Design of two-loop FOPID-FOPI controller for inverted cart-pendulum system

Abstract

The inverted cart-pendulum system (ICPS) consists in having a pendulum mounted on a sliding cart, with the pivot point fixed. This real time experiment indeed looks like a rocket and its functionality is akin to a rocket. These are the launchers and the missile guidance and control as well as construction anti-seismic measures also. The control aim in these systems is to maintain the inverted pendulum vertically stable. The system is causal but unstable and, therefore, has no minimum phase. Therefore, the right half plane pole and zero are close to each other. Therefore, the stability of the system can be considered as problematic at some points. Unfortunately, linear time- invariant (LTI) classical controllers are incapable of offering suffient loop robustness for such systems. This paper aims to project a two-loop fractional order controller (2-LFOC) design to stabilize a higher-order nonlinear inverted cart-pendulum system (ICPS). The modeling, linearization, and control of ICPS are demonstrated in this work. The control target is adjusted so that the inverted pendulum stabilizes in its upright state when the cart reaches the required point. To fulfill the control objective, two-loop FOPID-FOPI controllers are proposed, and the Levenberg Marquardt algorithm (LMA) is utilized to tune the controllers. A novel nonlinear integral of time-associated absolute-error (ITAE) based fitness formula considering the settling time and rise time is used to fit the controller parameters for 2-LFOC. A performance comparison with the PID controller in terms of different time domain parameters such as rise_time (T _R ), peak_time (T _P ), settling_time (T _S ), maximum overshoot (OS _M ), maximum undershoot (US _M ) and steady-state error (E _SS ) are investigated. Stability analysis using Riemann surface observation of the system compensated with the proposed controller is presented in this work. The robust behavior of the two-loop FOPID-FOPI controller is verified by the application of disturbances in the system and the Reimann surface observation.