar to the processes when set to MO. Yakscho something<4Т μ , то настройка регулятора на τ=Т μ теряет смысл. Необходимо выбрать другой тип регулятора.
TAU has other types of optimal adjustment of regulators, for example:
- binomial, if the characteristic equalization of the ACS is given at the sight (p + ω 0) n - de ω 0 - modulus of n - multiple root;
- Butterworth, if the characteristic alignment of self-propelled guns of different orders can be seen


The number of adjustments is dotally zastosovuvaty, if in the system there are victorious modal changes from the skin coordinates.

© V.M. Bakaev, Vologda 2004. Development of the electronic version: M.A. Gladishev, I.A. Churaniv.
Vologda State Technical University.

Establish three groups of methods to encourage transitional processes: analytical; graphic, which victorious frequency and transitional characteristics; prompting transitional processes with additional EOM. In the most advanced ways, you can use EOM, which allows you to model ACS, connect to the machine other parts of the real system, that is. close to the experimental method. The first two groups win over more importantly in times of simple systems, and go to the stage of forward follow-up with a simple simple system.
Analytical methods are based on the decoupling of differential equations of the system, or on the basis of the Laplace's reversal transformation as the transfer function of the system.
The analysis of transitional processes for the frequency characteristics of vicorist is the same, if the analysis of ACS on the cob is carried out by frequency methods. In engineering practice, for the assessment of performance indicators and induce transitional processes in automatic control systems, the widening method of trapezoidal frequency characteristics was developed by V.V. Solodovnikov.
It has been established that the system was single-spill, tobto. g(t)=1(t), and let’s say zero, then the reaction of the system, as a transitional characteristic, can be

(6.3)
(6.4)

de P(ω) - speech frequency response of a closed system; Q(ω) is the apparent frequency characteristic of a closed system, that is. Фg(jω)=P(ω)+jQ(ω).
The method is inspired by the fact that the speech characteristic P(ω) is divided into a number of trapezoids, replacing approximately the curved lines with rectilinear ribs so that when all the ordinates of the trapezoids are folded, the characteristic of Fig.6.10 appears.

6.10. Speech characteristic of a closed system

de: ω рi and ω срі - apparently the frequency of equal transmission and the frequency of the skin trapezium.
Then the skin trapezium will show the coefficient of sickness ω pi / ω срi and from the tables of h-functions there will be transitional processes in the form of skin trapezium hi. The table of h-functions has an infinite hour τ. To take away the real hour t i, it is necessary to divide the given trapezium into frequency. The transitional process of skin trapezium needs to be increased by P i (0) times, because the table of h-functions has transitional processes in single trapezoids. The transitional process of the ACS appears under the summation of the algebra of prompting h i processes in the form of the trapezoids.

© V.M. Bakaev, Vologda 2004. Development of the electronic version: M.A. Gladishev, I.A. Churaniv.
Vologda State Technical University.
Department of Distance and Correspondence Education

1. What can be understood about the extent of the management process and how can it be reached?
2. Name the standard linear law of care.
3. Tell about typical laws of control and typical regulators.
4. What is the recognition of building outbuildings? Indicate the ways of their inclusion and particularity.
5. Explain the formulation of problems for the synthesis of systems.
6. Revise the stages of systems synthesis.
7. Explain the rationale for the design system of the LAH.
8. How is the transfer function of the open-loop design system formed?
9. How are the transfer functions of the outbuildings determined, what should be corrected?
10. What are the advantages and shortcomings of parallel and subsequent corrigative outbuildings?
11. How do nomograms "flicker"?
12. Perekhuyte methods and encourage transitional processes.
13. How can one determine the meaning of a transitional process behind a speech characteristic?
14. How to change the bazhan l.a.g. increasing the reserves of resistance?

© V.M. Bakaev, Vologda 2004. Development of the electronic version: M.A. Gladishev, I.A. Churaniv.
Vologda State Technical University.
Department of Distance and Correspondence Education

Topic №7: Non-linear ACS

Most of the indications of real outbuildings in the case of non-linear and non-linear ones cannot be linearized, because Mayut develop a different kind and before them, a shmatkovo-linear approximation does not stagnate. The work of real lanoks (attachments) can be supported by such phenomena as saturation, hysteresis, backlash, the presence of a zone of insensitivity thinly. Non-linearities can be natural and piece-by-piece (navmisno introduced). Natural non-linearity of natural systems with non-linear manifestation of physical processes and capacities in other mechanisms. For example, the mechanical characteristic of an asynchronous motor. Piecemeal non-linearities are introduced by retailers in the system in order to ensure the necessary performance of the work: for systems that are optimal in terms of code, it is necessary to install relay control, the presence of non-linear laws in non-linear and non-linear extreme systems, systems with a changeable structure are too thin.
non-linear system such a system is called, to the warehouse of which one element wants to enter, the linearization of which is impossible without the loss of the power of the control system. Іstotnimi signs of non-linearity є: as a deyakі coordinates or їх pokhіdnі for an hour to enter at the same time as a creative step, in іdmіnіy vіd first; yakscho koefіtsієnti іvnyannya є functions deyakіh coordinates chi їх хідхіх. When folding the differential alignment of the non-linear systems, the differential alignment of the skin attachment of the system should be established. With this, the characteristics of the outbuildings, which allow linearization, are linearized. Elements that do not allow linearization are called strictly non-linear. Through the war, eliminate the system of differential equivalences, for some of them, there are non-linear equivalences. Extensions, which allow linearization, establish the linear part of the system, and extensions, which cannot be linearized, establish a non-linear part. In the simplest way, the block diagram of the automatic control system of the non-linear system is the last connection of the non-inertial non-linear element and the linear part, we will stun with the return link (Fig. 7.1). Shards for non-linear systems are not the stagnant principle of superposition, then, conducting structural transformations of non-linear systems, single exchanges against structural transformations of linear systems, those that cannot transfer non-linear elements through linear and navpacks.

Rice. 7.1. Functional diagram of a non-linear system:
NOT - non-linear element; LCH - linear part; Z(t) and X(t)
output and input of a non-linear element.

Classification of non-linear lines is possible for different signs. The widest nabula classification for static and dynamic characteristics. The first ones look like non-linear static characteristics, and the others - like non-linear differential equalities. Apply such characteristics to . In Fig.7.2. applied unambiguous (without memory) and richly meaningful (with memory) non-linear characteristics. In this way, it is directly protected (sign) of the security signal at the entrance.

7.2. Static characteristics of non-linear elements

Behavior of non-linear systems due to the obviousness of their non-linearities may have a number of features, indicative of the behavior of linear ACS:
1. the output value of the non-linear system is not proportional to the input injection, that is. the parameters of the non-linear lines are to be deposited according to the value of the input inflow;
2. transitions in non-linear systems to fall in the minds of the cobs (vіdkhilen). At zv'yazku z cim, for non-linear systems, the understanding of the stability "for the small", "for the great", "zagalom" was requested. The system of standing "at the little one", as if there is a standing at small (indistinctly small) cob vіdhilennyah. The system of standing "at the great", as if there was a standing at the great (kіntsevih by size) cob vіdhilennyah. The system of standing "as a whole", as if there was a standing for any great (non-negotiable for size) cob vіdhilen. In Fig. 7.3, the phase trajectories of the systems are pointed: steady "by fire" (a) that system is stable "for the great" and unstable "for the small" (b);

7.3. Phase trajectories of non-linear systems

3. for non-linear systems, the characteristic mode of undamped periodic surges with a constant amplitude and frequency (auto-collision), which is due to the presence of periodic surges in systems;
4. in case of fading colivans of the transient process in non-linear systems, it is possible to change the colivan period.
These features zoomed in on the number of high-profile approaches to the analysis and synthesis of non-linear systems. Expanded methods allow you to change only local non-linear tasks. All engineering methods for the investigation of non-linear systems are divided into two main groups: exact and close. Before exact methods, the method of A.M. Lyapunov, the phase-plane method, the method of point shifts, the frequency method of V. M. Popov. Nearby methods are based on the linearization of non-linear equalizations of the system from the harmonization of the statistical linearization. Cordoni zastosuvannya moreover method will be reviewed below. It should be noted that the nearest future one needs further development of the theory and practice of non-linear systems.
Let's try that effective method for solving non-linear systems - modeling, tools for that - a computer. In this hour of rich folding for the analytical solution of theoretical and practical nutrition, they can easily be improved with the aid of computational techniques.
The main parameters that characterize the work of non-linear ACS, є:
1. Availability or availability of autocooling. As an autocoil, it is necessary to assign their amplitude and frequency.
2. The hour of the output of the regulated parameter is the stabilization mode (speed).
3. Present or present to the forging regime.
4. Designated special points and special trajectories of movement.
This is far from the latest copy of the doslidzhuvanih showings that accompany the work of non-linear systems. Systems of extreme, self-adjusting, with changing parameters affect the assessments and dodatkovyh authorities.

© V.M. Bakaev, Vologda 2004. Development of the electronic version: M.A. Gladishev, I.A. Churaniv.
Vologda State Technical University.
Department of Distance and Correspondence Education.

The idea of ​​the method of harmonic linearization lies with N.M. Krilova and N.M. Bogolyubov and is based on the replacement of a non-linear element of the system with a linear line, the parameters of which are determined with a harmonic input inflow from the mind, the equalness of the amplitudes of the first harmonics at the output of the non-linear element and the equivalent linear line. p align="justify"> The method is approximating and can only be used at different times, if the linear part of the system is a low-pass filter, then. in the output of the non-linear element of the harmonic warehouse, the Crimean first harmonica. With which linear part can be described by differential equals of any order, and a non-linear element can be unambiguous, so richly meaningful.
At the basis of the method of harmonic linearization (harmonious balance) lies the allowance, that at the input of a non-linear element a harmonic surge is given from the frequency and amplitude A, tobto. x = A sinωt. In the case of the lowered, which is the linear part of the low-frequency filter, the spectrum of the output signal of the linear part is surrounded by the first harmonic, which is indicated by the Four's order (the method is closer to the other, since the other harmonics are seen from the view). The same connection between the first harmonic of the output signal and the input harmonic inflow of the non-linear element is represented by the transfer function:

(7.1)

Рівняння (7.1) називається рівнянням гармонійної лінеаризації, а коефіцієнти q і q" - коефіцієнтами гармонічної лінеаризації, що залежать від амплітуди А і частоти ω вхідного впливу. Для різних видів нелінійних характеристик коефіцієнти гармонійної лінеаризації зведені в таблицю. Слід зазначити. q"(А )=0. Taking into account (7.1) the transformation after Laplace with zero cob minds with the offensive replacement of the operator p by jω (p = jω), we take the equivalent complex transfer coefficient of the non-linear element

W not (jω,A) = q + jq". (7.2)

In addition, as a harmonic linearization has been carried out, for the analysis and synthesis of non-linear ACS, it is possible to apply all methods, which can be developed for further linear systems, including varying different stability criteria. In the case of advanced non-linear systems based on the method of harmonic linearization, we are faced with violating the power of the foundation and the stability of periodic (autocooling) modes. Although the periodic mode is stable, then in the system there is an auto-coagulation with a frequency of 0 and an amplitude of A 0. Let's take a look at the non-linear system, which includes a linear part with a transfer function

(7.3)

that non-linear element with an equivalent complex transfer coefficient (7.2). Rozrakhunkov's block diagram of the non-linear system looks like Fig.7.5.

7.5. Block diagram of non-linear ACS

To assess the possibility of vibrating auto-collisions in a non-linear system by the method of harmonic linearization, it is necessary to determine the mind between resistances, as the analysis of the stability of linear systems was carried out for an hour. If the linear part is described by the transfer function (7.3), and the non-linear element (7.2), then it is characteristically equal to the closed system

d(p) + k(p)(q(ω,A) + q"(ω,A)) = 0 (7.4)

According to Mikhailov's stability criterion, the cordon of stability will be the passage of Mikhailov's hodograph through the cob of coordinates. From viraziv (7.4) it is possible to know the frequency amplitude and frequency autocooling from the parameters of the system, for example, the transfer coefficient of the k linear part of the system. Therefore, it is necessary for equals (7.4) to change the transmission coefficient k into a variable value, tobto. tse equal to write down at the sight:

d(jω) + K(jω)(q(ω,A) + q"(ω,A)) = Re(ω 0 ,A 0 ,K) + Jm(ω 0 ,A 0 ,k) = 0 (7.5)

de ω o i A o - possible frequency and amplitude of auto-collision.
Todi, equating to zero the difference and the obvious part of the equation (7.5)

(7.6)

Dosi mi importantly studied the task of analyzing the ACS, if the mathematical model of the closed ACS was taken into account by the given task, and it is necessary to determine the accuracy of the work: stability, accuracy in response to the input signal only.

Important, and foldable, є zavdannya synthesis, if the mathematical model of the ceramic object is important (and can be vimiruval and vikonavchogo outbuildings). It is necessary to choose the structure of the ACS, the law of calculation and the numerical values ​​of the parameters of the controller, which determine the capacity of the ACS.

We have already discussed the tasks of the synthesis. The synthesis of ACS can be carried out using vicorous stability criteria, D-rozbity, root locus methods.

Synthesis of one-dimensional single-loop ACS with a single environmental protection system for the auxiliary LAFCH of a closed-loop system

This method is based on a close connection between the transitional function of a closed ACS with a stepwise inflow and a partial frequency response of a closed ACS.

Here. (one)

Incl. behind the frequency characteristics of the open-loop system, it is possible to determine the frequency characteristics of the closed-loop system in the same way. Є nomograms that show the frequency of power.

Therefore, we can evaluate the transitional process (div. (1)). From that, knowing, we can evaluate the transitional process in the system.

It is more convenient to solve the problem of ACS synthesis using frequency characteristics, if the frequency characteristics are inspired by the logarithmic scale.

At a logarithmic scale along the y-axis at included in db.

10 times the increase in the increase

On the abscissa axis, the frequency is plotted on a logarithmic scale.

A decade is a tenfold change in frequency.

The main thing is that the frequency characteristics of the logarithmic scale are considered in the fact that they can be approximately, practically without calculation.

Vіzmemo inertial lanka. Yogo transfer function ,

AFC. Frequency, de, tobto. - Frequency good luck.

When approaching LACHH:

1) nehtuemo i, but dB

2) nehtuemo 1 and y logarithmic scale

Significantly sick with:

Also, being the frequency response on a logarithmic scale, you can part of the characteristics that change, replace the straight line with the cheeky - 20db/dec. The biggest hit will be at the point of viguin ().

Integrating Lanka.

At .

I look ahead on the butt the principle of encouraging close LACHH (PCHH is financed exactly according to the formulas).

The proximity of the LACH to the one that has a frequency response in the members:

1) when not a member of the lanka, they look like a submissive;

2) when you don’t have 1 and look at them as an integrating line with a frequency response, - 20 dB/dec and when the magnitude of the amplitude is more 20lgK.

Frequency, de - called frequency of occurrence.

Significantly the frequency of occurrence, de ()

On scho to pretend with urakhuvannyam zroblenyh allow:

Vіdkladaєmo on the frequency axis of the frequency of occurrence.

Pobudova is repaired from an integrating lanka: at a frequency of input 20lgK=20lg100=40db that line is carried out with cheeky -20db/dec. At the frequency of "connecting" one more integrating lanka - becoming sick -40db/dec.

At the frequency, two differential lanes are “switching”. In one differentiation of Lanka nahil +20db/dec, two integrating lanoks will have a buff +40db/dec, otzhe, the resulting nakhil when bude -40db/dec+40db/dec=0db/dec.

The phase-frequency characteristic is being developed.

For the help of LACH and FCH, it is not important to establish the stability of a closed system.

According to the Nyquist stability criterion, the automatic control system is closed, so the AFC of the open-loop system can be seen (astatic system):

At the frequency, the amplitude is equal to 1, and the stability margin in phase.

If the phase is healthy, then the margin of stability in terms of amplitude.

For the stability of the ACS, it is necessary

Synthesis of ACS for help LACHH

be carried out in the following manner:

self-propelled guns represent

To enter the object and vіdomі elements of the regulator, for example, vimiryuvalnі, vykonavchі outbuildings.

Coryguchy attachment, which is required for the synthesis process.

The same transfer function of the open-loop system

Here - the transfer function of the ACS, the dynamics of which satisfies the vast majority to the design system.

Todi on a logarithmic scale

For the minimum-phase ACS, the type of LAFC usually indicates the transitional process and does not look at the phase-frequency characteristic.

Minimum-phase lankas (systems) - so, at some root of the numeral and sign of the roztashovan at the left side of the water. Thus, the transfer function of the minimum-phase system is not to blame for the mother of zeros and poles at the left side of the surface.

From a glance it is possible to write down the transfer function of the corrigative lanka. In this vipadka, I looked out matima:

In the literature, there are tables that show looking at

І s Vіdpovіdnimi schemes koriguvalnyh pristroїv, scho realіzuyut tsі. It is more likely to be implemented in the appearance of an offensive lancet:

Here we know.

Behind the schedule is the one , .

We know.

Behind the schedule is visible.

Zvіdsi vyznaєmo.

Zvіdsi vyznaєmo.

Zvіdsi vyznaєmo.

Zvіdsi vyznaєmo.

Zvіdsi vyznaєmo.

Having determined the parameters of the lanka, which is corrected, we introduce yoga into the system and model the ACS, and we take the transitional process. If wine is not sovereign - I change the parameters of Lanka.

Wimogi to .

Bazhana LACHH of the open-circuit system will be from the highest points to the system:

1. accuracy (determines the coefficient of strength),

2. order of astatism,

3. hour of the transitional process,

4. overshoot.

1. can change all frequencies at the point, which will ensure tasks for the hour of the transition process

And you can also:

To know the nomograms that signify fallowness, here - overregulation.

For example,

2. In order for the ACS to be stable, it is guilty of changing all the frequencies with a cheeky - 20 dB/dec.

3.For the safety of the given

4. The mid-frequency part of the characteristic requires more robustness. The larger the range, the closer the process is to exponential.

The mid-frequency part mainly determines the quality of the transitional process.

The low-frequency part determines the accuracy of the control process.

Іsnuє y іnshіy sposіbіb vznachennya vznachennya tsіtsevyh vіdіzka vіdіzka:

Margin of stability in phase at the point at , which is determined by the LFC, is no less to blame

Stability margin per module (by amplitude) at points L2 be selected fallow in the form of overshoot:

The lowering of the central section of the LACHH with a low-frequency part is carried out straight with a nahi - 40 dB/dec or - 60 dB/dec.

The high-frequency part, so as not to complicate the attachments, which is corrected, to choose a similar output LACH.

Please, promptly reconsider the stock of stability in phase. (on the)

Unfortunately, this synthesis method does not guarantee the necessary capacity of the transition process.

The order of distributions in the synthesis of ACS from the last ones

shortening outbuilding

1. There will be LACHH of the permanent part of the ACS (without the corrective installation

swarming).

2. According to the task of the helpers, the bazhana of the LaChKh will be to the point.

3. Depending on the future of LFCHG.

4. The stability margins are determined by the phase amplitude.

5. A way to see the LACHKh koriguvalny outbuilding.

6. By choosing yoga technical analogue.

7. As a technical analogue, it is necessary to adapt it to the improvement of the technical analogue.

Once a good result is achieved, the completion of the synthesis task will be completed. If the result is not satisfactory, another analogue is selected.

Synthesis of ACS by the root locus method

The quality of the designed ACS from the point of view of the swidcode and the margin of stability can be characterized by the expansion of the roots of the number and the standard of the transfer function of the closed system.

Knowing the roots, you can depict their roztashuvannya on the complex plane. The root can be designated by the rozrakhunkami from the standards of the standard programs.

The more - the degree of stability, and the less - the degree of knocking, the more the sharpness of the ACS.

With a smooth change in the value of any parameter, the root moves on the root plane, crossing the curve, as it is called the root trajectory or the root hodograph. Having inspired the trajectories of all roots, you can choose the same values ​​of the parameters that vary, as if they show the best development of the roots.

Let it be the transfer function of a closed system

The coefficients of the numeral and the banner are in the same order of change through the parameters of the object, regulator, outbuildings, which are corrected. It is also necessary to choose the value of any parameter, it is necessary to take several constant values ​​for all other parameters, and for the random parameter to set different numerical values. For the skin value, in order to vary the parameter, it is necessary to calculate the values ​​of the roots of the numeral and the standard and be the trajectories of the roots, for which those values ​​​​of the parameter should be selected, as to ensure the best possible expansion of the roots.

Synthesis of standard transitional processes

(method of standard coefficients)

A private way of using this method is the diagram of the Vishnegradsky systems of the third order.

Standard transitional processes will be in a standardized manner for a single input inlet for an unlimited hour, de

Synthesis of linear automatic control systems by way of seeing between resistance and between a given level of resistance

Seeing the method D-rozbittya resistance area, we can choose a working point (defined by the system parameters) in the middle of this area. Prote different points in vіdpovіdatime vіdnіvіdatіmі rіznі rіznіl rіznіl rіznіv characteristic rіvnyannja, і іrіznіy nіkеrіnії transitional process. I wish my mother would have a good transitional process.

It seems that the trivality of the transitional process is determined by the root closest to the obvious axis.

As we are given the necessary hour of the transitional process, we can choose. If the root is ruffled left, then the trivality of the transitional process will be less than the given one. .

Even though at equal (3) parameters, at the plane of which one wants to induce between a given degree of resistance, enter at the characteristic equal linearly independently, then equal (3) can be stopped by looking at the earlier method D-breakdown. Vision of the cordon will be the line of the given level of resistance.