Control relevant model reduction of Volterra series models

This paper presents a two-step method for control-relevant model reduction of Volterra series models. First, using the nonlinear IMC design as a basis, an explicit expression relating the closed-loop performance to the open-loop modeling error is obtained. Secondly, an optimization problem that seeks to minimize the closed-loop error subject to the restriction of a reduced-order model is posed. By showing that model reduction of kernels with different degrees can be decoupled in the problem formulation, the optimization problem is simplified into a mathematically more convenient form which can be solved with significantly less computational effort. The effectiveness of the proposed method is illustrated on a polymerization reactor example where a second-order Volterra model with 85 parameters is reduced to a Hammerstein model with 3 parameters. Despite the lower ‘open-loop’ predictive ability of the control-relevant model, the closed-loop performance of the reduced-order control system closely mimics that of the full order model.     

Control-relevant prefiltering: a systematic design approach andcase study

The authors examine the use of control-relevant prefiltering applied to parameter estimation using prediction-error methods. The prefiltering step ensures that the estimated model retains those plant characteristics that are most significant with regards to the user's control requirements. They describe how to systematically build the prefilter in terms of the estimated model structure, the desired closed-loop speed-of-response, and the setpoint/disturbance characteristics of the control problem. Two implementation algorithms are presented which are applied to the plant data obtained from a distillation column. The results show that substantial improvements are obtained from control-relevant prefiltering in output error and partial least-squares estimation, while some caution must be exercised when applied to FIR and low-order ARX estimation     

Least costly closed-loop performance diagnosis and plant re-identification

The inherent time-varying nature of dynamics in chemical processes often limits the lifetime performance of model-based control systems, as the plant and disturbance dynamics change over time. A critical step in the maintenance of model-based controllers is distinguishing control-relevant plant changes from variations in disturbance characteristics. In this paper, prediction error identification is used to evaluate a hypothesis test that detects if the performance drop arises from control-relevant plant changes. The decision rule is assessed by verifying whether an identified model of the true plant lies outside the set of all plant models that lead to adequate closed-loop performance. A unified experiment design framework is presented in the least costly context (i.e., least intrusion of nominal plant operation) to address the problem of input signal design for performance diagnosis and plant re-identification when the performance drop is due to plant changes. The application of the presented performance diagnosis approach to a (nonlinear) chemical reactor demonstrates the effectiveness of the approach in detecting the cause of an observed closed-loop performance drop based on the designed least costly diagnosis experiment.     

Practical application of model identification based on ARX models with transfer functions

A novel model identification methodology for ARX models based on transfer functions has been proposed. The identification approach converts transfer functions to ARX models with no approximation, except zero-order hold. Model parameters of the transfer functions are estimated directly. Model identification for process controls, especially MPCs, is of great importance for achieving the highest performance from them. However, step testing for model identification is a time-consuming task. Model identification techniques are necessary to save time for step tests. Therefore, a closed-loop identification method of multivariable systems is useful and helpful for time-saving. Herein, the proposed method, with control by model predictive controllers, is suited for a closed-loop identification technique and is applied in an industrial chemical plant.     

基于Volterra泛函级数的涡轮建模研究

给出了对非线性动态系统做任意精度逼近的Volterra级数高阶核的全新估算方法并将其应用在涡喷发动机的转速控制上。该方法在核函数理论基础上,构造线性空间,将求解Volterra级数各阶核的问题转化为求输出观测向量在希尔伯特空间中某一子空间上的投影的问题,使原本复杂的非线性系统的Volterra级数的逼近问题在线性空间中以向量内积的方式得到解决。与其他时域或频域估算Volterra核的方法相比较,该算法的优点在于理论体系严密、计算量不随阶数增高而成几何级数增加、辨识精度高。该方法理论上能够估算任意阶核,弥补了现有方法难以估算四阶以上核的缺点,可应用于动态系统和强非线性系统的建模。将发动机动态过程描述为四阶的Volterra级数模型。     

一类非线性系统的最小方差性能评估策略/

针对线性控制回路性能评估会因非线性因素的引入而出现过估计的问题,提出一种性能评估方法.通过计算输出信号的双相干系数对回路的非线性特征进行提前判断,然后使用Volterra级数将其最小方差性能评估问题转化为一类模型辨识问题.通过仿真实例,将所得结果和线性性能评估方法进行比较,比较结果验证了所提出算法的优越性.     

非线性系统的参数空间分割辨识方法

本文提出了一种新的非线性系统Volterra级数模型辨识方法,为非线性系统辨识中 的“维数灾难”问题提供了一种满意的解决．算法中参数空间分割和模型辨识同时完成,降 维依据采用输出拟合结果的均方误差,最终得到输出拟合均方误差意义上的准最优解．本算 法也可以作为非线性系统模型的结构辨识算法,并可以直接推广应用于其它很大一类非线性 系统模型．仿真试验结果表明,算法计算量小,精度高,并具有较好的稳定性,可以应用于 在线实时辨识．     

基于Volterra级数模型的非线性系统自适应控制稳定性研究

研究一类单输入单输出非线性系统的自适应控制问题, 这类系统能用有限阶离散Volterra级数模型表示. 采用递推最小二乘算法进行参数估计, 并通过解高次方程得到控制律. 结合反馈型Volterra级数系统的局部L稳定理论, 证明了算法的局部收敛性质. 通过对一个化工连续搅拌反应器 (CSTR)的过程控制进一步验证了该算法的有效性.     

Volterra filter modeling of nonlinear discrete-time system using improved particle swarm optimization

This paper focuses on the identification problem of nonlinear discrete-time systems using Volterra filter series model. Generally, to update the kernels of Volterra model, the most commonly used method is the gradient adaptive algorithm. However, this method probably traps at the local minimum for searching parameter solutions. In this study, a new intelligence swarm computation of the global search is considered. We utilize an improved particle swarm optimization (IPSO) algorithm to design the Volterra kernel parameters. It is somewhat different from the original algorithm due to modifying its velocity updating formula and this can promote the algorithm?s searching ability for solving the optimization problem. Using the IPSO algorithm to minimize the mean square error (MSE) between the actual output and model output, the identification problem for nonlinear discrete-time systems can be fulfilled. Finally, two different kinds of examples are provided to demonstrate the efficiency of the proposed method. Moreover, some examinations including the Volterra model memory size and algorithm initial condition are further considered.