Pole assignment in a specified disk
TL;DR: In this article, the problem of assigning all poles of a closed-loop system in a specified disk by state feedback is considered for both continuous and discrete systems, and a state feedback control law is determined by using a discrete Riccati equation.
Abstract: The problem of assigning all poles of a closed-loop system in a specified disk by state feedback is considered for both continuous and discrete systems. A state feedback control law is determined by using a discrete Riccati equation. This kind of pole assignment problem is named D -pole assignment, and its relation to the optimal control problem and its robustness properties are discussed. The gain and phase margins for all closed-loop poles to stay inside the specified disk D are determined for the proposed control.
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TL;DR: This paper addresses the design of state- or output-feedback H/sub /spl infin// controllers that satisfy additional constraints on the closed-loop pole location by derived in terms of linear matrix inequalities (LMIs).
Abstract: This paper addresses the design of state- or output-feedback H/sub /spl infin// controllers that satisfy additional constraints on the closed-loop pole location. Sufficient conditions for feasibility are derived for a general class of convex regions of the complex plane. These conditions are expressed in terms of linear matrix inequalities (LMIs), and the authors' formulation is therefore numerically tractable via LMI optimization. In the state-feedback case, mixed H/sub 2//H/sub /spl infin// synthesis with regional pole placement is also discussed. Finally, the validity and applicability of this approach are illustrated by a benchmark example.
2,036 citations
TL;DR: In this paper, a design procedure was developed that combines linear-quadratic optimal control with regional pole placement, in which the poles of the closed-loop system are constrained to lie in specified regions of the complex plane.
Abstract: A design procedure is developed that combines linear-quadratic optimal control with regional pole placement. Specifically, a static and dynamic output-feedback control problem is addressed in which the poles of the closed-loop system are constrained to lie in specified regions of the complex plane. These regional pole constraints are embedded within the optimization process by replacing the covariance Lyapunov equation by a modified Lyapunov equation whose solution, in certain cases, leads to an upper bound on the quadratic cost functional. The results include necessary and sufficient conditions for characterizing static output-feedback controllers with bounded performance and regional pole constraints. Sufficient conditions are also presented for the fixed-order (i.e. full- and reduced-order) dynamic output-feedback problem with regional pole constraints. Circular, elliptical, vertical strip, parabolic, and section regions are considered. >
250 citations
TL;DR: A necessary and sufficient condition for quadratic d stabilizability by output feedback is presented in terms of two parameter-dependent Riccati equations whose solutions satisfy two extra conditions.
Abstract: This paper presents a method for assigning the poles in a specified disk by state feedback for a linear discrete or continuous time uncertain system, the uncertainty being norm bounded. For this the "quadratic d stabilizability" concept which is the counterpart of quadratic stabilizability in the context of pole placement is defined and a necessary and sufficient condition for quadratic d stabilizability derived. This condition expressed as a parameter dependent discrete Riccati equation enables one to design the control gain matrix by solving iteratively a discrete Riccati equation. >
187 citations
TL;DR: In this paper, robust D-stability analysis for uncertain discrete singular systems with state delay and structured uncertainties is investigated and sufficient conditions are developed to ensure that, when the nominal discrete singular delay system is regular, causal and all its finite poles are located within a specified disk, the uncertain system still preserves all these properties when structured uncertainties are added into the nominal system.
Abstract: This work investigates the problem of robust D-stability analysis for uncertain discrete singular systems with state delay and structured uncertainties. Sufficient conditions are developed to ensure that, when the nominal discrete singular delay system is regular, causal and all its finite poles are located within a specified disk, the uncertain system still preserves all these properties when structured uncertainties are added into the nominal system. A computationally simple approach is proposed and a numerical example is given to demonstrate the application of the proposed method.
105 citations
Cites background from "Pole assignment in a specified disk..."
...[ 9 ] A. T. Chottera and G. A. Jullien, “A linear programming approach to...
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...Considerable amount of results on this issue have been reported in the literature, see, e.g., [3], [ 9 ], [10]....
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TL;DR: The idea of pole-region assignment is extended to interval gain and phase margin assignment and the internal model control proportional-integral-derivative (IMC-PID) design is examined from the frequency domain point of view.
Abstract: The idea of pole-region assignment is extended to interval gain and phase margin assignment. The internal model control proportional-integral-derivative (IMC-PID) design is examined from the frequency domain point of view. Equations for typical frequency domain specifications such as gain margin, phase margin and bandwidth are derived for the IMC-PID design. The gain and phase margins are monitored in real time and a self-tuning controller with interval gain and phase margin assignment is proposed. An implementation example in the laboratory is also given.
94 citations
References
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TL;DR: Two new algorithms for solution of the diserete-time algebraic Riccati equation are presented, related to Potter's and to Laub's methods, but based on the solution of a generalized rather than an ordinary eigenvalue problem.
Abstract: In this paper we shall present two new algorithms for solution of the diserete-time algebraic Riccati equation. These algorithms are related to Potter's and to Laub's methods, but are based on the solution of a generalized rather than an ordinary eigenvalue problem. The key feature of the new algorithms is that the system transition matrix need not be inverted. Thus, the numerical problems associated with an ill-conditioned transition matrix do not arise and, moreover, the algorithm is directly applicable to problems with a singular transition matrix. Such problems arise commonly in practice when a continuous-time system with time delays is sampled.
343 citations
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