Design of an Adaptive Super-Twisting Control for the Cart-Pole Inverted Pendulum System

Abstract

A cart-pole inverted pendulum system is one of the underactuated systems that has been used in many applications. This research aims to study the design and the effectiveness of the Adaptive Super-Twisting controller to stabilize the system by comparing it with other previous control methods. A stabilization control of the pendulum upright using the Adaptive Super-Twisting algorithm (ASTA), was investigated. The proposed controller was designed based on the decoupling algorithm method to solve the coupled control input in the system model. We then compared the proposed stabilizing controller with first-order sliding mode control (FOSMC) and Super-Twisting algorithm (STA) in Matlab/Simulink simulation and realistic computer simulation. We developed the computer simulation using anyKode Marilou software, which adopted Open-Dynamic Engine (ODE) as a physics engine. In Matlab/Simulink simulation, we considered three different scenarios: a nominal system, a system with uncertainty, and a disturbed system. Meanwhile, in a computer simulation, we only presented the comparison of different controllers' performances for the realized system. Both results showed that the three controllers could stabilize the pendulum upright with 0.1 rad initial angular position around the vertical axis. Under the same conditions, the ASTA and STA controllers had similar performances; they both have less chattering and faster convergence than the FOSMC approach. However, the FOSMC approach had the least energy delivered and smallest errors than the other two approaches.

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“…The sliding mode control is a robust nonlinear controller which can easily handle a system's nonlinearity, uncertainty and model mismatch [49]- [52]. It has been implemented to control both linear and nonlinear systems: hydraulic [53][54], single machine infinite bus system [55], inverted pendulum [56]- [58], DC motor [59], induction motor [60], suspension [61], permanent magnet synchronous generator [62], hyperchaotic system [63], quadcopter [64], mobile robot [65][66], stepper motor [67], tank system [68] and robot manipulator [69]. According to study findings, SMC has been reported to give promising results.…”

Stabilizing of Inverted Pendulum System Using Robust Sliding Mode Control

“…The Inverted Pendulum is a highly nonlinear [1], unstable [2], fast dynamic [3], under-actuated system [4], [5], and multivariable system [6]. This system belongs to the under-actuated mechanical system, which its control inputs are more than its degrees of freedom [7], [6], [8], [9], [10]. This characteristic encouraged many researchers to use it as a traditional benchmark for the creation, testing, assessing, and comparing of different classical and contemporary control techniques [6].…”

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