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针对控制系统增益手工优化方法效率低且稳定裕度无法保证的问题,提出了一种双回路增益优化方法。将增益优化视为系统增益与频域稳定裕度之间的非线性最优化问题,基于频域稳定裕度指标构造目标函数,并采用广义拉格朗日乘子法将有约束的非线性最优化问题转化为无约束最优化问题。外回路通过罚因子和拉格朗日乘子逐步迭代来调整目标函数,内回路则基于单纯形算法直接求解无约束最优化问题,搜索控制系统增益最优解。仿真结果表明,该算法可有效改善控制系统的鲁棒性和稳定性,提高了传统手工增益优化方法的效率,可应用于多种研究对象,有一定的工程应用价值。
Aiming at the problem that the manual optimization method of gain of the control system is inefficient and the stability margin can not be guaranteed, a double-loop gain optimization method is proposed. The gain optimization is regarded as the nonlinear optimization problem between the system gain and the frequency stability margin. The objective function is constructed based on the stability index in the frequency domain, and the generalized Lagrangian multiplier method is used to combine the constrained nonlinearity Optimization problem into unconstrained optimization problem. The outer loop adjusts the objective function by iteratively using the penalty factor and the Lagrange multiplier. The inner loop directly solves the unconstrained optimization problem based on the simplex algorithm, and searches for the optimal gain of the control system. The simulation results show that this algorithm can effectively improve the robustness and stability of the control system and improve the efficiency of the traditional manual gain optimization method. It can be applied to a variety of research objects and has certain engineering application value.