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This paper considers the numerical approximation for the optimal supporting position and related optimal control of a catalytic reaction system with some control and state constraints, which is governed by a nonlinear partial differential equations with given initial and boundary conditions. By the Galerkin finite element method, the original problem is projected into a semi-discrete optimal control problem governed by a system of ordinary differential equations. Then the control parameterization method is applied to approximate the control and reduce the original system to an optimal parameter selection problem, in which both the position and related control are taken as decision variables to be optimized. This problem can be solved as a nonlinear optimization problem by a particle swarm optimization algorithm. The numerical simulations are given to illustrate the effectiveness of the proposed numerical approximation method. [ABSTRACT FROM AUTHOR]

This paper proposes a numerical approximation method for computational optimal control of a time fractional convection-diffusion-reaction system. The proposed method involves discretizing the spatial domain by finite element method, approximating the admissible controls by control parameterization, and then obtaining an optimal parameter selection problem which can be solved by numerical optimization algorithms such as sequential quadratic programming. Specifically, an implicit finite difference method is employed to solve the time fractional system, and the sensitivity method for gradient computation in integer order optimal control problems is adjusted to the fractional order case. Simulation results demonstrate the validity and accuracy of the proposed numerical approximation method. [ABSTRACT FROM AUTHOR]

Stepless capacity control technology for reciprocating compressors is a key contributor to energy saving for the petroleum and petrochemical industries. Devices called 'unloaders' are utilized to control the capacity of the compressor by forcibly holding the suction valves open during a variable portion of the compression stroke to control the compressor output. This approach can also lead to various faults of the suction valve. This paper describes the simulation and experimental studies of the transient motion of suction valves under stepless capacity control. Beginning with mathematical models for the normal cycle, improved models of a reciprocating compressor under stepless capacity control have been built. A simulation study of the working process of a double-acting reciprocating compressor has been completed. Theoretical formulas for the transient motion of the valve plate under complicated conditions and the dynamic pressure in the cylinder are compared with the experimental results. Based on the above simulations, a finite element analysis of the valve plate and valve seat has been completed. The experiment results showed that the vibration of the compressor cylinder under complicated conditions was consistent with numerical simulation results. Research presented in this paper is significant in providing tools for diagnosing faults in order to optimize the design of reciprocating compressors that utilize a stepless capacity control system. [ABSTRACT FROM AUTHOR]