Optimal output feedback regulation with frequency-shaped cost functional

Cheok, Ka C.; Hu, H.X.; Loh, N.K.

doi:10.1080/00207178808906128

Cited by 20 publications

(7 citation statements)

References 10 publications

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“…Let Sx' and Sy, denote the orthonormal transformations that diagonalize, respectively, the symmetric matrices (AA; + A,A) and (A; V + VA,) such that AA; + A;A = SXiAx;S~i A; V + VA; = Sy,Ay,S~; where A xi and A y , are the diagonal matrices containing eigenvalues of (AA; + A;A) and (A; V + VA,), respectively. Then, a modification of the Algorithm I given by Cheok et al (1988) may be used for solving the robust control gain P specified by (29) and (30), and is given in the following algorithm.…”

Section: Remarkmentioning

confidence: 99%

Robust optimal parametric LQ control with a guaranteed cost bound and applications

Loh

1989

International Journal of Control

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For an optimal parametric linear quadratic (LQ) control problem, a design objective is to determine a controller of constrained structure such that the closedloop system is asymptotically stable and an associated performance measure is optimized. In the presence of system uncertainty, the system via a parametric LQ design is further required to be robust in terms of maintaining the closed-loop stability with a guaranteed cost bound. This problem is referred to as 'robust optimal parametric LQ control with a guaranteed cost bound' and is addressed in this work. A new design method is proposed to find an optimal controller for simultaneously guaranteeing robust stability and performance over a specified range of parameter variations. The results presented generalizesome previous work in this area. A versatile numerical algorithm is also given for computing the robust optimal gains. The usefulness of the design method is demonstrated by numerical examples and a design of the robust control of a VTOL helicopter. I. IntroductionThis work addresses the simultaneous robust stability and performance problem via optimal parametric linear quadratic (LQ) control of linear uncertain systems. The present work is motivated by the guaranteed cost control approach of Chang and Peng ( 1972) and the recent work of Bernstein and Haddad for robust stochastic LQ control problems (Bernstein 1987, Bernstein and Haddad 1988 a, b, and the references therein). Chang and Peng (1972) considered the robust optimal LQ control problems with a full-state feedback and showed that the solutions of a resultant modified Riccati equation are guaranteed to give both robust stability and performance over a specified range of parameter variations. Among various later extensions of this approach, Bernstein and Haddad recently extended this approach to the robust control problems for linear stochastic systems with structural real-valued parameter uncertainty (Bernstein and Haddad 1988 a, b), and for the systems with state-dependent and control-dependent white noise (Bernstein 1987). Instead of using the absolutevalue bound (Chang and Peng 1972), they utilized a quadratic Lyapunov bound suggested by Petersen and Hollot (1986) in conjunction with the guaranteed cost approach to provide a simultaneous robust stability and performance via fixed-order dynamic feedback (Bernstein and Haddad 1988 a), and further considered this problem along with a unified treatment and extension of several quadratic Lyapunov bounds developed previously for feedback control design (Bernstein and Haddad 1988 b). Explicit solutions for the robust control were then derived using the optimal projection control synthesis approach of Hyland and Bernstein (1984).In the present work, we propose to extend Chang and Peng's approach (1972) further into the robust optimal parametric LQ control problems for linear determin-

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Section: Remarkmentioning

confidence: 99%

Robust optimal parametric LQ control with a guaranteed cost bound and applications

Loh

1989

International Journal of Control

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“…A dynamic simulation of the system will certainly provide more student interest, a better appreciation of the difference between passive and active control, and a better feel for the physics of the vibration of the vehicle (Haug, Sohono, Kim and Seong, 1984;Hirose, Matsushige, Buma and Kamaya, 1986;Cheok, Loh, McGee and Petit, 1985;Cheok, Hu and Loh, 1988;1989). A dynamic simulation of the system will certainly provide more student interest, a better appreciation of the difference between passive and active control, and a better feel for the physics of the vibration of the vehicle (Haug, Sohono, Kim and Seong, 1984;Hirose, Matsushige, Buma and Kamaya, 1986;Cheok, Loh, McGee and Petit, 1985;Cheok, Hu and Loh, 1988;1989).…”

Section: P R O G R a M C: Vehicle Suspension Control Sys-temmentioning

confidence: 99%

Computer Simulation and Animation Environment for Control Education

Cheok

Kheir

Huang

1992

Advances in Control Education 1991

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“…The use of such a performance index with frequencydependent weighting matrices was suggested by Gupta [5]. According to the study by Cheok et a1 [6], the problem of finding an optimal control which minimizes the generalized frequency-shaped cost functional subject to the dynamic constraints can be equivalently transformed into a minimization of the performance index in the time domain with an augmented dynamic constraint. The presence of exciting frequencies to which the human body is sensitive is obviously to be avoided.…”

Section: Introductionmentioning

confidence: 99%

Semi-Active Suspension with Preview Using a Frequency-Shaped Performance Index

Kim

Yoon

1995

Vehicle System Dynamics

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The objective of this study is to develop a control law for a semi-active suspension for the purpose of ride quality improvement. The semi-active control law is determined by reproducing the control force of an optimally controlled active suspension while suppressing its damping coefficient variation. The performance index of the optimal control for the active suspension is modified to include frequency-shaping by use of Parseval's theorem, which allows us to de-emphasize the effects of particular variables over specific frequency bands.Through the numerical simulations, it was found that the semi-active suspension may reduce the vertical acceleration of the driver's seat and the sprung mass motions significantly. The road-holding and tire deflections were not affected much.

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Optimal output feedback regulation with frequency-shaped cost functional

Cited by 20 publications

References 10 publications

Robust optimal parametric LQ control with a guaranteed cost bound and applications

Robust optimal parametric LQ control with a guaranteed cost bound and applications

Computer Simulation and Animation Environment for Control Education

Semi-Active Suspension with Preview Using a Frequency-Shaped Performance Index

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