ADAPTATION OF LQG CONTROL DESIGN TO ENGINEERING NEEDS

The purpose of the paper is twofold: (I) to modify the standard LQG control design procedure so that it might better meet the requirements of practicing engineers, both with respect to quality of the resulting control and with respect to its robustness, (II) to design algorithms for the control synthesis which are robust with respect to numerical errors and are suitable for real-time operation in adaptive systems based on microprocessors with reduced precision of arithmetic operations. The control synthesis is based on the receding horizon philosophy. A suitable combination of robustness and quality of control is achieved by designing the control for the receding horizon optimally in the LQG sense but with restriction on the admissible control strategy. The process input planned for the receding horizon is restricted to be piece-wise constant for periods longer than the sampling period the control loop operates with. In addition, a modification of the quadratic criterion is recommended in order to reduce the overshoots. The resulting control is proved to be stable and the increase of robustness is demonstrated on examples. The algorithms are elaborated for the observable canonical state representation of the incremental ARMA or Delta model of the controlled process. Simulated examples are given for illustration.