Prediction Error Identification Methods Research Articles

Power System Oscillation Monitoring and Damping Control Redesign under Ambient Conditions and Multiple Operating Points

Using prediction-error identification methods, this paper proposes a measurement data-driven approach to monitor power system oscillations at a power plant, identify a data-based model using an input signal and redesign the plant’s power system stabilizer damping controller to mitigate the observed oscillations under ambient conditions and multiple operating points. The advantage of the proposed methodology is that the damping performance can be monitored continuously and the redesign only requires measurements at the power plant along with the controllers structure, which are known by the power plant operator.

Identification of Diffusively Coupled Linear Networks Through Structured Polynomial Models

Physical dynamic networks most commonly consist of interconnections of physical components that can be described by diffusive couplings. These diffusive couplings imply that the cause-effect relationships in the interconnections are symmetric and therefore physical dynamic networks can be represented by undirected graphs. This paper shows how prediction error identification methods developed for linear time-invariant systems in polynomial form can be configured to consistently identify the parameters and the interconnection structure of diffusively coupled networks. Further, a multi-step least squares convex optimization algorithm is developed to solve the nonconvex optimization problem that results from the identification method.

Prediction Error Identification Method for Continuous-time Systems Having Multiple Unknown Time Delays

This paper shows a continuous-time prediction error method for the identification of Multiple Input Single Output (MISO) Continuous-Time (CT) systems with multiple unknown time delays. The proposed algorithm entails the simultaneous estimation of both process parameters and multiple unknown time delays. Indeed, it minimizes the prediction error using the Levenberg-Marquardt (LM) optimization method with derivatives of the objective function with respect to the parameters including the multiple unknown time delays. An analysis is then presented which proves the convergence of the algorithm, and robustness issues are discussed as well. Finally, to verify the analysis and to demonstrate the feasibility of the algorithm, we present some of the simulation results which were carried out.

Some remarks on the bias distribution analysis of discrete-time identification algorithms based on pseudo-linear regressions

In 1998, A. Karimi and I.D. Landau published in this journal an article entitled “Comparison of the closed-loop identication methods in terms of bias distribution”. One of its main purposes was to provide a bias distribution analysis in the frequency domain of closed-loop output error identication algorithms that had been recently developed. The expressions provided in that paper are only valid for prediction error identification methods (PEM), not for pseudo-linear regression (PLR) ones, for which we give the correct frequency domain bias analysis, both in open- and closed-loop. Although PLR was initially (and is still) considered as an approximation of PEM, we show that it gives better results at high frequencies.

Robust Nonlinear Regulation: Continuous-Time Internal Models and Hybrid Identifiers

The paper deals with the problem of robust output regulation for minimum-phase nonlinear systems in a semiglobal setting. We present a different perspective to the problem of adaptive regulation in which prediction error identification methods, which are routinely used in other control contexts, can be adopted to design robust nonlinear regulators. The proposed control structure combines continuous-time dynamics and “hybrid identifiers”, the latter specifically designed to estimate the actual steady state control law. Besides presenting the main idea and a general framework, the paper addresses the specific case in which a linear regression law is used as model structure for the steady state control law and a least square optimization criterion is adopted as estimation method. The proposed framework encompasses existing frameworks proposed so far in the nonlinear continuous-time literature.

Identification of dynamic networks with rank-reduced process noise

In dynamic network identification usually the assumption is made that there is a full rank process noise affecting the network. For large scale networks with many variables this assumption is not realistic as the noise could be generated by a limited number of sources. We extend prediction error identification methods by allowing rank-reduced process noise in the network. The developed method is based on a modification of the typical predictor expression and an appropriate modification of the identification criterion. It is shown that this method leads to consistent estimates, and we provide a method to reduce the variance of the estimates, which is confirmed by simulations.

Convergence analysis for recursive Hammerstein identification

This paper derives a recursive prediction error identification method based on the Hammerstein model structure. The convergence properties of the algorithm are analysed by application of Ljung’s associated differential equation method. It is proved that the algorithm can only converge to stable stationary points of the associated ordinary differential equation. General conditions for local convergence to the true parameter vector are given, and the cases with piecewise linear and polynomial nonlinearities are treated in detail. The derived identification method is illustrated in a numerical study that treats identification of a subsystem of a cement mill.

Comparison of subspace and prediction error methods of system identification for cement grinding process

Maintaining product quality in cement grinding process in the presence of clinker heterogeneity is a challenging task. Model predictive controllers (MPC) are argued to be one possible solution to handle the variability, and the lack of models that relates clinker heterogeneity with product quality makes the MPC design challenging. This investigation addresses the suitability of two data-driven modelling approaches for cement grinding process-prediction error and subspace identification methods. Data collected from cement grinding process is used to build the model of the same. The collected data is used to build different candidate state-space models using the prediction error and subspace identification methods. The candidate models were validated using Akaike's information criterion and mean square error to study the suitability of these modelling techniques. The validation tests are used to identify the most suitable candidate models for the prediction error and subspace methods. The models developed in this investigation are inputs to design predictive controllers for cement industries and assure product quality in the presence of clinker grindability variations.

Errors-in-variables identification in dynamic networks — Consistency results for an instrumental variable approach

In this paper we consider the identification of a linear module that is embedded in a dynamic network using noisy measurements of the internal variables of the network. This is an extension of the errors-in-variables (EIV) identification framework to the case of dynamic networks. The consequence of measuring the variables with sensor noise is that some prediction error identification methods no longer result in consistent estimates. The method developed in this paper is based on a combination of the instrumental variable philosophy and closed-loop prediction error identification methods, and leads to consistent estimates of modules in a dynamic network. We consider a flexible choice of which internal variables need to be measured in order to identify the module of interest. This allows for a flexible sensor placement scheme. We also present a method that can be used to validate the identified model.

Errors-in-Variables Identification in Dynamic Networks by an Instrumental Variable Approach

In this paper, the objective is to obtain an estimate of a particular module embedded in a dynamic network using noisy measurements of the internal variables. This is an extension of the errors-in-variables (EIV) framework to the case of dynamic networks. The consequence of measuring the variables with noise is that the prediction error identification methods no longer result in consistent estimates. The method proposed in this paper is based on a combination of the instrumental variable approach and closed-loop prediction-error identification methods.

Identification and modeling of the three rotational movements of a miniature coaxial helicopter

This paper presents the identification of a miniature coaxial helicopter system. First, the helicopter flying principles are described and the hardware setup of the developed platform is presented. Further, linear models are developed for the movements of the helicopter using prediction error identification methods. The results in this case are accurate and can be used for performant controller design in some operating points. But in order to model the complete dynamics of the helicopter, nonlinear models are developed using recurrent dynamic neural networks. In this case the models obtained present a higher accuracy compared with the linear case and also with the results published until now. In the end, the advantages of nonlinear modeling based on neural networks is emphasized and some conclusions are drawn.

A study of bicycle dynamics via system identification approaches

This study investigates bicycle dynamic properties by using system identification approaches. The non-linear bicycle model with configuration parameters from a previously developed benchmark model is studied. The roll angle of the bicycle is controlled at different speeds to generate input–output data including steering torque, roll, and steering angles. The collected data are then used to identify the one-input two-output linear model by a prediction-error identification method using parameterization in canonical state-space form derived as Whipple's model. Simulations are used to verify the accuracy of the generated linear model. Numerous properties for various speed ranges are discussed from the pole and zero locations of the identified linear model. The system stability, limit-cycle phase portraits of the roll and steering angles, and the non-minimum phase property of the non-linear system are further investigated and compared with the corresponding linearized results from previous studies in the literature.

Path Tracking Control of a Motorcycle Based on System Identification

This study investigates the roll angle tracking and path tracking controls of a motorcycle. For the control design, a required linear model is obtained from the system identification method. The roll angle is controlled at a specific speed via a simple PID controller to generate input-output data, including steering torque, as well as roll and steering angles. The collected data are then used to identify a one-input two-output linear model by a prediction error identification method using parameterization in a canonical state-space form derived as a Whipple model. With the obtained linear model, full-state feedback (FSF) is designed for roll angle tracking control. Simulations and comparisons with a PID controller show that this FSF is robust against changes in speed as well as external disturbances. On the basis of the roll angle tracking controller, a path tracking controller by path preview is developed with consideration of disturbance rejection. The simulations show the effectiveness of the proposed control scheme.

Sliding-mode control for the roll-angle tracking of an unmanned bicycle

This study investigates the roll-angle tracking control of an unmanned bicycle using a sliding-mode controller (SMC). The roll angle is controlled at a specific speed via a simple proportional, derivative (PD) controller to generate input–output data including steering torque as well as roll and steering angles. The collected data are then used to identify a one-input two-output linear model by a prediction-error identification method using parameterisation in a canonical state-space form derived as a Whipple model. Once the linear model is obtained, the SMC can be designed to control the bicycle. Simulations and comparisons with a proportional, integral, derivative (PID) controller show that this SMC is robust against changes and variations in speed as well as external disturbances.

Multivariable identification and controller design of an integrated flight control system

This paper investigates the multivariable identification and controller design for the longitudinal channel of a Boeing 747 transport. The transfer function matrix of the system is identified using the prediction error (PE) identification method with multivariable ARX model. An ellipsoidal parametric uncertainty set is constructed from the covariance matrix of the identified parameters. It contains the parameters of actual system at a certain probability level. The identified models and the associated uncertainty sets are validated by measuring the worst-case ν-gap and then compared with the maximum value of the generalized stability margin. In automatic flight control system or autopilots, multiple specifications criteria are needed to be satisfied concurrently, such as good holding (small static altitude holding error), fast response, smooth transition (less oscillation, overshoot). The design of a Multiple Simultaneous Specifications (MSS) controller effectively and practically is a very significant and challenging job. Liu and Mills [H.H.T. Liu, J.K. Mills, Multiple specification design in flight control system, in: Proceedings of the American Control Conference, Chicago, Illinois, 2000, pp. 1365–1369] proposed a MSS controller design method using a convex combination approach. In this paper, we apply the method [H.H.T. Liu, J.K. Mills, Multiple specification design in flight control system, in: Proceedings of the American Control Conference, Chicago, Illinois, 2000, pp. 1365–1369; H.H.T. Liu, Design combination in integrated flight control, in: Proceedings of the American Control Conference, Arlington, Virginia, 2001, pp. 494–499; H.H.T. Liu, Multi-objective design for an integrated flight control system: a combination with model reduction approach, in: Proceedings of IEEE International Symposium on Computer Aided Control System Design, Glasgow, 2002, pp. 21–26] to design a MSS controller based on the identified models of the Boeing 747 transport aircraft longitudinal channel. The controllers are also validated by simulation using the true plant transfer functions.

When are two multivariate random processes indistinguishable

Prediction error identification methods have been recently the objects of much study, and have wide applicability. The maximum likelihood (ML) identification methods for Gaussian models and the least squares prediction error method (LSPE) are special cases of the general approach. In this paper, we investigate conditions for distinguishability or identifiability of multivariate random processes, for both continuous and discrete observation time T. We consider stationary stochastic processes, for the ML and LSPE methods, and for large observation interval T, we resolve the identifiability question. Our analysis begins by considering stationary autoregressive moving average models, but the conclusions apply for general stationary, stable vector models. The limiting value for T → ∞ of the criterion function is evaluated, and it is viewed as a distance measure in the parameter space of the model. The main new result of this paper is to specify the equivalence classes of stationary models that achieve the global minimization of the above distance measure, and hence to determine precisely the classes of models that are not identifiable from each other. The new conclusions are useful for parameterizing multivariate stationary models in system identification problems. Relationships to previously discovered identifiability conditions are discussed.

Combined Deterministic−Stochastic Approach for Pharmacokinetic Modeling

We develop a systematic methodology for pharmacokinetic (PK) modeling to predict drug exposure profiles accurately. First, the number of compartments is determined by inspecting the singular values of an augmented matrix composed of the bolus (or impulse) drug response in the central compartment. The prediction error identification method is then applied to estimate model parameters based on the proposed deterministic−stochastic model structure in which stochastic dynamics and various dosing strategies as well as physiological delays are incorporated simultaneously. The deterministic part of the model is represented by a physical continuous-time compartmental model, whereas the stochastic part is a discrete-time empirical finite impulse response form. Three examples demonstrate that the proposed modeling strategy not only provides a good criterion to determine the appropriate compartment number but also describes well-combined deterministic−stochastic dynamics of the PK system with optimally estimated model parameters.

Modeling and Control of Thermal Microsystems

Abstract A thermal microsystem is developed which consists of a microreactor integrated with a platinum sensor/heater, and automation equipment/software such as data acquisition system, control program and graphic user interface. From the control point of view, we analyze the dynamic characteristics of the fabricated microreactor and find some interesting dynamic features. On the basis of the analysis, we suggest an appropriate model structure and estimate the model parameters using the prediction error identification method. Requirements for a high-performance operation are discussed and a nonlinear control strategy is proposed to Iinearize the non linear dynamics of the thermal microsystem. We determine the parameters of the non linear controller using the optimal tuning method. The developed thermal microsystem shows much better control performances compared to commercial polymerase chain reaction (PCR) thermal cyclers. We successfully demonstrate the PCR of plasmid DNA using the thermal microsystem.

Modeling and Control of a Microthermal Cycler for DNA Polymerase Chain Reaction

We have developed a microthermal cycler composed of a microreactor integrated with a platinum sensor/heater and automation equipment/software such as a data acquisition system, a control program, and a graphical user interface. From the control point of view, we have analyzed the dynamic characteristics of the fabricated microreactor and found some interesting dynamic features. On the basis of the analysis, we suggest an appropriate model structure and estimate the model parameters using the prediction error identification method. Requirements for high-performance operation are discussed, and a nonlinear control strategy is proposed to linearize the nonlinear dynamics of the microthermal cycler. We determine the parameters of the nonlinear controller using the optimal tuning method. The developed microthermal cycler shows excellent control performances and performs a successful DNA polymerase chain reaction.

Prediction Error Identification Method for Continuous-Time Processes with Time Delay

We propose a continuous-time prediction error identification method to identify combined deterministic−stochastic continuous-time processes with time delay. It minimizes the prediction error using the Levenberg−Marquardt optimization method with exact derivatives of the objective function with respect to the adjustable parameters that include the time delay. Compared with previous discrete-time identification methods, the proposed method does not suffer from a small sampling time problem. Also, while previous continuous-time approaches using transforms cannot treat a large sampling time, the proposed method can incorporate directly both small and large sampling times as well as irregular sampling time. It can determine the time delay systematically; meanwhile, previous methods use ad hoc approaches. We derive the error covariance matrix and justify the small sampling problem of discrete-time identification methods.