Interval linear quadratic regulator and its application for speed control of DC motor in the presence of uncertainties

An analytical investigation of a DC motor with interval uncertainties is performed in this study and a new approach by interval analysis is suggested for optimal control of the system. The main advantage of using an interval model for uncertainties is that makes the system independent from the probability distribution models of the system; therefore, it can be analyzed by only having information about minimum and maximum bounds. Here, the interval analysis deals with linear quadratic feedback control (LQR) to simulate and optimal control of the DC motor in the realistic state. To do this, the Pontryagins principle is used to solve the interval linear quadratic regulator to obtain the essential conditions, and thus, they have been reconstructed as ordinary differential equation by applying several algebraic manipulations. Afterward, by solving the interval nonlinear system of the ODE, the confidence interval for the feedback controller is achieved. The confidence interval is to guarantee the solution which is included in it. The Chebyshev inclusion approach is applied here to find solution for the ODE system with uncertainties. A comparison of the step response of the suggested approach with the centered approach and Monte Carlo methods a statistical approach is performed. The simulation results indicated that the suggested approach retains tighter and more sensible results than the Monte Carlo method.