Stabilization and Tracking Control of Inverted Pendulum Using Fractional Order PID Controllers

This work focuses on the use of fractional calculus to design robust fractional-order PID (PIλDμ) controller for stabilization and tracking control of inverted pendulum (IP) system. A particle swarm optimisation (PSO) based direct tuning technique is used to design two PIλDμ controllers for IP system without linearizing the actual nonlinear model. The fitness function is minimized by running the SIMULINK model of IP system according to the PSO program in MATLAB. The performance of proposed PIλDμ controllers is compared with two PID controllers. Simulation results are also obtained by adding disturbances to the model to show the robustness of the proposed controllers. 1. Introduction The inverted pendulum (IP) system, nonlinear and unstable system, is widely used in laboratories to implement and validate new ideas emerging in control engineering. The control of IP system can be broadly divided into three sections, swing-up control, stabilization, and tracking control. Swing-up control is basically used to swing the pendulum rod from pending position to stabilization zone. Then a balancing or stabilization control is essential to uphold it in upright position for long interval. A switching mechanism between swinging and stabilization zone is necessary for effective control [1, 2]. For swing-up control, a technique based on energy control had been proposed by ？str？m and Furuta [3]. There are several different techniques accessible in literature for stabilization and tracking control of IP system, for example, linear quadratic regulator (LQR), PID control, neural network control, fuzzy logic control, neural-fuzzy control, sliding mode control, and so forth. The LQR, an optimal state feedback controller designed by minimizing a performance index, is ordinarily used controller for IP system modelled in state space form [4]. Here, the state space model of IP system is to be inevitably linearized which leads to modelling error. The PID controller, most widely used controller in several industrial control problems, is one of the favourite controllers for IP system. The comparison of PID controller with other control techniques of IP system was carried out in many studies [5, 6]. The major task of PID controller design is the selection of control parameters for desired response. Some tuning methods of PID controller for IP system could be found in literature [7–9]. In [10], the stabilization as well as tracking control of IP system with actual nonlinear model using PID controllers was investigated but how to choose controllers parameters was not clarified.