Proxy-Based Sliding Mode Vibration Control with an Adaptive Approximation Compensator for Euler-Bernoulli Smart Beams

Abstract

Proxy-based sliding mode control PSMC is an improved version of PID control that combines the features of PID and sliding mode control SMC with continuously dynamic behaviour. However, the stability of the control architecture maybe not well addressed. Consequently, this work is focused on modification of the original version of the proxy-based sliding mode control PSMC by adding an adaptive approximation compensator AAC term for vibration control of an Euler-Bernoulli beam. The role of the AAC term is to compensate for unmodelled dynamics and make the stability proof more easily. The stability of the proposed control algorithm is systematically proved using Lyapunov theory. Multi-modal equation of motion is derived using the Galerkin method. The state variables of the multi-modal equation are expressed in terms of modal amplitudes that should be regulated via the proposed control system. The proposed control structure is implemented on a simply supported beam with two piezo-patches. The simulation experiments are performed using MATLAB/SIMULINK package. The locations of piezo-transducers are optimally placed on the beam. A detailed comparison study is implemented including three scenarios. Scenario 1 includes disturbing the smart beam while no feedback loop is established (open-loop system). In scenario 2, a PD controller is applied on the vibrating beam. Whereas, scenario 3 includes implementation of the PSMC+AAC. For all previously mentioned scenarios, two types of disturbances are applied separately: 1) an impulse force of 1 N peak and 1 s pulse width, and 2) a sinusoidal disturbance with 0.5 N amplitude and 20 Hz frequency. For impulse disturbance signals, the results show the superiority of the PSMC+AAC in comparison with the conventional PD control. Whereas, both the PSMC+ACC and the PD control work well in the case of a sinusoidal disturbance signal and the superiority of the PSMC is not clear.

Design of Optimal Sliding Mode Control of Elbow Wearable Exoskeleton System Based on Whale Optimization Algorithm

“…This study can be extended to apply other recent control strategies for the elbowexoskeleton system. Accordingly, one can conduct a comparison study between the SMC and the suggested control schemes to show their effectiveness in trajectory tracking [41][42][43][44][45][46][47][48][49][50][51].…”

Function approximation technique (FAT)-based nonlinear control strategies for smart thin plates with cubic nonlinearities

“…The Lyapunov theory is used as a basis for guaranteeing the stability of the proposed control law and the corresponding updating laws associated with unknown parameters. For unknown time-varying parameters, adaptive approximation control is used instead to comprise model-free techniques or so-called intelligent control [25][26][27][28][29][30][31][32][33][34]. On the other hand, robust control requires knowledge of limits of uncertainty.…”