Effect of adaptation gain and reference model in MIT and Lyapunov rule–based model reference adaptive control for first- and second-order systems

An adaptive control law encompasses a regulating control rule compensating for system dynamics variations by adjusting the controller characteristics to maintain the overall system performance. Recently, some techniques have been developed based on fundamental aspects of the adaptability of living organisms. The adaptive control method is a technique that measures the dynamic characteristics of the plant automatically and continuously to make a comparison with its required output. It utilizes the difference between these two to commute adaptable system parameters to maintain optimal performance regardless of the system variations. The behavior of the adaptation rule is significantly affected by the adaptation gain value. Here, it has also been investigated that the adaptation gain range is wide for the systems with the lower order. The appropriate range of adaptation gain decreases as the order of the system increases. In the present work, the model reference adaptive control (MRAC) for first- and second-order systems has been designed and investigated using a wide range of values for the adaptation gain and variations in the reference model parameters. The MIT (Massachusetts Institute of Technology) and Lyapunov rules are applied for the analyses of systems. On the MATLAB/Simulink platform, all the adaptation process comparisons, variations, and investigations have been carried out by altering the adaptation gain and the reference model parameters. The obtained results present encouraging outcomes.