Model-Free Controller Design for Nonlinear Underactuated Systems With Uncertainties and Disturbances by Using Extended State Observer Based Chattering-Free Sliding Mode Control

Abstract

Most of the control strategies require a mathematical model or reasonable knowledge that is difficult to obtain for complex systems. Model-free control is a good alternative to avoid the difficulties and complex modeling procedures, especially if the knowledge about the system is insufficient. This paper presents a new control scheme completely independent of the system model. The proposed scheme combines sliding mode control (SMC) with intelligent proportional integral derivative (iPID) control based on a local model and extended state observer (ESO). Although the iPID control makes the proposed method model-free, it cannot guarantee that the tracking errors converge to zero asymptotically except the system is in a steady-state regime. Therefore, the SMC is added to the control scheme to ensure the convergence by minimizing the estimation errors of the observer. The proposed iPIDSMC controller is tested in the presence of different parameter variations and external disturbances on an inverted pendulum -cart (IPC), which is a highly unstable underactuated system with nonlinear coupled dynamics. The proposed controller is compared with the PID, iPID and Hierarchical Sliding Mode Control (HSMC) for a clearer evaluation. Simulation results showed that the proposed controller is extremely insensitive to parameter variations, matched and mismatched disturbances and the control signal of the proposed method is chattering-free, even though it is based on a discontinuous control action.INDEX TERMS Extended state observer, external disturbance, intelligent PID, model-free control, robust control, sliding mode control, uncertainties, underactuated system.

Comprehensive Review of Different Pendulum Structures in Engineering Applications

“…Simplified parameters description of the DLRIP are given in Table 5, see appendix. (17) The expression of the mass matrix of the DLRIP is given in equation ( 16)…”

“…Therefore, the application of linear controllers to the IPS depends on the degree of freedom (DOF) and its complex dynamics. During the past few years, different kinds of nonlinear controllers have been applied for IPS control such as nonlinear time-invariant controllers, (sliding mode control (SMC), fuzzy logic control (FLC), [13,15,16], self-learning and adaptive nonlinear controllers, model-free controllers [17], neural network (NN) control [14,20], hybridization of a PID controller and adaptive NN, adaptive NN + PID and adaptive NN + PD controllers [15,18,19], etc. FLC, one of the most used nonlinear controller structures, can approximate any nonlinear control law based on the number of fuzzy sets.…”

A model independent constrained predictive control for the Furuta Pendulum

“…From another perspective, the works of (Liu et al, 2019) and (Chen et al, 2022) address an improvement in the nonlinear function of the non-linear ADRC formulation to better compensate for the discrepancies between the dynamics of a cart inverted pendulum and the integrator chain commonly assumed as the modified plant in the ADRC methods. The benefits of switching between the non-linear and linear ADRC are also presented for the aforementioned sub-actuated system in (Xian et al, 2020), and more recently, (Onen, 2023) studied the combination of the Extended State Observer (ESO) from ADRC with PID control and Sliding Mode Control (SMC) for this type of benchmark.…”