Control of Zeros and Poles in Problems of Synthesis of Regulation Systems. Part I. Compensation Approach

A highly important place in the theory and practice of automatic systems occupy the problems of synthesis of automatic regulation systems (ARS) based on the requirements for the dynamic quality of regulation processes. For class of linear stationary ARS such requirements are imposed upon the type and parameters of its transition characteristic which is uniquely determined by its transfer function (TF). In this connection the setting of problem of ARS synthesis with desired TF, corresponding to the given amplification coefficient, zeros and poles of the synthesized system is regularity. The given problem is worth while to call as the control problem of zeros and poles of ARS. In the present paper consists into two parts, the questions of control of zeros and poles ARS, which are important for engineering applications are considered. A critical analysis of the known compensation and compensation-modal regulation schemes is given. And also the new circuit solutions combining the functionality possibilities of compensation and modal approaches are proposed. The first part of the article the effect of compensation of zeros and poles of control objects in ARS is analyzed. The understanding of this effect gives the representation of the system of canonical structure of R. Kalman, according to which the compensation of zeros and poles of object does not mean their physical liquidation. As a result of compensation, they become the poles of its unobservable and unmanageable parts, which will be tell upon the regulation processes in the conditions of disturbances of the state of control object. The given effect and its negative results are clearly detected in the classical method of constructing of controllers on a priori given (desired, reference) TF of closed ARS. The influence of the factor of non-minimal phase zeros on the dynamics of control systems is studied. The effect of negative ejection in the transition characteristic of the system is described and its quantitative assessment is given for the case of a single real right zero. In the second part of the article the well-known methods for ARS synthesis with desired TF, based on use of polynomial calculus apparatus are considered and analyzed. New compensatory modal methods which may be of interest in engineering applications are proposed.

synthesis of regulation systems, dynamic quality, compensation of zeros and poles, not minimal-phase zeros, effect of negative ejection

1. Solodovnikov V. V., Filimonov N. B. Dy namic Quality of Automatic Control Systems, Moscow, Publishing house of BMSTU, 1987, 84 р. (in Russian).

2. Sokolov N. I. Analytical Method for the Synthesis of Linearized Automatic Control Systems, Moscow, Mashinostroenie, 1966, 326 p. (in Russian).

3. Pervozvansky A. A. Course of Automatic Control Theory, Moscow, Nauka, 1986, 616 p. (in Russian).

4. Methods of classical and modern theory of automatic control. Texbook in 5 volumes, vol. 3, "Synthesis of Regulators and Automatic Control System", under the ed. K.A. Pupkov and N.N D. Egupov, Moscow, Publishing house of MBSTU, 2004, 616 p. (in Russian).

5. Volgin L. N. Elements of the Theory of Controlling Machines (Method of Polynomial Equations in the Problems of Synthesis of Automatic Control Systems with Digital Computers), Moscow, Sovetskoe radio, 1962, 164 p. (in Russian).

6. Krut’ko P. D. Inverse Problems of Dynamics of Controlled Systems. Linear Model, Moscow, Nauka, 1987, 304 p. (in Russian).

7. Grimble M. J., Kučera V. Polynomial Methods for Control Systems Design, Springer-Verlag, 1996, 260 p.

8. Chen C. T. Linear System Theory and Design, New York, Oxford University Press, 1999, 334 p.

9. Tyutikov V. V., Tararykin S. V. Robust Modal Management of Technological Objects, Ivanovo, IGEU named after V. I. Lenin, 2006, 256 p. (in Russian).

10. Ishmatov Z. S. Microprocessor Based Control of Electric Drives and Production Facilities. Polynomial Methods, Yekaterinburg, Publishing house of UGTU-UPI, 2007, 278 p. (in Russian).

11. Gaiduk A. R. Theory and Methods of Analytical Synthesis of Automatic Control Systems (Polynomial Approach), Moscow, Fizmatlit, 2012, 360 p. (in Russian).

12. Kim D. P. Algebraic Methods of Automatic Control System Synthesis, Moscow, Fizmatlit, 2014, 164 p. (in Russian).

13. Kučera V. Diophantine Equations in Control — A survey, Automatica, 1993, vol. 29, no. 6, pp. 1361—1375.

14. Volgin L. N. Diophantine Polynomial Calculus and its Application to Solving Mathematical Problems in Control Theory, Automatic, 1987, no. 1, pp. 43—52 (in Russian).

15. Filimonov N. B. Control of Transients in Linear Finite-Dimensional Objects: Dis. ... Cand. Tech. Science: 05.13.02. Bauman Moscow State Technical University, Moscow, 1979, 395 p. (in Russian).

16. Filimonov N. B. The Question of the Solvability of Problem ofV.V V. Solodovnikov. Proceedings of the Bauman, no. 314, Automatic Control Systems, iss. 7, Moscow, Publishing house of BMSTU, 1979, pp. 60—71 (in Russian).

17. Filimonov A.B., Filimonov N. B. On the Problem of Dynamic Quality of Linear Stationary Control Systems. Analytical Methods of Synthesis of Regulators: Interuniversity Science, Saratov, Publishing house of SPTU, 1981, pp. 94—106 (in Russian).

18. Filimonov A. B., Filimonov N. B. Factor of the Right Transmission Zeroes in the Problems of Automatic Regulation, Journal of Advanced Research in Technical Science, 2019, iss. 15, pp. 103—109 (in Russian).

19. Solodovnikov V. V., Filimonov A. B., Filimonov N. B. Analysis of the Compensation Approach to the Synthesis of Control Systems, Izvestiya vysshikh uchebnykh zavedeniy. Priborostroenie, 1979, no. 2, pp. 27—32 (in Russian).

20. Filimonov A. B., Filimonov N. B. Some Aspects of Modal Synthesis of Automatic Regulation Systems, Journal of Advanced Research in Technical Science, 2018, iss. 11, pp. 82—88 (in Russian).

21. Mita T., Yoshida H. Undershooting Phenomenon and its Control in Linear Multivariable Servomechanism, IEEE Transactions on Automatic Control, 1990, vol. 35, no. 5, pp. 578—580.

22. Voronoi V. V., Voevoda A. About the Right Zeros Influence to System Transients, Transaction of Scientific Papers of the Novosibirsk State Technical University, 2013, no. 2 (72), pp. 19—29 (in Russian).