[Paper Review] Stabilization of Underactuated Mechanical Systems with Time-Varying Uncertainty using Adaptive Fuzzy Sliding Mode

Mohammad Azimi, Hamid Reza Koofigar+1 more|arXiv (Cornell University)|Feb 8, 2017

Adaptive Control of Nonlinear Systems5 references3 citations

TL;DR

This paper proposes an Adaptive Fuzzy Sliding Mode Controller (AFSMC) for underactuated mechanical systems subject to time-varying uncertainties and external disturbances. By integrating adaptive fuzzy logic with sliding mode control, the method enhances robustness and reduces chattering, demonstrating effective stabilization in simulations of an inverted pendulum and a TORA system with two degrees of freedom.

ABSTRACT

In this paper, the control problem for underactuated systems in the presence of external disturbances and model uncertainties is considered. An adaptive fuzzy sliding mode controller (AFSMC) is proposed to solve the problem, satisfying the robustness properties against uncertainties and disturbances. The designed controller can be applied to a wide class of underactuated systems and have fewer restrictions, compared with many pervious works. To evaluate the performance of proposed algorithm, it is applied to an underactuated inverted pendulum and a Translational Oscillator/Rotational Actuator (TORA) system with two degrees of freedom. The simulations are also demonstrated to show the effectiveness of the proposed strategy.

Motivation & Objective

• To address the stabilization of underactuated mechanical systems under time-varying model uncertainties and external disturbances.
• To develop a control strategy with fewer restrictions compared to prior methods.
• To enhance robustness against uncertainties while minimizing control chattering.
• To validate the controller’s effectiveness through simulation on benchmark underactuated systems.

Proposed method

• Designs a sliding mode control law with a switching surface that ensures system states converge to the equilibrium.
• Introduces a fuzzy logic system to approximate the upper bound of uncertainties and disturbances online.
• Employs adaptive laws to update the fuzzy system parameters in real time, improving estimation accuracy.
• Uses a Lyapunov-based stability analysis to prove asymptotic stability of the closed-loop system.
• Applies the controller to two test cases: a 1-DOF inverted pendulum and a 2-DOF TORA system.
• Employs simulation tools to evaluate transient response, robustness, and chattering reduction.

Experimental results

Research questions

• RQ1 How can an adaptive fuzzy sliding mode controller stabilize underactuated systems with time-varying uncertainties?
• RQ2 What is the effectiveness of fuzzy logic in approximating unknown system uncertainties in real time?
• RQ3 To what extent does the proposed controller reduce chattering compared to conventional sliding mode control?
• RQ4 How does the controller perform under external disturbances in nonlinear, underactuated systems?
• RQ5 Can the controller be applied to a wide class of underactuated mechanical systems without restrictive assumptions?

Key findings

• The AFSMC successfully stabilizes the underactuated inverted pendulum and TORA system under time-varying uncertainties and disturbances.
• The controller exhibits reduced chattering compared to conventional sliding mode control, as confirmed by simulation trajectories.
• The fuzzy logic component effectively estimates the upper bound of uncertainties in real time, enhancing robustness.
• Stability analysis confirms asymptotic convergence of system states to the equilibrium point using Lyapunov theory.
• Simulations demonstrate fast transient response and strong robustness to external disturbances in both test systems.
• The proposed method imposes fewer structural and modeling constraints than previous approaches, broadening its applicability.