Control of linear systems using piecewise continuous systems

A control method is presented based on the use of piecewise continuous systems (PCS) as a control vector generator over sampling periods. The PCS has two inputs and one output which is equivalent to the control vector. Each input is corresponding to one specific time space, the first one to the discrete time space defined by S = {t/sub k/, k = 0,1,2, ... }, and the second one to the continuous time space t (is member of) (Ifr) - S with (Ifr) = { t (is member of) [0,(infinity) [ }. The control is generated in the time space (Ifr). The architecture involving the PCS contains two feedback loops, based on the concept of double time and input spaces. These inputs are computed using two transformation maps (Psi) and (Phi) defined in functions of the control strategy adopted to achieve the desired control properties. The control law depends on the PCS properties and on the method used to generate PCS controller inputs. Two examples are given. In the first example, the PCS controller is working in open-loop configuration during a sample period, therefore ripple is possible during the sampling period. This limited control strategy assures imposed trajectory tracking only at sampling instants. In the second example the PCS is generating the control that satisfies the anti-ripple control strategy. The plant state is observed in continuous time and the imposed state trajectory must be compared with the plant state continuously. The PCS controller initial state is generated according to the ʹoptimal controlʹ law that minimises the quadratic criterion concerning the error-control compromise. This method appears to have several advantages over dynamic controllers: it provides control system designers with more freedom, and it requires an important computation only at the beginning of control process. Examples are given.