Three degrees of freedom rotary double inverted pendulum stabilization by using robust generalized dynamic inversion control: Design and experiments

Abstract

The aim of this article was to determine control strategy for balance control of rotary double inverted pendulum system, which is highly nonlinear and unstable under-actuated system. The complexities involved in rotary double inverted pendulum dynamics make this system a useful engineering test bed to test and verify newly designed controllers. In this article, a constraint-based control approach titled robust generalized dynamic inversion is designed and implemented for robust stabilization of rotary double inverted pendulum system. The robust generalized dynamic inversion control is designed in two stages; in the first stage, constraint differential equations of the controlled state variables are prescribed, which encompasses the control objectives. To enforce the constraint dynamics, the equivalent control is realized by means of Moore–Penrose generalized inversion. To enhance robustness, the switching (discontinuous) control is introduced in second stage, whose design principle is based on classical sliding mode control theory. Finally, the controllers obtained in two stages are augmented to form the resultant robust generalized dynamic inversion control law. The proposed controller ensures robustness along with improved time domain performance regardless of system nonlinearities, uncertainties, and unwanted disturbances. The stability analysis is presented for guaranteeing semi-global asymptotically stable closed loop performance via Lyapunov stability criteria. Numerical simulation and experimental investigations are carried out along with comparative analysis, to demonstrate the effectiveness of robust generalized dynamic inversion control algorithm over other conventional control methods.

Experimental Application of Robust and Converse Dynamic Control for Rotary Flexible Joint Manipulator System

“…Figure 6 shows the hardware setup required for performing the experiments. RCD control expression consists of two components in experimental setup, i.e., V m eq and V m eq given by (22) are implemented in Matlab Simulink environment. QUARC (Quanser Real-Time Control) is used to interact with RFJ hardware via Simulink.…”

“…e stability analysis of the derived RCD control expression given by ( 22) is demonstrated using Lyapunov stability criterion. e finite time convergence of ϱ θ and ϱ α to zero is assured by suitable selection of the gain matrix K. To prove this convergence, substitute the expression of V m given by (22) in the sliding mode dynamics given by (20), which yields the following expression:…”

“…In order to introduce the RCD control scheme, the authors studied different approaches of general dynamic conversion schemes. For example, the literature shows a constraint-based approach to solve many engineering problems that encapsulates the control objectives in the form of constraint differential equation [22]. To fulfill the control objectives, the constraint dynamics along the trajectories of the dynamical system are inverted by engaging Moore-Penrose Generalized Inverse (MPGI) to establish the control law [22].…”

“…For example, the literature shows a constraint-based approach to solve many engineering problems that encapsulates the control objectives in the form of constraint differential equation [22]. To fulfill the control objectives, the constraint dynamics along the trajectories of the dynamical system are inverted by engaging Moore-Penrose Generalized Inverse (MPGI) to establish the control law [22]. e conventional BI strategy explicitly depends on the modeled dynamics; therefore, it lacks robustness to handle system uncertainties and nonlinearities.…”

“…Using the RCD control technique, both numerically and experimentally, this is the first study to systematically investigate the control of a flexible joint manipulator. Using the sliding mode control (SMC) theory that has been proven extremely robust, we have proposed a combination of baseline controllers and a discontinuous controller [22]. e integration of discontinuous control term makes the control strategy capable to handle the variations in the plant dynamics very effectively while suppressing the strong joint flexibility.…”