Performance enhancement of model reference adaptive control through normalized Lyapunov design

Abstract

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.

Nonlinear output path following control using a two-loop robust model predictive control approach

“…In order to validate the theoretical benefits of the proposed TL-PFC controller, it is used for controlling FUM SCARA robot (Farajzadeh-Devin et al, 2019; Mousavi et al, 2015; Shariatee et al, 2014) (Figure 3). The robot has a nonlinear dynamic as…”

An improved two‐loop model predictive control design for nonlinear robust reference tracking with practical advantages

“…Industrial Example . In order to validate the aforementioned theoretical benefits of the proposed ITL‐NMPC controller, the FUM SCARA robot 35‐37 Figure 3 is controlled with this approach. The robot has a nonlinear dynamic as where θ is the vector of joint space coordinates, τ is the torque vector, M rob (.…”