The nature of data pre-filters in MPC relevant identification—open- and closed-loop issues

In this paper a model predictive control relevant identification (MRI) method is applied to a general class of linear PEM models and the effect of bias distribution on the multistep ahead predictions is studied. Good multistep ahead predictions are essential for model predictive controllers. Therefore, it is important to distribute the bias in such a way that it is compatible with the predictive control objective. This paper deals with the impact of MRI methods on the bias distribution and its effect on control loop performance.     

Prediction Error Based Performance Monitoring,Degradation Diagnosis and Remedies in Offset‐Free MPC: Theory and Applications

We present in this paper a control performance monitoring method for linear offset‐free model predictive control (MPC) algorithms, in which the prediction error sequence is used to detect whether the internal model and the observer are correct or not. When the prediction error is a white noise signal, revealed by the Ljung‐Box test, optimal performance is detected. Otherwise, we use a closed‐loop subspace identification approach to reveal the order of a minimal realization of the system from the deterministic input to the prediction error. When such order is zero, we prove that the model is correct and the source of suboptimal performance is an incorrect observer. In such cases, we suggest an optimization method to recalculate the correct augmented state estimator. If, instead, such order is greater than zero we prove that the model is incorrect, and re‐identification is suggested. A variant for (large‐scale) block‐structured systems is presented, in which diagnosis and corrections are performed separately in each block. Two examples of different complexity are presented to highlight effectiveness and scalability of the method.     

Probabilistic characterisation of model error using Gaussian mixture model—With application to Charpy impact energy prediction for alloy steel

A novel approach to characterise the model prediction errors using a Gaussian mixture model is proposed. The motivation for this work lies behind many data models that are developed through prediction error minimisation with the assumption of a normal noise distribution. When the noise is non-normal, which may often be the case in complicated data modelling scenarios, the model prediction errors may contain rich information, which can be further exploited for model refinement and improvement. The key contents presented in this paper include: choosing the relevant variables to form the error data, optimising the number of Gaussian components required for the error data modelling, and fitting the Gaussian mixture parameters using an expectation-maximisation algorithm. Application of the proposed method for further model improvement, within the framework of hybrid deterministic/stochastic modelling, is also discussed. Preliminary results on the real industrial Charpy impact energy data for heat-treated steels show its effectiveness for model error characterisation, and the potential for model performance improvement in terms of prediction accuracy as well as providing accurate prediction confidence intervals.     

Estimation and optimal control design of a biological wastewater treatment process

This paper deals with the on-line estimation and optimal control of a biological wastewater treatment process. The objective of the control is to force the residual substrate and the dissolved oxygen concentrations to track a given reference model despite the disturbances and system parameter uncertainties. The control law is based on one step ahead prediction of the controlled variables and minimization of an appropriate quadratic cost function. The technique is based on direct exploitation of the nonlinear model representing the wastewater treatment process and is coupled with an asymptotic estimator for on-line tracking of simultaneously unavailable states and time varying parameters. The estimated variables are used in the explicit design of the control algorithm according to certainty equivalence principle. A simulation study subject to measurement noise and abrupt jumps in the kinetic parameters shows the feasibility and robustness of the control strategy.     

基于运动预测的路径跟踪最优控制研究

针对自动导引车的路径跟踪.提出一种基于运动预测的线性二次型调节器优化模型.在速度约束下.从全局角度通过运动预测达到多步控制的最优协调性.在目标函数中只包含速度控制量,避免了加权矩阵选择的难题,算法的快速性由控制步数的最小化来保证.数字仿真和实验均表明.对于不同速度和路径偏差,该算法均能产生可实现的最优控制序列,同步、快速和平稳地消除两种偏差,且计算量小,可满足嵌入式控制系统实时滚动优化的需求.     

H∞ prediction and unconstrained H∞ predictive control: multi‐input–multi‐output case

Through the combination of the sequential spectral factorization and the coprime factorization, a k‐step ahead MIMO H_∞ (cumulative minimax) predictor is derived which is stable for the unstable noise model. This predictor and the modified internal model of the reference signal are embedded into the H_∞ optimization framework, yielding a single degree of freedom multi‐input–multi‐output H_∞ predictive controller that provides stochastic disturbance rejection and asymptotic tracking of the reference signals described by the internal model. It is shown that for a plant/disturbance model, that represents a large class of systems, the inclusion of the H_∞ predictor into the H_∞ control algorithm introduces a performance/robustness tuning knob: an increase of the prediction horizon enforces a more conservative control effort and, correspondingly, results in deterioration of the transient and the steady‐state (tracking error variance) performance, but guarantees large robustness margin, while the decrease of the prediction horizon results in a more aggressive control signal and better transient and steady‐state performance, but smaller robustness margin. Copyright © 2001 John Wiley & Sons, Ltd.     

含ARMA噪声系统模型的参数辨识方法*

实际问题中，大量的动态系统控制问题可归结为含ＭＡ，ＡＲＭＡ噪声系统模型的参数辨识问题。本文提出ＲＭＡ，ＲＡＲＭＡ两种系统模型参数辨识的一种新方法，主要手段是构造和研究特殊的辅助线性模型。理论分析和实际计算表明，本文方法较传统表度有明显提高。     

A study of frequency prediction for power systems

A frequency predictor is identified from simulated measurements of power and frequency on a power system. An on-line Ieast-squares algorithm is used along with a new system structure test for model order identification. A comparison of this system structure test with other model order identification tests is also included. The performance of the resultant predictor is then determined as a function of both the prediction interval and the sampling rate and measurement noise levels on the power and frequency measurements used for the predictor. The results indicate an increase in prediction error with the length of the prediction interval because the predictor loses its principal dependence of "P-f" (power-frequency) dynamics in the power system and depends more strongly on the random load fluctuations over the prediction interval. The modeling error was shown to be unaffected by sampling rate and by measurement noise levels below that of the present power-frequency recorder [2], but was affected by measurement noise levels above the values on the present recorder. This accuracy of the model for small prediction intervals justifies the future use of frequency measurements in power system identification and justifies the use of least-squares algorithms using these measurements. The results on sampling rate and measurement noise imply that the present recorder [2] is an "optimal" design and that the RTDAS [5] will be an even better tool for use in power system model identification.     

Identification of dynamic models in complex networks with prediction error methods—Basic methods for consistent module estimates

The problem of identifying dynamical models on the basis of measurement data is usually considered in a classical open-loop or closed-loop setting. In this paper, this problem is generalized to dynamical systems that operate in a complex interconnection structure and the objective is to consistently identify the dynamics of a particular module in the network. For a known interconnection structure it is shown that the classical prediction error methods for closed-loop identification can be generalized to provide consistent model estimates, under specified experimental circumstances. Two classes of methods considered in this paper are the direct method and the joint-IO method that rely on consistent noise models, and indirect methods that rely on external excitation signals like two-stage and IV methods. Graph theoretical tools are presented to verify the topological conditions under which the several methods lead to consistent module estimates.     

Design variables for bias distribution in transfer function estimation

Estimation of transfer functions of linear systems is one of the most common system identification problems. Several different design variables, chosen by the user for the identification procedure, affect the properties of the resulting estimate. In this paper it is investigated how the choices of prefilters, noise models, sampling interval, and prediction horizon (i.e., the use ofk-step ahead prediction methods) influence the estimate. An important aspect is thai the true system is not assumed to be exactly represented within the chosen model set. The estimate will thus be biased. It is shown how the distribution of bias in the frequency domain is governed by a weighting function, which emphasizes different frequency bands. The weighting function, in turn, is a result of the previously listed design variables. It is shown, e.g., thai the common least-squares method has a tendency to emphasize high frequencies, and that this can be counteracted by prefiltering. It is also shown that, asymptotically, it is only the prediction horizon itself, and not how it is split up into sampling interval times number of predicted sampling instants, that affects this weighting function.     

膀胱肿瘤恒温热灌注治疗模拟设备的控制实验研究

众所周知,对实际被控对象的模型辨识是进行良好控制的重要前提。本论文研究了一种开环辨识方法。被辨识的对象是膀胱恒温热灌注治疗仪模拟设备,对该对象进行了开环飞升曲线测试,根据记录的输出曲线,采用改进的面积法对被控过程的一阶惯性加时滞模型进行参数估计,得到被控对象的传递函数。然后,根据所得到的过程模型,进行PID参数整定并进行了闭环的控制试验。实验表明,此方法具有较好的辨识精度,对测量噪声不敏感,闭环控制实验也表明了该控制系统的可行性。     

Optimal Control of Fed-Batch Processes Based on Multiple Neural Networks

The performance of empirical model based fed-batch process optimal control is strongly affected by the model prediction reliability at the end-point of a batch. An optimal control profile calculated from an empirical model may not give the best performance when applied to the actual process due to model-plant mismatches. To tackle this issue, a new method for improving the reliability of fed-batch process optimal control by incorporating model prediction confidence bounds is proposed. Multiple neural networks (MNN) are used to build an empirical model of fed-batch process based on process operation data. Model prediction confidence bounds are calculated based on predictions of all component networks in an MNN model and the model prediction confidence bound at the end-point of a batch is incorporated into the optimization objective function. The modified objective function penalizes wide prediction confidence bounds in order to obtain a reliable optimal control profile. The non-linear optimization problem based on MNN with augmented objective function is solved by iterative dynamic programming. The proposed control strategy is illustrated on a simulated fed-batch ethanol fermentation process. The results demonstrate that the optimal control profile calculated from the proposed approach is reliable in the sense that its performance degradation is limited when applied to the actual process.     

Constrained minimum variance control using hybrid genetic algorithm – An industrial experience

This paper develops a method for minimum variance control of proportional–integral (PI) controllers in the presence of input stochastic noise, the abatement of which is an important issue in many control systems. The underlying objective is to mitigate the effect of input noise in the process output, subject to process inequality constraints. For this purpose, a hybrid genetic algorithm is used. It combines the genetic operations of selection, crossover, and mutation with Newton search. The developed method is applied in an industrial setting to find the optimal controller parameters of different control loops at Falconbridge Smelter in Sudbury, Canada. The optimal parameters significantly improve the performance of the PI controllers.     

A Learning‐Theoretic Approach To Model‐Set Identification

A new approach to model‐set identification is proposed based on an agnostic learning theory. The squared prediction error is estimated together with its uncertainty uniformly in some parameter region. Based on this estimation, a model set is constructed so as to include the best model. The proposed approach does not require assumptions on the true dynamics or the noise, neither does it need infinite number of input‐output data in order to justify its result. But it guarantees that the size of the identified model set converges to zero as the number of input‐output data increases. Improvement of the precision is considered on the proposed identification method. Generalization of the approach is discussed and a numerical example is presented.     

Constrained output feedback model predictive control for nonlinear systems

A constrained output feedback model predictive control approach for nonlinear systems is presented in this paper. The state variables are observed using an unscented Kalman filter, which offers some advantages over an extended Kalman filter. A nonlinear dynamic model of the system, considered in this investigation, is developed considering all possible effective elements. The model is then adaptively linearized along the prediction horizon using a state-dependent state space representation. In order to improve the performance of the control system as many linearized models as the number of prediction horizons are obtained at each sample time. The optimum results of the previous sample time are utilized for linearization at the current sample time. Subsequently, a linear quadratic objective function with constraints is formulated using the developed governing equations of the plant. The performance and effectiveness of the proposed control approach is validated both in simulation and through real-time experimentation using a constrained highly nonlinear aerodynamic test rig, a twin rotor MIMO system (TRMS).     

Achieving a More Robust Neural Network Model for Control of a MR Damper by Signal Sensitivity Analysis

Most neural network models can work accurately on their trained samples, but when encountering noise, there could be significant errors if the trained neural network is not robust enough to resist the noise. Sensitivity to perturbation in the control signal due to noise is very important for the prediction of an output signal. The goal of this paper is to provide a methodology of signal sensitivity analysis in order to enable the selection of an ideal Multi-Layer Perception (MLP) neural network model from a group of MLP models with different parameters, i.e. to get a highly accurate and robust model for control problems. This paper proposes a signal sensitivity which depends upon the variance of the output error due to noise in the input signals of a single output MLP with differentiable activation functions. On the assumption that noise arises from additive/multiplicative perturbations, the signal sensitivity of the MLP model can be easily calculated, and a method of lowering the sensitivity of the MLP model is proposed. A control system of a magnetorheological (MR) fluid damper, which is a relatively new type of device that shows the future promise for the control of vibration, is modelled by MLP. A large number of simulations on the MR damper’s MLP model show that a much better model is selected using the proposed method.     

Multi-output process identification

In model based control of multivariate processes, it has been common practice to identify a multi-input single-output (MISO) model for each output separately and then combine the individual models into a final MIMO model. If models for all outputs are independently parameterized then this approach is optimal. However, if there are common or correlated parameters among models for different output variables and/or correlated noise, then performing identification on all outputs simultaneously can lead to better and more robust models. In this paper, theoretical justifications for using multi-output identification for a multivariate process are presented and the potential benefits from using them are investigated via simulations on two process examples: a quality control example and an extractive distillation column. The identification of both the parsimonious transfer function models using multivariate prediction error methods, and of non-parsimonious finite impulse response (FIR) models using multivariate statistical regression methods such as partial least squares (PLS2), canonical correlation regression (CCR) and reduced rank regression (RRR) are considered. The multi-output identification results are compared to traditional single-output identification from several points of view: best predictions, closeness of the model to the true process, the precision of the identified models in frequency domain, stability robustness of the resulting model based control system, and multivariate control performance. The multi-output identification methods are shown to be superior to the single-output methods on the basis of almost all the criteria. Improvements in the prediction of individual outputs and in the closeness of the model to the true process are only marginal. The major benefits are in the stability and performance robustness of controllers based on the identified models. In this sense the multi-output identification methods are more ‘control relevant’.     

Variable Structure Control with chattering elimination and guaranteed stability for a generalized T-S model

In this paper, a fuzzy based Variable Structure Control (VSC) with guaranteed stability is presented. The main objective is to obtain an improved performance of highly non-linear unstable systems. The main contribution of this work is that, firstly, new functions for chattering reduction and error convergence without sacrificing invariant properties are proposed, which is considered the main drawback of the VSC control. Secondly, the global stability of the controlled system is guaranteed.The well known weighting parameters approach, is used in this paper to optimize local and global approximation and modeling capability of T-S fuzzy model.A one link robot is chosen as a nonlinear unstable system to evaluate the robustness, effectiveness and remarkable performance of optimization approach and the high accuracy obtained in approximating nonlinear systems in comparison with the original T-S model. Simulation results indicate the potential and generality of the algorithm. The application of the proposed FLC-VSC shows that both alleviation of chattering and robust performance are achieved with the proposed FLC-VSC controller. The effectiveness of the proposed controller is proven infront of disturbances and noise effects.     

A comparison of adaptive control strategies for hot steel strip rolling mills

Many modeling situations occur in which the plant has uncertain dynamics, nonlinearities, time varying characteristics and noise corrupted input and output measurements. These processes generally require a human operator whose function is to provide intelligent modeling and control. This exact situation occurs in the modeling and control of roll force in a hot steel rolling mill. It is the purpose of this paper to investigate and compare various adaptive control strategies for this problem.The first strategy uses a parameter identification technique to track the parameters in the roll force setup model from one steel run to the next. The next algorithm provides feedback control from run to run by an adaptive controller which uses a linear reinforcement learning scheme to adjust its parameters. The third method accounts for the above complexities by approaching the problem from a behavioral and structural point of view. The behavior of the model is assessed through a performance evaluator and the model is modified structurally and parametrically to improve the performance of the system as the process evolves. The derivation is based on correlation techniques and linear reinforcement learning theory, the latter of which provides memory and intelligence to the algorithm to model the decision process of the human operator. The results of this work serve to reinforce the opinion that the nonlinear mathematical structure of the model should be able to change from one steel run to the next in order to compensate for changes in mill characteristics and in the mill environment. Modeling results are presented from actual mill data and comparisons are made with time invariant models. In addition, the algorithms are general enough so that they may be easily applied to other processes that seem to defy traditional modeling techniques. They are not case dependent.     

Variable Structure Control with Chattering Reduction of a Generalized T‐S Model

In this paper, a fuzzy logic controller (FLC) based variable structure control (VSC) is presented. The main objective is to obtain an improved performance of highly non‐linear unstable systems. New functions for chattering reduction and error convergence without sacrificing invariant properties are proposed. The main feature of the proposed method is that the switching function is added as an additional fuzzy variable and will be introduced in the premise part of the fuzzy rules; together with the state variables. In this work, a tuning of the well known weighting parameters approach is proposed to optimize local and global approximation and modelling capability of the Takagi‐Sugeno (T‐S) fuzzy model to improve the choice of the performance index and minimize it. The main problem encountered is that the T‐S identification method can not be applied when the membership functions are overlapped by pairs. This in turn restricts the application of the T‐S method because this type of membership function has been widely used in control applications. The approach developed here can be considered as a generalized version of the T‐S method. An inverted pendulum mounted on a cart is chosen to evaluate the robustness, effectiveness, accuracy and remarkable performance of the proposed estimation approach in comparison with the original T‐S model. Simulation results indicate the potential, simplicity and generality of the estimation method and the robustness of the chattering reduction algorithm. In this paper, we prove that the proposed estimation algorithm converge the very fast, thereby making it very practical to use. The application of the proposed FLC‐VSC shows that both alleviation of chattering and robust performance are achieved.