## Abstract

Control system design is the task of finding a controller which satisfies prescribed specifications, under a given set of constraints. Desirable controller parameters must satisfy a certain set of identities and inequalities that represent the plant dynamics, constraints and specifications. Hence, control system design amounts to solving a set of equations subject to inequality constraints that contain the controller parameters as unknowns. Since the given set of equations and inequalities is often very complicated and not precisely known, a solution should be found by a cut-and-try method guided by intuition and experience, which has been a major tool of practical control system design.

## Keywords

State Feedback Design Theory Optimal Control Theory Optimal Regulator Control System Design## Preview

Unable to display preview. Download preview PDF.

## References

- [1]R.E. Kalman, “Contributions to the theory of optimal control,” Boletin de la Sociedad Matematica, Mexicana, Vol 5, pp 102–119, 1960MathSciNetGoogle Scholar
- [2]G.C. Newton, L.A. Gould and J.F. Kaiser,
*Analytical Design of Linear Feedback Controls*, John Wiley and Sons, New York, 1957Google Scholar - [3]L.S. Pontryagin, et. al.,
*The Mathematical Theory of Optimal Process*, Interscience Publishers, New York, 1962Google Scholar - [4]R.E. Kalman, “When is a linear control system optimal?”
*Trans ASME, J of Basic Engineering*, Vol 86, pp 1–10, 1964Google Scholar - [5]H. Akaike, `Markovian representation of stochastic process by canonical variables,“
*SIAM J Control*,*Vol*13, pp 162–173, 1975MathSciNetMATHCrossRefGoogle Scholar - [6]Special Issue on Linear-Quadratic-Gaussian Estimation and Control Problems,
*IEEE Trans Automat Contr*,*Vol*AC-16, 1971Google Scholar - [7]I. Prigogine and I. Stengers, Order Out of Chaos: Man’s New Dialogue with Nature, Bantam Books, New York, 1984Google Scholar
- [8]P. Dorato (ed.),
*Robust Control*IEEE Press, New York, 1987Google Scholar - [9]B.D.O. Anderson and J.B. Moore,
*Linear Optimal Control*, Prentice-Hall, New Jersey, 1971MATHGoogle Scholar - [10]B.D.O. Anderson, “Sensitivity improvement using optimal design,”
*Proc IEE*, Vol 113, pp 1084 – 1086, 1966Google Scholar - [11]J.B. Cruz and W.R. Perkins, “A new approach to the sensitivity problem in multivariable feedback systems,”
*IEEE Trans Automat Contr*, Vol AC-9, pp 216 – 223, 1964Google Scholar - [12]E. Kreindler, “Closed-loop sensitivity reduction of linear optimal control systems,”
*ibid*, Vol AC-13, pp 254 – 262, 1968Google Scholar - [13]T. Fujii, “A complete optimality condition in the inverse problem of optimal control,”
*SIAM J Control and Optimiz*, Vol 22, pp 327–341, 1984MATHCrossRefGoogle Scholar - [14]T. Fujii, “A new approach to the LQ design from the viewpoint of the inverse regulator problem,”
*IEEE Trans Automat Contr*, Vol AC-32, pp 995–1004, 1987Google Scholar - [15]M.G. Safonov and M. Athans, “Gain and phase margin for multiloop LQG regulators,”
*ibid*, Vol AC-22, pp 173–179, 1977Google Scholar - [16]J.C. Doyle and G. Stein, “Robustness with observers,”
*ibid*, Vol AC-24, pp 607 – 611, 1979Google Scholar - [17]M. Athans, “Editorial: On the LQG Problems,”
*IEEE Trans. Automat Contr*, Vol AC-16, p 528, 1971Google Scholar - [18]H. H. Rosenbrock, “Good, Bad or Optimal,”
*ibid*, Vol AC-16, 1971Google Scholar - [19]I.R. Petersen, “A Riccati equation approach to the design of stabilizing controllers and observers for a class of uncertain linear systems,”
*IEEE Trans Automat Contr*, Vol AC-30, pp 904 – 907, 1985Google Scholar - [20]K. Zhou and P.P. Khargonekar, “An algebraic Riccati equation approach to
*H*° optimization,” Systems & Control Letters, Vol 11, pp 85–92, 1988MathSciNetMATHCrossRefGoogle Scholar - [21]J.C. Doyle, K. Glover, P.P. Khargoneker and B.A. Francis, “State-space solutions to standard H2 and HL control problems,”
*ibid*, Vol AC-34, pp 831 – 847, 1989Google Scholar - [22]H.A. Simon,
*The Sciences of the Artificial*, MIT Press, 1969Google Scholar