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A unified approach for designing robust linear feedback controllers. (English) Zbl 0611.93026
This paper gives a general approach for designing robust multivariable controllers. The model uncertainties are dealt with as unknown-but- bounded uncertainties by means of multi-input multi-output comparison systems. To describe the imcompletely known original system (OS) a model is used that consists of two subsystems SS1 and SS2. SS1 is completely known and described by some operator equations \[ (1)\quad y=S_{yu}u+S_{ys}s,\quad z=S_{zu}u+S_{zs}s \] where u, y, s and z are the control input, control output, interconnection input and interconnection output respectively. They are elements of extended function spaces \(L_ e\) of appropriate dimensions with the same \({\mathbb{T}}\). The choice of \({\mathbb{T}}\) \(({\mathbb{T}}\subseteq {\mathbb{C}}_+\), \({\mathbb{T}}\subseteq {\mathbb{R}}_+)\) determines whether the system is continuous- or discrete-time and whether it it described in the time or in the frequency domain. SS2 describes all the imcompletely known properties of the OS, which are to be neglected in the controller design. In principle, it could be described by some I/O-relation \(s=S_ 2z\). It is only assumed that an auxiliary system \(r_ 2=\) \(V_ 2w\) is known that majorizes the I/O-behaviour of SS2 \[ (2)\quad r_ 2=V_ 2| z| >| s|. \] This system is called a comparison system (CS) of the OS, if the inequality (2) holds for all input z(\(\cdot).\)
Assume that a linear feedback controller \[ (3)\quad u=S_{ry}y+S_{rv}v \] is given, where v denotes the command signal. A robust multivariable controller is a linear time-invariant feedback controller (3) that satisfies the given design requirements in connection with the original system (OS) with certainty, although the given model (1) describes the plant with severe uncertainties. Criteria are derived which allow to check the robustness requirement for controllers designed in the time and frequency domains.
Reviewer: M.Kono
MSC:
93B50 Synthesis problems
93B35 Sensitivity (robustness)
93C35 Multivariable systems, multidimensional control systems
93C05 Linear systems in control theory
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