×

Structural synthesis of multivariable controllers. (English) Zbl 0557.93029

The paper concerns the problem of achieving a desired transfer matrix between external inputs and controlled outputs of linear multivariable systems by connecting proper, stabilizing controllers between measured outputs and control inputs. Solutions are given in both transfer function and state-space frameworks. A constructive characterization of the class of achievable transfer matrices is given via the theory of transfer function valuations. For each admissible transfer matrix the class of synthesizing controllers is determined.
Reviewer: A.Varga

MSC:

93B50 Synthesis problems
93C05 Linear systems in control theory
93C35 Multivariable systems, multidimensional control systems
93C99 Model systems in control theory
93D15 Stabilization of systems by feedback
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Antoulas, A. C., A new approach to synthesis problems in linear system theory, (Technical Report No. 8302 (1983), Department of Electrical Engineering, Rice University: Department of Electrical Engineering, Rice University Houston, TX) · Zbl 0565.93027
[2] Bhattacharyya, S. P.; Howze, J. W., Transfer function conditions for stabilizability, (IEEE Trans. Auto. Contr., AC-29 (1984), Department of Electrical Engineering, Texas A&M University: Department of Electrical Engineering, Texas A&M University College Station, TX), 253, also Technical Report No. 8300 · Zbl 0542.93055
[3] Bhattacharyya, S. P.; Pearson, J. B., On the linear servomechanism problem, Int. J. Control, 12, 795 (1970) · Zbl 0205.16201
[4] Bhattacharyya, S. P.; del Nero Gomes, A. C.; Howze, J. W., The structure of robust disturbance rejection control, IEEE Trans Aut. Control, AC-28, 874 (1983) · Zbl 0515.93016
[5] Callier, F. M.; Desoer, C. A., Multivariable Feedback Systems (1982), Springer Verlag: Springer Verlag Berlin · Zbl 0248.93017
[6] Cheng, B. C.; Pearson, J. B., Optimal disturbance reduction in linear multivariable systems, (Technical Report No. 8214 (1982), Department of Electrical Engineering, Rice University: Department of Electrical Engineering, Rice University Houston, TX) · Zbl 0551.93017
[7] Cheng, L.; Pearson, J. B., Frequency domain synthesis of multivariable regulators, IEEE Trans Aut. Control, AC-23, 3 (1978) · Zbl 0379.93037
[8] Cheng, L.; Pearson, J. B., Synthesis of linear multivariable regulators, IEEE Trans Aut. Control, AC-26, 194 (1981) · Zbl 0465.93044
[9] Davison, E. J.; Goldenberg, A., The robust control of a general servomechanism problem: the servo compensator, Automatica, 11, 461 (1975) · Zbl 0319.93025
[10] Desoer, C. A.; Chen, M. J., Design of multivariable systems with stable plant, IEEE Trans Aut. Control, AC-26, 408 (1981) · Zbl 0486.93037
[11] Desoer, C. A.; Wang, Y. T., Linear time-invariant robust servomechanism problem: a self-contained exposition, (Adv. in Contr. Dynam. Syst., XVI (1979), Academic Press) · Zbl 0416.93057
[12] Howze, J. W.; Thisayakorn, C.; Cavin, R. K., Model following using partial state feedback, IEEE Trans Aut. Control, AC-21, 844 (1976) · Zbl 0344.93033
[13] Imai, H.; Akashi, H., Disturbance localization and pole shifting by dynamic compensation, IEEE Trans Aut. Control, AC-26, 226 (1981) · Zbl 0464.93045
[14] Kailath, T., Linear Systems (1980), Prentice-Hall: Prentice-Hall Englewood Cliffs, N.J · Zbl 0458.93025
[15] Kung, S.; Kailath, T., Some notes on valuation theory in Linear Systems, (Proc. IEEE Conf. Decision and Control. Proc. IEEE Conf. Decision and Control, San Diego, CA (1979)) · Zbl 0428.93024
[16] Malabre, M., The model following problem for linear constant \((A, B, C, D)\) quadruples, IEEE Trans Aut. Control, AC-27, 458 (1982) · Zbl 0484.93022
[17] Morse, A. S., Structure and design of linear model following systems, IEEE Trans Aut. Control, AC-18, 346 (1973) · Zbl 0264.93005
[18] Ohm, D. Y.; Bhattacharyya, S. P.; Howze, J. W., Transfer function conditions for \((C\)′, \(A, B)\) pairs, IEEE Trans Aut. Control, AC-29, 172 (1984) · Zbl 0531.93031
[19] Ohm, D. Y.; Bhattacharyya, S. P.; Howze, J. W., Multivariable controller synthesis via the generalized disturbance rejection problem, (Technical Report No. 8301 (1983), Department of Electrical Engineering, Texas A&M University: Department of Electrical Engineering, Texas A&M University College Station, TX) · Zbl 0557.93029
[20] Ozguler, A. B., Skew-primeness in the regulator problem with internal stability, (Ph.D dissertation (1982), University of Florida)
[21] Pernebo, L., An algebraic theory for the design of controllers for linear multivariable systems—Part I and II, IEEE Trans Aut. Control, AC-26, 171 (1981) · Zbl 0467.93040
[22] Schumacher, J. M., Compensator synthesis using \((C, A, B)\) pairs, IEEE Trans Aut. Control, AC-25, 1133 (1980) · Zbl 0483.93035
[23] Schumacher, J. M., Regulator synthesis using \((C, A, B)\) pairs, IEEE Trans Aut. Control, AC-27, 1211 (1982) · Zbl 0498.93031
[24] Vidyasagar, M.; Viswanadham, N., Algebraic design techniques for reliable stabilization, IEEE Trans Aut. Control, AC-27, 1085 (1982) · Zbl 0496.93044
[25] Willems, J. C.; Commault, C., Disturbance decoupling by measurement feedback with stability or pole shifting, SIAM J. Control Optim., 19, 490 (1981) · Zbl 0467.93036
[26] Willems, J. C., Almost invariant subspaces: an approach to high gain feedback design—Part V: almost conditionally invariant subspaces, IEEE Trans Aut. Control, AC-27, 1071 (1982) · Zbl 0491.93022
[27] Wolovich, W. A.; Antsaklis, P.; Elliott, H., On the stability of solutions to minimal and nonminimal design problems, IEEE Trans Aut. Control, AC-22, 88 (1977) · Zbl 0346.93037
[28] Wonham, W. M., Linear Multivariable Control: A Geometric Approach (1979), Springer-Verlag: Springer-Verlag New York · Zbl 0393.93024
[29] Wonham, W. M.; Pearson, J. B., Regulation and internal stabilization in linear multivariable systems, SIAM J. Control Optim., 12, 5 (1974) · Zbl 0248.93013
[30] Yoshikawa, T. and T. Sugie. Analysis of multivariable servo systems considering sensor dynamics. IEEE Trans Aut. Control; Yoshikawa, T. and T. Sugie. Analysis of multivariable servo systems considering sensor dynamics. IEEE Trans Aut. Control · Zbl 0562.93030
[31] Youla, D. C.; Jabr, H. A.; Bongiorno, J. J., Modern Wiener-Hopf design of optimal controllers, Part II: the multivariable case, IEEE Trans Aut. Control, AC-21, 319 (1976) · Zbl 0339.93035
[32] Zames; George; Francis, Bruce A., Feedback, minimax sensitivity and optimal robustness, IEEE Trans Aut. Control, AC-28, 585 (1983) · Zbl 0528.93026
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.