7

Predictive Control in Uncertain Systems

7.1 Model-Based Predictive Control

At each sampling instant an explicit mathematical model is used to predict the future behaviour of the plant over a specified prediction horizon in response to a given sequence of changes in the control input over a control horizon (see Figure 7.1). The sequence of changes in the control signal that produces a response that is closest to the desired behaviour is found. Only the first change in the sequence is applied to the plant as the whole process is repeated at the next sampling instant (a so-called receding horizon control strategy).

Several different forms of model-based predictive control (MPC) have been proposed (Garcia et al., 1989). In its simplest form the requirement is that the controlled variable is equal to the value of the setpoint at every sampling instant (so-called dead-beat control). A cost function is usually used to define the desired behaviour of the plant and a constrained optimization problem must be solved to find the most appropriate control action.

MPC can handle constraints in a systematic way and is robust to uncertainty in the estimated value of any time delay associated with the response of the plant. The main difficulties associated with the practical application of MPC are identifying a suitable mathematical model and specifying an appropriate control objective (Richalet, 1993).

The optimal value of the control signal must ...