Adaptive decoupling of multivariable systems. (English) Zbl 0647.93044

Adaptive decoupling is an important practical problem in industrial control. The idea is to compensate, adaptively, for interactions in multivariable control and then complete the design with single-input single-output techniques.
In the paper a decoupling precompensator is first derived based on results by C. A. Desoer and A. N. Gündes [IEEE Trans. Avtom. Control AC-31, 744-750 (1986; Zbl 0603.93029)], when the model is known. The prior knowledge needed for the design of the precompensator is the “delay structure” of the process. Computationally common factors of polynomials must be found at each step. For adaptive implementation, it is assumed that the shortest delay in each row of the control matrix is known. This means assuming that delay between each of the inputs and outputs is known. Parameters are updated by a recursive estimation scheme, which is slightly modified from the basic least squares estimation. Under some technical assumptions convergence of the adaptive decoupler is shown. This together with complete decoupling is the major contribution of the paper.
Reviewer: H.Koivo


93C40 Adaptive control/observation systems
93C05 Linear systems in control theory
93C35 Multivariable systems, multidimensional control systems
93B50 Synthesis problems
93E10 Estimation and detection in stochastic control theory
93E12 Identification in stochastic control theory


Zbl 0603.93029
Full Text: DOI


[1] ÅSTRÖM K., Computer Controlled Systems (1984) · Zbl 0558.93028
[2] DOI: 10.1016/0005-1098(79)90071-2 · Zbl 0398.93035
[3] DOI: 10.1109/TAC.1986.1104391 · Zbl 0603.93029
[4] DOI: 10.1016/0005-1098(84)90019-0 · Zbl 0547.93077
[5] DOI: 10.1016/0005-1098(84)90005-0 · Zbl 0545.93043
[6] FAVIER , G. , and HASSANI , M. , 1982 ,Proc. 21st I.E.E.E. Decision and Control Conf., Orlando , Florida , 770 .
[7] DOI: 10.1109/TAC.1986.1104264 · Zbl 0584.93012
[8] DOI: 10.1109/TAC.1985.1103999 · Zbl 0562.93077
[9] DOI: 10.1016/0009-2509(85)85081-8
[10] DOI: 10.1002/aic.690320606
[11] JOHANSSON , R. , 1983 , Multivariable adaptive control . Ph.D. thesis, TFRT-1024 , t nDepartment of Automatic Control, Lund Institute of Technology|pn.
[12] DOI: 10.1016/0005-1098(80)90020-5 · Zbl 0447.93034
[13] DOI: 10.1002/oca.4660070105 · Zbl 0608.93044
[14] DOI: 10.1109/TAC.1971.1099820
[15] PERNEBO , L. , 1978 , Algebraic control theory for linear multivariable systems . Ph.D. thesis, TFRT-1016 , Department of Automatic Control, Lund Institute of Technology ; 1981 a, I.E.E.E. Trans, autom. Control, 26, 171; 1981 b, Ibid., 26, 183 .
[16] PRAGER D. L., Proc. Instn elect. Engrs 128 pp 9– (1981)
[17] DOI: 10.1109/TAC.1984.1103441 · Zbl 0551.93044
[18] WILLEMS J. L., Stability Theory of Dynamical Systems (1970)
[19] WOLOVICH W. A., Linear Multivariable Systems (1974) · Zbl 0291.93002
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.