实际控制器的输出信号是有界信号,即控制器输出饱和问题.针对控制器输出饱和问题,本文提出了低阶被控过程含延迟的一种饱和最优PID控制器设计方法.将控制误差及1阶、2阶、3阶微分项,及它们的混合项作为优化性能指标,建立了含有状态约束、稳定性及代数约束的非线性最优控制问题.应用共同李亚普诺夫函数定理与李亚普诺夫定理,约束最优控制问题被转化为非线性约束最优化问题,通过求解相应的非线性约束最优化问题,可获得饱和最优PID控制器参数.仿真结果表明了设计方法的可行性和有效性. The output signal of the actual controller is a bounded signal, that is, the controller output saturation problem.Aiming at the controller output saturation problem, this paper presents a design method of a saturated optimal PID controller with low-order controlled process delay.The control error And the first order, the second order, the third order differential terms, and their mixed terms as the optimal performance index, a nonlinear optimal control problem with state constraints, stability and algebraic constraints is established. By using the common Lyapunov function theorem and Li Yapu Knove theorem, the constrained optimal control problem is transformed into a non-linear constrained optimization problem, and the parameters of saturated optimal PID controller can be obtained by solving the corresponding nonlinear constrained optimization problem. The simulation results show that the design method is feasible and Effectiveness.