Method of controlling the regulated object

Abstract

A method of controlling a controlled object, involving the use of a PID controller, in which the output signal from the controlled object is differentiated by comparison with a setpoint signal, is characterized in that the output signal from the controlled object is compared with the setpoint signal, obtaining their difference, which is simultaneously amplified with the derivative of the output signal from the controlled object using a gain matrix obtained from the LQR algorithm according to the equation Ky=KX2(CX2)-1. K is the gain matrix for the auxiliary LQR problem, with canonical dynamics and the standard criterion J(u)=ʃ0∞(xTQx+uTRu)dt. Vector x is the state of the system, u is the control vector of the controlled object, while Q and R are criterion matrices. X2 is a matrix composed of two eigenvectors of the matrix Ac=(A—BK). C is a matrix defining an artificially introduced additional output. A and B are known matrices of the canonical system.After amplification, two signals are obtained - the overdrive signal and the main control signal, and the main control signal is added with the integral of the overdrive signal to obtain the control signal of the regulated object.

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