Analogue Computation of the Switching Surfaces in Three-dimensional Phase Space for the Optimization of Non-Linear Control Systems†

Abstract

ABSTRACT The paper deals with the method of using an analogue computer to determine the optimum control for systems in which there is a bounded constraint on the control signal. The difficulties arising out of this method are also discussed. Two problems are considered. In each case the criterion of optimality is minimization of integral square error. The first problem concerns the control of a plant consisting of two integrators ; the control to take place in a given finite time, the command signal input being a step or a step plus a ramp. Ail analytic/numerical solution of this problem is given and compared with the analogue solution. The switching boundary is calculated. The second problem concerns the control of a plant consisting of three integrators with a command signal input of a step plns a ramp plus a parabola. The switching surface obtained is only optimal if the initial conditions are specially chosen, otherwise a result is obtained which is similar to Feldbnum's (1955) switching enrve for the...