Abstract
A control problem of an inverted pendulum in the presence of parametric uncertainty has been investigated in this paper. In particular, synthesis and implementation of an automatic self-tuning regulator for a real inverted pendulum have been given. The main cores of the control system are a swing-up control method and a stabilisation regulator. The first one is based on the energy of an inverted pendulum, whereas the second one uses the linear-quadratic regulator (LQR). Because not all of the inverted pendulum parameter values are exactly known an automatic self-tuning mechanism for designed control system has been proposed. It bases on a devised procedure for identifying parameters. The entire derived control system enables effective a pendulum swing-up and its stabilisation at an upper position. The performance of the proposed control system has been validated by simulation in Matlab/Simulink environment with the use of the inverted pendulum model as well as through experimental works using the constructed inverted pendulum on a cart.
Highlights
An inverted pendulum (IP) is one of the widespread benchmarks of a non–linear, unstable and under–actuated mechanical dynamic systems
This paper focuses on the latter ones, which are known as adaptive control systems
The influence of parametric uncertainty on these elements is discussed. As it has been mentioned in the second paragraph, for control system synthesis purposes, a proper IP mathematical model has been prepared
Summary
An inverted pendulum (IP) is one of the widespread benchmarks of a non–linear, unstable and under–actuated (more degrees of freedom than the number of control inputs) mechanical dynamic systems. An adaptation of the control system by adjusting the LQR gains bases on improving the IP model which is devised in the paper. The influence of parametric uncertainty on these elements is discussed As it has been mentioned in the second paragraph, for control system synthesis purposes, a proper IP mathematical model has been prepared. Summarised, the main contributions of this paper are as follows: 1) an adaptation of the control system by adjusting the LQR gains bases on improving the IP model which allows to take into account parametric uncertainty is proposed, VOLUME 8, 2020. 2) an appropriate IP model parameters identification procedure for the control system adaptation purposes is devised, 3) the IP workstation has been constructed for experimental research of the proposed control system.
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