Application of idea of time-scale control to synthesis of control signals for linear and non-linear plants

Abstract

The concept of control of plants represented by (1) has been proposed. Using (2),(3),(4),(5) one can determine plant input U(t) forming its output as Y(T), where “new” time T depending on time-scale A(t) is defined by dT=A(t) dt, whereas Y(t) is plant “reference” output obtained for A=1. Signal A(t) is obtained as result of static operation A(t)=q(e(t)), where q(0)=0 and e(t) is control system error. The technical applications can base on MFC structure (Fig. 4). The idea of control is simple: if e(t)=A(t)=0, then model (2) is decoupled, values of its state variables and output y are conserved. Because Y follows y (Fig. 4), then changes of plant output are stopped too. If e(t)=A(t) ≠0, then y and Y tend to reference signal yo and rate of follow-up action depends on q(e(t)). During this process the consecutive outputs of model and plant are y(T) and Y(T). Thus, the “reference” response Y(t) defines Y (T). The impressive results illustrating properties of proposed concept are shown in Fig. 5,6. Application of described method simplifies the analysis of system dynamics and yields perfect results of follow-up action (lack of overshoots, short setting times). The idea for SISO case has been generalized to form enabling control of MIMO plants.