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 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 risetime(TR),
peaktime(TP ), settlingtime(TS), maximum overshoot (OSM), maximum undershoot
(USM) and steady-state error (ESS) 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 FOPIDFOPI
controller is verified by the application of disturbances in the system and
the Reimann surface observation.