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本文作者曾经提供在最小二乘方的误差意义下有关高阶传递函数简化成低阶传递函数的一种频率域上的简化方法。曾经也通过具有纯滞后的一阶惯性环节(或二阶振荡环节),并借助Pade近似式首先将具有纯滞后的传递函数简化;同时就以得到具有Pade近似的一阶惯性环节(或二阶振荡环节)的低阶传递函数,而在最小二乘方的误差意义下作为有关高阶传递函数的近似式。不过,上述的简化低阶传递函数所描述的系统有可能是不稳定的。本文针对这个问题,提出在最小二乘方的误差的要求下还考虑稳定性约束条件。这样一来,将频率域上模型简化问题转化成具有不等式约束的最优化问题。因此,就可借助罚函数法解决线性系统模型在频率域上简化问题,同时简化模型所描述的系统仍是稳定的。
The authors of the paper have provided a simplified method in the frequency domain of the low-order transfer function in the sense of the least squares error regarding the transfer of higher order functions to lower order transfer functions. Once again, the transfer function with pure hysteresis was first simplified by a first-order inertial link (or second-order oscillator link) with pure hysteresis, and first by Pade approximation. At the same time, a first-order inertial link with Pade approximation Oscillation), while in the sense of the least square error as the approximation of the higher order transfer function. However, the systems described for simplified lower order transfer functions above may be unstable. In this paper, we propose to consider the stability constraints under the requirement of least-square error. In this way, the problem of model simplification in frequency domain is transformed into an optimization problem with inequality constraints. Therefore, it is possible to solve the linear system model by the penalty function method to simplify the problem in the frequency domain, and to simplify the system described by the model is still stable.