Model reference adaptive control is one of the popular methods that simultaneously deals with uncertainties and reduces conservatism. However, it usually suffers from slow convergence and poor tracking at the beginning of the adaptation. On the other hand, attaining fast convergence by increasing the learning rate could cause oscillation in the control response, which results in system instability. Some of the solutions that have been presented so far use prediction error, low-pass filter, or normalizing the control signal. In this article, a novel robust normalized Lyapunov design is proposed for model reference adaptive control to achieve fast convergence and to avoid oscillatory response. In contrast to the other solutions, it uses a new Lyapunov function to guarantee the global asymptotic stability and to prove the robustness of the closed-loop system against bounded uncertainties. The performance of the proposed method is compared with two other model reference adaptive controls using simulations. In addition, an industrial selective compliance assembly robot arm is used for further verification. Results indicate that that the proposed normalized Lyapunov design reduces the tracking error by 62.4% on average; it also has faster convergence and shows robustness against uncertainties such as payload changes.
Lyapunov design of least-squares model-reference adaptive control