In this paper, a new direct discrete approximation based internal model control design is proposed to the linear discrete dynamical systems. The approximation method is used to determine an accurate and stable reduced-order model for the considered original higher-order discrete-time system. The method involves an enhanced Differential Evolution algorithm to ascertain the stable denominator polynomial coefficients, and the preferable reduced numerator polynomial coefficients are evaluated by using the improved discrete multi-point Padé approximation approach. The method deploys on discrete step integral square error minimization between the original dynamical system and the approximated model, together with retaining their discrete impulse response energy values. The approximated model has been considered an internal (predictive) model and proceeds with an optimal internal model controller design to improve the discrete dynamical system behaviour according to the reference input/the set point. The controller's best performance is attained by tuning the single filter parameter ′λ′ by minimizing the integral square error between the reference input and the actual output of the dynamical system using the enhanced differential evolution algorithm. The acceptability and applicability of the proposed process reduction-based controller design have been validated on a single-input single-output supersonic jet engine inlet dynamical model. The controller robust study is conducted by inserting 10% disruption uncertainty in the system dynamical model poles and zeros. The method has also been extended to the discrete multi-input multi-output dynamical model of the single machine infinite bus power system to develop an optimal internal model control-based power system stabilizer. The simulation results showing better reference input tracking, comparison of performance indices, and also highlight the efficacy of the proposed controller design.

本文针对线性离散动力系统提出了一种新的基于直接离散逼近的内模控制设计方法。近似方法用于确定所考虑的原始高阶离散时间系统的准确和稳定的降阶模型。该方法包括一种改进的差分演化算法，以确定稳定的分母多项式系数，并使用改进的离散多点Padé逼近方法对优选的减小的分子多项式系数进行评估。该方法在原始动力学系统和近似模型之间的离散步长积分平方误差最小化上进行了部署，同时保留了它们的离散冲激响应能量值。近似模型已被视为内部（预测）模型，并进行了最佳内部模型控制器设计，以根据参考输入/设定点改善离散动态系统的性能。控制器的最佳性能是通过使用增强的差分演化算法通过最小化动态系统的参考输入与实际输出之间的积分平方误差来调整单个滤波器参数'λ'来实现的。所提出的基于过程简化的控制器设计的可接受性和适用性已在单输入单输出超音速喷气发动机进气动力学模型上得到验证。通过在系统动力学模型的极点和零点插入10％的干扰不确定性来进行控制器鲁棒性研究。该方法还扩展到单机无限母线电力系统的离散多输入多输出动力学模型，以开发基于最优内部模型控制的电力系统稳定器。仿真结果显示了更好的参考输入跟踪，性能指标的比较，并且还突出了所提出的控制器设计的功效。