Performance of First and Second Order Sliding Mode Control Strategies for a Simple Pendulum

Author Name(s): B.Amarendra Reddy, B.Pavan Kumar, G.Ananda Rao, K. Anusha
Author Email: bamarendrareddy@yahoo.com

Abstract

Sliding mode control approach is recognized as one of the efficient tools to design robust controllers for complex high-order dynamic plant operating under uncertainty conditions. The main advantages of sliding mode are low sensitivity to plant parameter variations and disturbances can be completely eliminated. This paper deals with the modeling and control of simple pendulum with different SMC strategies under various perturbed conditions. Here, first-order sliding mode control and second-order sliding mode control strategies are considered for regulation of simple pendulum. Control of simple pendulum, under different initial conditions is demonstrated in simulation in MATLAB environment.

Introduction

A simple pendulum system is a mechanical system that exhibits periodic motion. It consists of a particle like bob suspended by a light string that is fixed at the upper rigid surface. The motion occurred in the vertical plane is driven by its weight [1].Pendulums have been known to be a good resonators and also suitable for reference in high quality clocks for a long time. In this paper a robust control strategy to control the oscillations of a simple pendulum was designed. This can be achieved by using Sliding Mode Control (SMC) which is one of the Variable Structure Control Systems (VSCS).

Variable structure control systems, as the name suggests, these are a class of systems where the ‘control law’ is deliberately changed during the control process  according to some predefined rules, which depend on the states of the system. Variable Structure Control Systems have been described in the literature by numerous authors [2]-[5]. The most distinguished feature of  variable structure control (VSC) is its ability towards robust control systems and using VSC in many cases results in invariant control systems. The term “invariant” means that the system is completely insensitive to parametric uncertainty and external disturbances.

The basic idea of sliding mode control is that the structure of the control signal is altered as the state trajectory crosses switching surfaces in the state space as a result the desirable properties are achieved. SMC design entails the choice of the switching control and the associated switching logic to yield sliding motion on the sliding surface. Although sliding mode control method provides a robust controller for nonlinear dynamic systems [4]-[6] and it inherits a discontinuous control action forces the system to reach the sliding surface.

This paper is organized as follows. (i) Mathematical modeling aspects of the Simple Pendulum is discussed in the section II. (ii) Sliding mode Control law aspects and Control strategy are discussed in section III. (iii) Simulation studies using MATLAB are discussed in section IV. (iv) Conclusions are presented in section V

Conclusion

This paper presents first order sliding mode controller for a simple pendulum. The second order sliding mode controllers are also designed using twisting and super-twisting algorithm. Using these controllers simulation studies are performed under different initial conditions. Angular displacement, control signals and trajectories are plotted.  It is observed from the simulation results that, steady state convergence time for angular displacement is less in twisting SMC strategy and further less in Super-Twisting SMC strategy than compared to First order sliding mode control strategy.

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