Hybrid Control of a Pendubot System Using Nonlinear H∞ and LQR

In this paper, a hybrid control approach is synthesized for stabilizing an under-actuated mechanical system, the Pendubot. This kind of system is divided into two modes, the swing-up mode, and the balancing mode. First, dynamic modeling is established by the Euler-Lagrange method. Next, the robust nonlinear H∞ is designed for the swing-up mode, which handles with the nonlinear model. To weaken the under-actuation characteristic, the control law is developed for the active link with its coupling with the passive link. The LQR is designed for the balancing mode where LQR handles with the linearized model about the unstable top equilibrium position. A simulation is achieved under the MATLAB/Simulink environment. It shows robustness against the external inputs and the fast convergence to the equilibrium position.

Uncertain nonlinear system control using hybrid fuzzy LQR-sliding mode technique optimized with evolutionary algorithm

Purpose This paper aims to propose an advanced tracking control of the uncertain nonlinear dynamic system using a novel hybrid fuzzy linear quadratic regulator (LQR)-proportional-integral-derivative (PID) sliding mode control (SMC) optimized by differential evolution (DE) algorithm. Design/methodology/approach First, a swing-up and balancing control is presented for an experimental uncertain nonlinear Pendubot system perturbed with friction. The DE-based optimal SMC scheme is used to optimally swing up the Pendubot system to the top equilibrium position. Then the novel hybrid fuzzy-based on LQR fusion function and PID controller optimized by DE algorithm is innovatively applied for balancing and control the position of the first link of the Pendubot in the down-right position with tracking sinusoidal signal reference. Findings Experimental results demonstrate the robustness and effectiveness of the proposed approach in balancing control for an uncertain nonlinear Pendubot system perturbed with internal friction. Originality/value This manuscript is an original research paper and has never been submitted to any other journal.