Precise angular speed control of permanent magnet DC motors in presence of high modeling uncertainties via sliding mode observer-based model reference adaptive algorithm

Abstract

The major concentration of this study is on developing a control scheme with parameter- and load-insensitive features capable of precise angular speed regulation of a permanent magnet (PM) DC motor in the presence of modeling uncertainties. Towards this objective, first, an appropriate nonlinear dynamic model of friction, the modified LuGre model, is opted and incorporated into the mathematical model of a PM DC motor. Then a sliding mode observer (SMO) is designed to estimate the state variable of the friction model. Next, a model reference adaptive control system into which estimated values of the friction state and parameters are fed is designed to track the desired speed trajectory while alleviating the adverse effects of model uncertainties and friction. Stability of the proposed SMO-based MRAC system is discussed via the Lyapunov stability theorem, and its asymptotic stability is verified. In addition to simulation studies, the algorithm is implemented on a new variable structure test-bed which gives us the ability to simulate desired parameter variations and external disturbance changes in experiment. The main contribution of the proposed scheme is the bounded estimation of the system’s friction parameter. While similar control solutions do estimate these parameters, there is no guarantee that they will estimate the correct value of friction parameters. However, in the proposed method, by properly choosing the design parameters, if certain criteria is satisfied, the estimated friction parameters will be in the bounded vicinity of their actual values. The obtained results show the effectiveness of the proposed tracking algorithm and its robustness against load and system parameters’ variations.