Abstract:  In order to improve the speed and accuracy of PID control parameter optimization and guarantee the global optimum solution, an improved dynamic mutation differential evolution (DMDE) algorithm is proposed. The DMDE algorithm employs the random mutation and dynamic population, and increases the learning probability of the elite individual, to improve the speed and accuracy of optimization. Furthermore, the DMDE algorithm is used to find out the optimum solution of PID control for five types of common industrial plant models under seven types of integral performance indices of errors. The results of simulations and sensitivity analysis of the optimal control system indicate that the DMDE algorithm has better performance than the normal DE algorithm, and is more suitable to evaluate the system stability and speediness by the criterions of integrated time absolute error (ITAE), integrated root absolute error (IRAE) and developed integrated time absolute error (DITAE).

Key words: Optimal control, differential evolution, dynamic mutation, integral of error, sensitivity

摘要：

为了在加快PID控制参数优化求解的同时保证解的全局性以及精度，提出一种改进的动态变异差分进化（Dynamic Mutation Differential Evolution，DMDE）算法。该算法在差分进化（Differential Evolution，DE）算法中，引入随机变异和动态种群策略，增加对精英的学习概率，提高了优化速度和精度。将改进DMDE算法应用于最优PID控制中，对5种常用工业对象模型和7种偏差积分性能指标进行优化求解。仿真实验和对系统在最优控制时灵敏度分析的结果表明，改进DMDE算法可有效提高系统性能，且采用时间乘偏差绝对值积分、偏差的绝对值平方根积分和改进的综合积分指标更有利于综合评判控制系统的稳定性和快速性。

关键词: 最优控制, 差分进化, 动态变异, 偏差积分, 灵敏度