Data-Driven Adaptive Steady-State-Integral-Derivative Controller Using Recursive Least Squares With Performance Conditions

This paper presents a data-driven adaptive steady state-integral-derivative (SS-ID) control algorithm that uses gradient descent and recursive least squares (RLS) with a forgetting factor. A simplified first-order differential equation of the control system was designed and its parameters were estimated in real-time using the RLS algorithm. The steady-state control input for target-state tracking was derived based on the estimated parameters and steady-state performance conditions. The gradient of the integrated control error to the gain was estimated based on the least-squares method, using the saved past error and gain data in a finite sliding window to determine the control input. The integral gain was adapted based on the gradient descent method, using the estimated gradient, integrated error, and adaptation rate. Simplified control error dynamics were designed, and their parameter was estimated using the RLS algorithm. The derivative control gain can be adapted in real time using the estimated parameters from the simplified control error dynamics and time constant-based performance conditions. The proposed controller was designed in the MATLAB/Simulink environment. A performance evaluation was conducted under various scenarios using a DC motor simulation model and an actual test platform equipped with an optical encoder.