Optimal fractional order PI^λD^μ controller for stabilization of cart‐inverted pendulum system: Experimental results

Abstract

The cart-inverted pendulum is a non-minimum phase system having right half s-plane pole and zero in close vicinity to each other. Linear time invariant (LTI) classical controllers cannot achieve satisfactory loop robustness for such systems. Therefore, in the present work the fractional order PI λ D μ (FOPID) controller is addressed for robust stabilization of the system, since fractional order controller design allows more degrees of freedom compared to its integer order counterparts by virtue of its two parameters λ and μ. The controller parameters are tuned by three evolutionary optimization techniques. In order to select the controller parameters optimally, a novel non-linear fitness function using integral time square error (ITSE), settling-time, and rise time is proposed here. The control algorithm is implemented successfully in real-time. Moreover, stability analysis of the system compensated with a fractional order controller is presented using Riemann surface. Robustness of the physical cartinverted pendulum system towards multiplicative gain variations and plant parameter variations is verified. In this regard, it is shown that the fractional order controller provides satisfactory robust performance in both simulation and real-time system. KEYWORDS cart-inverted pendulum system, FOPID controller, gain margin (GM), non-minimum phase system, Riemann surface, robust stability

Contour Tracking Control of a Linear Motors-Driven X-Y-Y Stage Using Auto-Tuning Cross-Coupled 2DOF PID Control Approach

“…If the searched source position of food from the employed bees cannot be improved over an interaction's numbers, the employed bees are changed as the scout bees and they randomly replace the original source with another one via the mechanism (22). This process can be determined according to the parameter limit in the designed controller.…”

“…However, it is difficult to obtain satisfactory control performance in nonlinear and time-varying systems using the conventional PID controller since it is not robust enough to achieve satisfactory control performance [18]. As a relief to this problem, many advanced PID control strategies have been developed, such as two-degree-of-freedom PID (2PID) [19], internal model controller PID [20], automatic tuning PID [21], and fractional-order PID [22]. Among these improved PID control methods, a 2PID controller acquires a better response as compared to that of a conventional one-degree-of-freedom PID (PID) controller due to its additional control loop [23].…”

Tuning rules: Graphical analysis and experimental validation of a simplified fractional order controller for a class of open‐loop unstable systems

“…The applicability of the proposed method is shown by the experimental results of the two well-known test bench setups: one is rotary inverted pendulum (ROTPEN), and another is the magnetic levitation system (MAGLEV). Number of controllers based on the FO control [9,11,12,14,15] and some other nonlinear control methods [37][38][39] have been reported in the literature for the nonlinear system, and for comparison purpose, the sliding mode controller (SMC) has been taken in account to validate the superiority of proposed FO controller tuning.…”

“…KEYWORDS fractional order controller, MAGLEV, ROTPEN, tuning Abbreviations: ROTPEN, Rotary inverted pendulum; MAGLEV, Magnetic levitation system; PM, Phase margin of the system under consideration; GM, Gain margin of the system under consideration; GCF, Gain crossover frequency of the system under consideration; SMC, Sliding mode controller; FOMCON, Fractional order modeling and control toolbox; FOPID, Fractional order PID controller; k p , Proportional controller gain; k i , Integral controller gain; k d , Derivative controller gain; , Order of fractional integrator; , Order of fractional differentiator; q 1 and q 2 , Feed forward controller gain parameters.of many scholars in the previous years from academic as well as the industry. Fractional order (FO) controller has been studied, tested, and successfully implemented on the experimental setups such as the inverted pendulum, magnetic levitation system, manipulators, direct current (DC) motors, oscillators, and other electrical circuits [2,4,[8][9][10][11][12][13][14][15][16][17]. It has been validated in the abovementioned…”

“…of many scholars in the previous years from academic as well as the industry. Fractional order (FO) controller has been studied, tested, and successfully implemented on the experimental setups such as the inverted pendulum, magnetic levitation system, manipulators, direct current (DC) motors, oscillators, and other electrical circuits [2,4,[8][9][10][11][12][13][14][15][16][17]. It has been validated in the abovementioned…”