Restricted structure predictive optimal control

Abstract

The design of low-order predictive optimal controllers, that involve a multi-step cost index and future setpoint knowledge, is considered. The usual predictive controller is of high order and the aim is to develop simpler structures, suitable for applications where PID controllers might be employed. The system is assumed to be represented by a discrete-time state-space model, which is very general, and the quadratic cost-function may include dynamic cost weighting terms. Using this approach, it is straightforward to generate a much lower-order predictive controller and thereby simplify implementation. Even with a continuing improvement in computational power there are many good reasons why low-order simple controllers have advantages in real applications

Restricted structure predictive control for linear and nonlinear systems

“…2008). A RS predictive control approach was described in (Grimble 2004c), but the numerical solution involved an approximation to a frequency response.…”

Reduced‐order non‐linear generalised minimum variance control for quasi‐linear parameter varying systems

“…Early work has often involved the use of black‐box optimisation algorithms that provide few insights into the design aspects [1, 2]. The most recent contributions have involved a numerical solution involving the approximation of an integral cost‐term [3, 4]. The philosophy here does not involve such approximations.…”

“…There have been attempts to derive RS optimal controllers probably beginning with the work of Zakian [1] and Polak [2]. RS controllers/estimators for linear systems were derived [3, 4] with constant optimal gains.…”

“…The optimisation process for this controller of RS is unusual. There is no approximation in the optimisation procedure that occurs in [3, 4], and the controller structure is defined in a form where functions are pre‐specified. These are multiplied by gains that are to be optimised.…”

Restricted Structure Non-Linear Generalized Minimum Variance Control of a 2-Link Robot Arm

“…There comes the need to restrict such advanced control strategies to simpler structures when the design simplicity and the range of applications are taken into account. As a consequence, researchers have taken initiatives [14,15] to use optimal and predictive control methods that have restricted structures.…”