Abstract
In actual industrial control processes, quantized control signals are frequently used due to the simplicity of manipulating mechanism. In this paper an analytical method for obtaining a suboptimal feedback control law is presented for linear systems actuated by the quantized discrete control signals.
The technique consists of transforming the state space by an orthonormal matrix, approximating the minimum cost performance with one quadratic hypersurface in the transformed state space, and then deriving the switching hyperplanes seperating the state regions each of which is assigned a suboptimal quantize control. The suboptimal control law is given in the form of the switching hyperplanes obtained by the solution of a nonlinear matrix difference equation for time-discrete systems or of a matrix differential equation for time-continous systems. Advantages of the technique are that the computation of inverse matrices is not required and that only a simple analytical computation is utilized, even in the case when the dimension of the control system increases.
Furthermore, it is proved that the suboptimal control law approaches to the known nonquantized linear optimal control law as the number of quantization becomes large and the quantized level becomes small.
