Nonlinear analysis and control of a reaction wheel pendulum: Lyapunov-based approach

This paper presents a nonlinear analysis, control, and comparison of controllers based on the dynamical model of the reaction wheel pendulum (RWP) in a tutorial style. Classical methodologies such as proportional integral derivative (PID) control and state variables feedback control are explored. Lyapunov's method is proposed to analyze the stability of the proposed nonlinear controllers, and it is also used to design control laws guaranteeing globally asymptotically stability conditions in closed-loop. A swing up strategy is also included to bring the pendulum bar to the desired operating zone at the vertical upper position from an arbitrary initial location. Simulation results show that it is possible to obtain the same dynamical behavior of the RWP system adjusting the control gains adequately. All simulations were conducted via MATLAB Ordinary Differential Equation packages. © 2019 Karabuk Universit

MATLAB-based Tools for Modelling and Control of Underactuated Mechanical Systems

Underactuated systems, defined as nonlinear mechanical systems with fewer control inputs than degrees of freedom, appear in a broad range of applications including robotics, aerospace, marine and locomotive systems. Studying the complex low-order nonlinear dynamics of appropriate benchmark underactuated systems often enables us to gain insight into the principles of modelling and control of advanced, higher-order underactuated systems. Such benchmarks include the Acrobot, Pendubot and the reaction (inertia) wheel pendulum. The aim of this paper is to introduce novel MATLAB-based tools which were developed to provide complex software support for modelling and control of these three benchmark systems. The presented tools include a Simulink block library, a set of demo simulation schemes and several innovative functions for mathematical and simulation model generation

Sliding mode control of the reaction wheel pendulum

textThe Reaction Wheel Pendulum (RWP) is an interesting nonlinear system. A prototypical control problem for the RWP is to stabilize it around the upright position starting from the bottom, which is generally divided into at least 2 phases: (1) Swing-up phase: where the pendulum is swung up and moves toward the upright position. (2) Stabilization phase: here, the pendulum is controlled to be balanced around the upright position. Previous studies mainly focused on an energy method in swing-up phase and a linearization method in stabilization phase. However, several limitations exist. The energy method in swing-up mode usually takes a long time to approach the upright position. Moreover, its trajectory is not controlled which prevents further extensions. The linearization method in the stabilization phase, can only work for a very small range of angles around the equilibrium point, limiting its applicability. In this thesis, we took the 2nd order state space model and solved it for a constant torque input generating the family of phase-plane trajectories (see Appendix A). Therefore, we are able to plan the motion of the reaction wheel pendulum in the phase plane and a sliding mode controller may be implemented around these trajectories. The control strategy presented here is divided into three phases. (1) In the swing up phase a switching torque controller is designed to oscillate the pendulum until the system’s energy is enough to drive the system to the upright position. Our approach is more generic than previous approaches; (2) In the catching phase a sliding surface is designed in the phase plane based on the zero torque trajectories, and a 2nd order sliding mode controller is implemented to drive the pendulum moving along the sliding surface, which improves the robustness compared to the previous method in which the controller switches to stabilization mode when it reaches a pre-defined region. (3) In the stabilization phase a 2nd order sliding mode integral controller is used to solve the balancing problem, which has the potential to stabilize the pendulum in a larger angular region when compared to the previous linearization methods. At last we combine the 3 phases together in a combined strategy. Both simulation results and experimental results are shown. The control unit is National Instruments CompactRIO 9014 with NI 9505 module for module driving and NI 9411 module for encoding. The Reaction Wheel Pendulum is built by Quanser Consulting Inc. and placed in UT’s Advanced Mechatronics Lab.Mechanical Engineerin

Synchronization of clocks

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Global stabilization of a reaction wheel pendulum: A discrete-inverse optimal formulation approach via a control lyapunov function

This paper deals with the global stabilization of the reaction wheel pendulum (RWP) in the discrete-time domain. The discrete-inverse optimal control approach via a control Lyapunov function (CLF) is employed to make the stabilization task. The main advantages of using this control methodology can be summarized as follows: (i) it guarantees exponential stability in closed-loop operation, and (ii) the inverse control law is optimal since it minimizes the cost functional of the system. Numerical simulations demonstrate that the RWP is stabilized with the discrete-inverse optimal control approach via a CLF with different settling times as a function of the control gains. Furthermore, parametric uncertainties and comparisons with nonlinear controllers such as passivity-based and Lyapunov-based approaches developed in the continuous-time domain have demonstrated the superiority of the proposed discrete control approach. All of these simulations have been implemented in the MATLAB software