A note on robust pole assignment for periodic systems
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Robust dynamical compensator design for discrete-time linear periodic systems
- Published: 08 February 2011
- Volume 52 , pages 291–304, ( 2012 )
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- Lingling Lv 1 nAff2 ,
- Guangren Duan 1 &
- Haibin Su nAff2
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This paper considers dynamical compensators design for purpose of pole assignment for discrete-time linear periodic systems. Similar to linear time-invariant systems, it is pointed out that the design of a periodic dynamical compensator can be converted into the design of a periodic output feedback controller for an augmented system. Utilizing the recent result on output feedback pole assignment, parametric solutions for this problem are obtained. The design approach can be used as a basis for the robust dynamical compensator design for this type of systems. Combined with a robustness index presented in this paper, robust dynamical compensator design problem is converted into a constrainted optimization problem. A numerical example is employed to illustrate the validity and feasibility of the methods.
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Lingling Lv & Haibin Su
Present address: College of Electric Power, North China Institute of Water Conservancy and Hydroelectric Power, Zhengzhou, 450011, People’s Republic of China
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Center for Control Theory and Guidance Technology, Harbin Institute of Technology, Harbin, 150001, People’s Republic of China
Lingling Lv & Guangren Duan
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Lv, L., Duan, G. & Su, H. Robust dynamical compensator design for discrete-time linear periodic systems. J Glob Optim 52 , 291–304 (2012). https://doi.org/10.1007/s10898-011-9666-5
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Received : 14 January 2011
Accepted : 25 January 2011
Published : 08 February 2011
Issue Date : February 2012
DOI : https://doi.org/10.1007/s10898-011-9666-5
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Abstract: In this note a robust periodic pole assignment algorithm is proposed for linear, time-invariant, discrete-time systems. The condition numbers of the eigenvector matrices of the closed-loop system are assumed as a robustness measure and a periodic state-feedback law is deduced by the minimization of the condition numbers associated to the eigenvectors of the monodromy matrix of the ...
A robust periodic pole assignment algorithm is proposed for linear, time-invariant, discrete-time systems and has been tested on a number of examples, giving satisfactory results. In this note a robust periodic pole assignment algorithm is proposed for linear, time-invariant, discrete-time systems. The condition numbers of the eigenvector matrices of the closed-loop system are assumed as a ...
Parametric pole assignment and robust pole assignment for discrete-time linear periodic systems. SIAM J. Control Optim. (6) (2010), p. 48, 10.1137/080730469. ... Iterative algorithms for discrete-time periodic Sylvester matrix equations and its application in antilinear periodic system. Appl. Numer. Math., 168 ...
A robust pole assignment algorithm is proposed for linear periodic discrete-time systems with time-varying dimensions of the state and/or input spaces that deduces a periodic state feedback law by the minimization of the condition numbers of the eigenvector matrices of the closed-loop system. In this note a robust pole assignment algorithm is proposed for linear periodic discrete-time systems ...
For the sake of clarity, a detailed algorithm for robust pole assignment of second-order linear discrete-time periodic systems is given. Algorithm 2 Robust pole assignment. 1. Construct the lifted coefficient matrices A c, C c, B c and real Jordan canonical matrix F c according to (15); 2.
There are some good methods of periodic pole assignment algorithms [1,8,13,14,19]. ... By using exact pole placement theory and the harmony search algorithm, robust pole assignment for linear ...
This paper considers pole assignment and robust pole assignment problems for discrete-time linear periodic systems by using linear periodic state feedback using the monodromy matrix of the closed-loop system in a special form and proposes a complete parametric approach. Expand. 47. Highly Influenced. 10 Excerpts.
case of periodic systems. One such example is the pole assignment problem for periodic systems discussed theoretically in [7] and [4] and addressed as well from a computational point of view in [14] and [9]. Consider the linear discrete-time periodic system of the form x k +1 = A k x k + B k u k (1) where the matrices A k 2 nand B k 2 m are ...
This paper considers pole assignment and robust pole assignment problems for discrete-time linear periodic systems by using linear periodic state feedback. The monodromy matrix of the closed-loop system is represented in a special form. By combining this special form with our recent result on solutions to a class of generalized Sylvester matrix equations, a complete parametric approach for ...
We believe that the proposed robust pole assignment approach is a viable way to solve large DEAPs in the perspective of the requirements formulated by recent sensitivity analysis results [10]. In a broader context, the Sylvester equation-based approach provides a unified framework to solve various eigenvalue assignment problems for standard ...
Andr ́e L. Tits. Abstract— Two algorithms for robust pole assignment by state feedback, proposed by Kautsky, Nichols and Van Dooren (1985) and by Tits and Yang (1996) are briefly reviewed. MATLAB code implementations of these algorithms, place (from the MATLAB Control System Toolbox) and robpole (from SLICOT), are then numerically compared ...
In this note a robust pole assignment algorithm is proposed for linear periodic discrete-time systems with time-varying dimensions of the state and/or input spaces. The algorithm deduces a periodic state feedback law by the minimization of the condition numbers of the eigenvector matrices of the closed-loop system. Numerical examples are provided to show the performances of the algorithm.
solve robust pole assignment problems for linear sys-tems using state feedback. The new framework uses Sylvester equation based parametrizations of the pole assignment problems. The non-uniqueness of solutions is exploited by minimizing additionally sensitivity of closed-loop eigenvalues and the norm of the correspond-ing state feedback matrix.
This paper considers dynamical compensators design for purpose of pole assignment for discrete-time linear periodic systems. Similar to linear time-invariant systems, it is pointed out that the design of a periodic dynamical compensator can be converted into the design of a periodic output feedback controller for an augmented system. Utilizing the recent result on output feedback pole ...
This paper considers pole assignment and robust pole assignment problems for discrete-time linear periodic systems by using linear periodic state feedback using the monodromy matrix of the closed-loop system in a special form and proposes a complete parametric approach. This paper considers pole assignment and robust pole assignment problems for discrete-time linear periodic systems by using ...
The periodic state feedback pole assignment problem of high-order periodic discrete systems is investigated, and the pole assignment problem for such systems is transformed into a class of problems for resolving periodic Sylvester matrix equations with constraints. Using the technique of cyclic lifting, such equations can be transformed into high-order time-invariant Sylvester matrix equations ...
The robust pole assignment problem is converted into a static nonconvex optimization problem, which is easily solved by Matlab optimization toolbox and can be regarded as a generalization of robustness index of normal LTI systems. This paper considers robust pole assignment problem for discrete-time linear periodic systems via linear periodic output feedback. To character a measure for the ...
An iterative algorithm for generalized periodic multiple coupled Sylvester matrix equations. 2021, Journal of the Franklin Institute ... In this paper the robust pole assignment problem using combined velocity and acceleration feedback for second-order linear systems with singular mass matrix is illustrated. This is promising for better ...
The discussion of main functional and numerical aspects reveals many desirable features of the underlying algorithms which recommend them to serve as bases for robust numerical software implementations. A unifying computational framework to solve robust pole assignment problems for linear systems using state feedback using Sylvester equation ...
A computational method for designing controllers which attempt to place the roots of the characteristic polynomial of an uncertain system inside some prescribed regions is presented. A computational method for designing controllers which attempt to place the roots of the characteristic polynomial of an uncertain system inside some prescribed regions is presented. The analysis is based on ...