A Nonlinear Dynamic Optimization Algorithm of a Novel Energy Efficient Pneumatic Drive System

A standard pneumatic system is usually controlled by a 5/2 directional control valve in which compressed-air utilization rate is low. To solve the problem, scholars have proposed a bridge pneumatic circuit controlled by four switch valves that uses expansion energy of compressed air to do work. The key to this bridge circuit lies in the accuracy and speed of on-off sequence of the valves. To realize this goal, we study dynamic optimization control of the circuit and establish an optimal valve opening and closing time-sequence control model with a continuous-discrete time differential algebraic equation on the base of the dynamic characteristics of the pneumatic drive system. We use the direct method in modern optimal control theory to solve the problem. Because the model has the characteristics of more equality constraints, lower freedom of variables, and a sparse structure, we use the simplified space sequential quadratic programming algorithm and interior-point methods for computation and analysis so that the process optimization and partial-differential equations are solved simultaneously. To improve the precision and the speed of solving the derivative during the solution-optimization process, the derivative information is obtained with a combination of symbol and numerical automatic differentiation. By analyzing the efficiency of the two algorithms, the interior-point method was proved to be more suitable for use in obtaining the sequence. Finally, the experimental results were realized and showed that our contribution builds a good foundation for the energy-saving research of pneumatic systems.