Abstract
Research in the field of underactuated systems shows that control algorithms which take the natural dynamics of the system’s underactuated part into account are more energy-efficient than those utilizing fully-actuated systems. The purpose of this paper to apply the two-degrees-of-freedom (feedforward/feedback) control structure to design a swing-up manoeuver that involves tracking the desired trajectories so as to achieve and maintain the unstable equilibrium position of the pendulum on the cart system. The desired trajectories are obtained by solving the boundary value problem of the internal system dynamics, while the optimal state-feedback controller ensures that the desired trajectory is tracked with minimal deviations. The proposed algorithm is verified on the simulation model of the available laboratory model actuated by a linear synchronous motor, and the resulting program implementation is used to enhance the custom Simulink library Inverted Pendula Modeling and Control, developed by the authors of this paper.
Highlights
Underactuated systems are mechanical systems that have fewer control inputs than degrees of freedom to control, which make both the control design and the analysis more difficult when compared to their fully actuated alternatives
The obtained results, such as functions that automate the generation of mathematical models for the n-link inverted pendulum system on the cart or a rotary base, implemented control algorithms and demo simulations, have been included in the custom MATLAB/Simulink library, Inverted Pendula Modeling and Control (IPMaC) [12], developed since 2011
The present paper proposes the algorithm for calculating the swing-up trajectories and their subsequent tracking in the two-degree of freedom control scheme, which is verified on the simulation model of the laboratory single inverted pendulum system on a cart, The Multipurpose Workplace for Nondestructive Diagnostics with Linear Synchronous Motor, located in the CMCT&II’s Laboratory of Production Lines and Image Recognition at DCAI, FEEI TU in Košice
Summary
Underactuated systems are mechanical systems that have fewer control inputs than degrees of freedom to control, which make both the control design and the analysis more difficult when compared to their fully actuated alternatives. This paper is a follow-up to the research of our Underactuated Systems group at the Center of Modern Control Techniques and Industrial Informatics (CMCT&II) at DCAI, FEEI, TU in the field of modelling and control of underactuated systems (http: //matlab.fei.tuke.sk/underactuated) The obtained results, such as functions that automate the generation of mathematical models for the n-link inverted pendulum system on the cart or a rotary base, implemented control algorithms and demo simulations, have been included in the custom MATLAB/Simulink library, Inverted Pendula Modeling and Control (IPMaC) [12], developed since 2011. The obtained results are evaluated and future research directions are outlined
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