Abstract
This express brief deals with the problem of the state variables regulation in the ball and beam system by applying the discrete-inverse optimal control approach. The ball and beam system model is defined by a set of four-order nonlinear differential equations that are discretized using the forward difference method. The main advantages of using the discrete-inverse optimal control to regulate state variables in dynamic systems are (i) the control input is an optimal signal as it guarantees the minimum of the Hamiltonian function, (ii) the control signal makes the dynamical system passive, and (iii) the control input ensures asymptotic stability in the sense of Lyapunov. Numerical simulations in the MATLAB environment allow demonstrating the effectiveness and robustness of the studied control design for state variables regulation with a wide gamma of dynamic behaviors as a function of the assigned control gains.
Highlights
The ball and beam dynamical system is a classical and well-known nonlinear dynamical system that attracts much attention in the control area [1]
It is important to mention that after an exhaustive revision of the literature about the ball and beam dynamical system modeling and control, we identify that the discrete-inverse optimal control has not been studied in this system
Regulation of the State Variables. In this simulation we present the ability of the proposed control to regulate all the state variables using the anti-symmetry nature of the P matrix, where the control gains were assigned as follows, r = 10.37, j1 = 16, j2 = 20, and j3 = 5
Summary
The ball and beam dynamical system is a classical and well-known nonlinear dynamical system that attracts much attention in the control area [1]. The application of the discrete-inverse optimal control to regulate all the state variables of the ball and beam system guaranteeing passivity, stability, and optimality properties. It is important to mention that after an exhaustive revision of the literature about the ball and beam dynamical system modeling and control, we identify that the discrete-inverse optimal control has not been studied in this system. This indicates that it is a clear opportunity for research that this article tries to fill.
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