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

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 y_o 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.