Abstract
This paper presents the investigation of the optimal valve control which minimizes the consumption of air, or that of energy. At first, the simultaneous differential equations which describe the dynamics of a pneumatic cylinder are changed into a set of discrete equations, and the nonlinear optimization problem of several variables, which aims the minimization of the consumption of air, is set up. And then, we apply the nonlinear mathematical programming to this problem, and the optimal state variables at each time are obtained. Finally, we simulate the continuous model with the optimal valve control patterns which are obtained by solving the optimization problem, and compare the simulated responses with the solutions of the problem. The comparison between the two systems shows that the solutions of the problem agree well with the results of the simulation. And with this control, the consumption of air will be decreased to about 50∼60%, and it will be possible to position a piston precisely. We can conclude that the proposed method is very effective when we decide the position of the piston under condition of minimizing its energy consumption.
