Strongly stable GPC with suppression of steady state gain and closed-loop poles

This paper proposes a design procedure to satisfy steady state and stable transient characteristics of closed loop and poles of controller of strongly stable generalized predictive control(GPC) systems. Strongly stable control system is defined as a system having both of stable poles of closed loop systems and stable poles of controllers. The strong stability is important for safety, that is, the system is stable even when feedback loop get breakdown by an accident. The authors have already derived a strongly stable controller for GPC systems. In designing the strongly stable GPC, three characteristics should be specified. (1) The poles of the closed loop system. (2) The poles of the controller. (3) The steady state gain. The existing strong stable GPC by authors is extended from the standard GPC to two degree of freedom compensators by using coprime factorization approach and introducing new design parameters. In the extended GPC, there exist hidden poles brought by pole-zero cancellation. And in initial condition mismatch or sudden change of state by impulsive disturbances, the effect of the hidden poles appears. This means for safety, all the poles including the hidden poles should be stable. To design safe GPC, it requires to satisfy these three characteristics and needs complicated trade-off between design parameters. The paper proposes to calculate the mathematical expressions by using symbolic computation software to make the trade-off simple. In an example of a water level control plant, the mathematical expressions are obtained explicitly and using the expressions, a controller is designed to satisfy the three specifications.