The digital control of industrial systems in which the measurement system sample-time is longer than the controller and filter scan rate is considered. The problem is posed using a stochastic linear optimal control framework, and a separation principle is shown to apply. If the plant is assumed to be time-invariant and the noise sources are stationary, then the control gain matrix can be shown to be a constant matrix; however, the filter Riccati equation gives a periodic solution and the filter gain matrix is only non-zero at the measurement points. The conditions under which the dual rate feedback control system is asymptotically stable are established.
Get full access to this article
View all access options for this article.
References
1.
Davies, M.H.A. and Vinter, R.B.1985. Stochastic modelling and control, Chapman and Hall.
2.
Feng, W.1987. Notes on the stabilizability and detectability of discrete-time systems', ICU Report/128/1987, University of Strathclyde.
3.
Grimble, M.J.1979. 'Design of optimal stochastic regulating systems including integral action', Proc IEE, 126, (9) 841—848.
4.
Grimble, M.J.1980a. 'A combined state and state estimate feedback solution to the ship positioning control problem', Optimal Cont App & Methods, 1, 55-67.
5.
Grimble, M.J.1980b. 'A reduced order optimal controller for discrete-time stochistic systems', Proc IEE127, Pt. D, (2), 55-63.
6.
Grimble, M.J.1982. 'Structure of large stochastic optimal and sub-optimal systems', Proc IEE129, Pt. D. (5), 167-176.
7.
Johnson, M.A. and Grimble, M.J.1987. 'Recent trends in linear optimal quadratic multivariable control system design', Proc IEE134, Pt. D. (1), 53-71.
8.
Kalman, R.E.1960. 'A new approach to linear filtering and prediction problems ', J Basic Engng, March, 35-45.
9.
Kwakernaak, H., and Sivan, R.1972. Linear optimal control systems, Wiley Interscience, New York.
10.
Sage, A.P. and Melsa, J.L.1971. Estimation theory with applications to communications and control, p. 259, McGraw Hill.
