【作者】 徐玲；

【导师】 徐保国；

【作者基本信息】 江南大学 ， 控制理论与控制工程， 2015， 博士

【摘要】 传递函数在经典控制理论中具有很重要的地位.经典的PID控制算法大多基于系统的传递函数模型.现存统计辨识方法大多基于系统的离散时间模型.论文首次将统计辨识方法中的非线性优化原理用于研究连续时间系统传递函数参数估计问题,提出了“传递函数参数估计方法”研究课题,选题具有理论意义和实用价值.论文的主要工作如下.1.线性动态系统的传递函数是一个有理分式函数,其分子和分母多项式的系数定义为系统参数.众所周知:系统的脉冲响应和阶跃响应都是关于系统参数和时间的高度非线性函数.论文首先针对一般非线性函数的滚动优化问题,使用递推辨识思想,提出了基于梯度搜索和基于牛顿搜索的递推参数估计方案.利用系统脉冲(阶跃)响应输出的离散观测数据,推导了传递函数的梯度递推参数估计方法、多新息随机梯度参数估计方法和动态数据长度下的牛顿递推参数估计方法,进一步为了减小计算量,提高算法的稳定性,推导了基于分解的牛顿递推参数估计方法.2.针对有限数据长度的一般非线性函数优化问题,使用迭代辨识原理,提出了基于梯度搜索和基于牛顿搜索的迭代参数估计方案.利用系统脉冲和(或)阶跃响应输出的离散观测数据,推导了传递函数的有限数据梯度迭代参数估计方法和牛顿迭代参数估计方法,以及滑动数据窗梯度迭代参数估计方法;基于递阶辨识原理,提出了基于分解的牛顿迭代参数估计方法.对牛顿迭代方法中海赛矩阵求逆引起稳定性差的问题,采取了增加步长因子、修正海赛矩阵的措施,提高了牛顿算法的稳定性.基于拟牛顿思想,进一步推导了高斯–牛顿迭代参数估计方法和变尺度迭代参数估计方法,仿真结果表明提出的方法减小了算法的计算量,提高了算法的稳定性.3.前述方法是在脉冲输入和(或)阶跃输入信号激励下,研究了传递函数参数的递推估计方法和迭代估计方法.在此基础上,论文研究传递函数在正弦激励信号下的频率响应参数估计方法.采用从简单到复杂的研究思路,从单频率的正弦信号,到双频率正弦信号,再到多频率正弦组合信号,研究了正弦信号激励下的传递函数参数可辨识性问题,即传递函数参数数目与信号频率数之间的关系.针对单一频率和多频率正弦组合信号特征参数估计问题,提出了代数求解参数估计算法、最小二乘参数估计算法,梯度迭代参数估计算法.进一步,在单一频率及多频率正弦组合信号激励下,研究和提出了传递函数频率响应的代数求解参数估计算法、最小二乘参数估计算法,梯度迭代参数估计算法、高斯-牛顿迭代参数估计以及阻尼迭代参数估计方法.仿真例子和比较分析结果表明,提出的频率响应辨识方法能有效地估计传递函数的参数.更多还原

【Abstract】 Transfer functions play an important role in the classical control theory. The classical PID control algorithm is based on the transfer function model of systems. The existing statistical identi?cation methods are based on the discrete-time model of systems. In this paper, the nonlinear optimization principles of statistical identi?cation methods are used to study the parameter estimation of transfer functions for continuous-time systems. The study subject has theoretical signi?cance and practical value. The main works of this paper are as follows.1. The transfer functions of linear dynamical systems are rational fraction functions.The coe?cients of the numerator and denominator polynomial of the transfer functions are de?ned as the system parameters. It is well known that the impulse response and the step response of systems are highly nonlinear functions with respect to the system parameters and time. In terms of the rolling optimization problem of the nonlinear function, this paper proposes a recursive parameter estimation scheme based on the gradient search and the Newton search utilizing the recursive identi?cation idea. Using the discrete observation data by the pulse or step response test, this paper derives the stochastic gradient algorithm, the multi-innovation stochastic gradient algorithm and the Newton recursive algorithm in the condition of the dynamical datum length. Furthermore, in order to reduce the computation load and enhance the stability of the algorithm, the Newton recursive algorithm based on decomposition is deduced.2. In terms of the optimization problem of the general nonlinear function for the measured datum of ?nite length, the iterative parameter estimation schemes based on gradient search and Newton search are proposed according to the iterative principle. Using the discrete observation data based system the pulse or step responses, this paper derives the iterative parameter estimation methods based gradient and the Newton iterative parameter estimation method of the ?nite data. Meanwhile, the iterative parameter estimation method based gradient of sliding datum window. Furthermore, based on the hierarchical identi?cation principle, the Newton iterative parameter estimation method based on decomposition is proposed for the aim of reducing the computation load. In order to improve the stability of the Newton algorithm, this paper presents some modi?ed measures by adding step size or modi?ed factors. Moreover, according to the quasi-Newton idea,the Gauss-Newton algorithm parameter estimation algorithm and the Davidon-FletcherPowell parameter estimation algorithm are proposed for improving the stability of the Newton algorithms. The simulation results show that the proposed method can reduce the computation load and improve the stability of algorithms.3. The above-mentioned parameter estimation algorithms are based on the impulse or step signal excitation. On this basis, the paper studies the parameter estimation method of transfer functions under the sinusoidal excitation signal. From simple to complex, by applying the single frequency sine excitation signal, the double different frequency sine excitation signal and multi-frequency combination sine excitation signal, this paper studies the problem of parameter identi?ability, i.e., the relationship between the parameter number and the signal frequency number. For the characteristic parameter estimation problem of the sine excitation signals, this paper proposes the algebraic solution parameter estimation method, the least square parameter estimation algorithm and the algorithm based gradient. Furthermore, this paper proposes the algebraic solution parameter estimation method, the least square parameter estimation algorithm, the parameter estimation algorithm based gradient iteration, the Gauss-Newton parameter estimation algorithm and the damping iterative parameter estimation method for the parameter estimation of transfer function using the frequency responses. The results of the simulation examples and the comparison analysis show that the proposed methods can estimate the parameters of transfer functions effectively.更多还原