Sub-Optimal Stabilizers of the Pendubot Using Various State Space Representations

Abstract

This paper considers the issue of linear-quadratic regulator (LQR) design for nonlinear systems with the use of smooth state and input transformations. The proposed design methodology is considered in the stabilisation task of the Pendubot, which is based on the concept of feedback equivalent control systems. It turns out that it is possible to find a controller that ensures comparable dynamics of the closed-loop system in the vicinity of the set point regardless of the state-space representation adopted. In addition, the synthesis of suboptimal controllers according to the LQR strategy ensuring equal dynamics at the equilibrium point is presented. The properties of the studied controllers were investigated in a simulation environment and using experimental tests. The detailed forms of transformations and linear approximations given can be regarded as ready-made procedures that can be applied to stabilise similar mechanical systems in robotics.

Tracking Control of Unforced and Forced Equilibrium Positions of the Pendubot System: A Nonlinear MHE and MPC Approach

“…Despite their relatively simple mechanical structure, they represent a challenge to the nonlinear control community. This has given rise to a number of studies devoted to control design and stability analyses for particular classes of nonlinear UMSs, such as the essential overview in [3]; the relevant books [1,4]; and several recent distinct publications, e.g., [5][6][7].…”