Control-Relevant System Identification using Nonlinear Volterra and Volterra-Laguerre Models

One of the key impediments to the wide-spread use of nonlinear control in industry is the availability of suitable nonlinear models. Empirical models, which are obtained from only the process input-output data, present a convenient alternative to the more involved fundamental models. An important advantage of the empirical models is that their structure can be chosen so as to facilitate the controller design problem. Many of the widely used empirical model structures are linear, and in some cases this basic model formulation may not be able to adequately capture the nonlinear process dynamics. One of the commonly used nonlinear dynamic empirical model structures is the Volterra model, and this work develops a systematic approach to the identification of third-order Volterra and Volterra-Laguerre models from process input-output data.First, plant-friendly input sequences are designed that exploit the Volterra model structure and use the prediction error variance (PEV) expression as a metric of model fidelity. Second, explicit estimator equations are derived for the linear, nonlinear diagonal, and higher-order sub-diagonal kernels using the tailored input sequences. Improvements in the sequence design are also presented which lead to a significant reduction in the amount of data required for identification. Finally, the third-order off-diagonal kernels are estimated using a cross-correlation approach. As an application of this technique, an isothermal polymerization reactor case study is considered.In order to overcome the noise sensitivity and highly parameterized nature of Volterra models, they are projected onto an orthonormal Laguerre basis. Two important variables that need to be selected for the projection are the Laguerre pole and the number of Laguerre filters. The Akaike Information Criterion (AIC) is used as a criterion to determine projected model quality. AIC includes contributions from both model size and model quality, with the latter characterized by the sum-squared error between the Volterra and the Volterra-Laguerre model outputs. Reduced Volterra-Laguerre models were also identified, and the control-relevance of identified Volterra-Laguerre models was evaluated in closed-loop using the model predictive control framework. Thus, this work presents a complete treatment of the problem of identifying nonlinear control-relevant Volterra and Volterra-Laguerre models from input-output data

Modified Volterra model-based non-linear model predictive control of IC engines with real-time simulations

Modelling of non-linear dynamics of an air manifold and fuel injection in an internal combustion (IC) engine is investigated in this paper using the Volterra series model. Volterra model-based non-linear model predictive control (NMPC) is then developed to regulate the air–fuel ratio (AFR) at the stoichiometric value. Due to the significant difference between the time constants of the air manifold dynamics and fuel injection dynamics, the traditional Volterra model is unable to achieve a proper compromise between model accuracy and complexity. A novel method is therefore developed in this paper by using different sampling periods, to reduce the input terms significantly while maintaining the accuracy of the model. The developed NMPC system is applied to a widely used IC engine benchmark, the mean value engine model. The performance of the controlled engine under real-time simulation in the environment of dSPACE was evaluated. The simulation results show a significant improvement of the controlled performance compared with a feed-forward plus PI feedback control

Enhanced MPC for Omnidirectional Robot Motion Tracking Using Laguerre Functions and Non-Iterative Linearization

To cope with the computational complexity of the traditional model predictive control, and to reduce the error of the linearization and prediction processes, this paper presents an improved model predictive control algorithm, based on Laguerre functions, for the motion tracking of an omnidirectional mobile robot with non-iterative linearization. To design the controller, the kinematic modeling of the three-wheeled omnidirectional robot was first performed. Next, the model predictive algorithm was developed using Laguerre functions to parametrize the control signals. At each sampling instant of the online optimization, a linearization along the predicted trajectory, based on the duality principle between optimal control and stochastic filtering, was carried out to deal with the nonlinearities of the system. This non-iterative linearization provides better approximation of the nonlinear behavior which improves the prediction process and the tracking performance, with lower computational burden due to the use of the Laguerre functions. The new controller is applied to solve the trajectory-tracking problem of an omnidirectional robot. A comparative study between the proposed controller, the conventional model predictive control, and the nonlinear model predictive approach is made. Simulation results confirm that the new controller outperform the latter ones regarding tracking accuracy with considerably low computational effort. The feasibility of the controller is demonstrated by real-time experiment on the Robotino-Festo omnidirectional mobile robot

Model Predictive Control of a Nonlinear Aeroelastic System Using Volterra Series Representations

The purpose of this study is to investigate the potential effectiveness of using a Volterra-based Model Predictive Control strategy to control a nonlinear aeroelastic system. Model Predictive Control (MPC), also known as Receding Horizon Control (RHC), entails computing optimal control inputs over a finite time horizon, applying a portion of the computed optimal control sequence, and then repeating the process over the next time horizon. The Volterra series provides input-output models of a dynamical system in terms of a series of integral operators of increasing order, where the first-order Volterra operator models the linear dynamics and the higher-order operators model the nonlinear dynamics. In this thesis, Volterra-based Model Predictive Control is applied to simulated linear and nonlinear pitch-plunge aeroelastic systems. A linear MPC controller based on a first-order Volterra model is used to control the linear aeroelastic system, and the results are compared to those obtained using a standard LQR controller and a LQR-based MPC strategy. The controller is implemented for regulator and tracking cases for a free-stream velocity of 6 m/s, a condition for which the open-loop linear system is stable, and a free-stream velocity of 12.5 m/s, which corresponds to an unstable flutter condition. Nonlinear MPC controllers, using second- and third-order Volterra models, are then used to control the nonlinear aeroelastic system for regulator and tracking cases at the stable flight condition. The stability and performance of the linear and nonlinear Volterra-based MPC strategies are discussed, and a detailed analysis of the effect of different parameters such as the optimization horizon, control horizon and control discretization, is provided. The results show that the linear MPC controller is able to successfully track a reference input for the stable condition and stabilizes the system at the unstable flutter condition. It is also shown that the incorporation of the second- and third-order Volterra kernels in the nonlinear MPC controller provides superior performance on the nonlinear aeroelastic system compared to the results obtained using only a linear model

MODELLING OF NONLINEAR SYSTEMS USING INTEGRATED OBFARX PLUS NEURAL NETWORK MODELS

The objective of this project is to develop a new model, which is by combining OBFARX linear model with nonlinear NN model. The results obtained will be compared with the previous models to show performance improvement by the new model. The new model development is based on the model developed by (Zabiri et al 2011) which is OBF linear model combination with nonlinear NN model. The OBF-NN model cannot work efficiently on some problems due to the limitations of the OBF part of the equation. So it is important to analyze the new model which is OBFARX-NN with OBF-NN model. The scope for this project will be the development of the parallel OBFARX-NN model, methods for estimating the model parameter, simulation analysis using MATLAB and evaluation on OBFARX-NN model performance. The method for completing the project will be firstly, make sure all the necessary information about the individual model is available. Then develop a theoretically working OBFARX-NN model. After that, analysis of the performance of the created model is done and also alterations here and there for better clarification. All in all, the result are the improve performance of process control by OBFARX-NN model compared to OBF-NN model.The most important aspect of the model development is the extrapolation capabilities of the model itself. When a model is forced to perform prediction in regions beyond the space of original training, then it can be said that the model can function well even when the process parameter is changed. This aspect is very important because in practical plant, the process conditions are continually changing making extrapolation inevitable. Thus, by testing the extrapolation capabilities of the OBFARX-NN model, the project had come up with the subsequent RMSE value and compared with previous model. The RMSE value indicates superior performance in the extrapolation region

ОЦЕНКА КАЧЕСТВА ИДЕНТИФИКАЦИИ ДИНАМИЧЕСКИХ ПАРАМЕТРОВ ПРОЦЕССА ПРОИЗВОДСТВА КАРБАМИДА

The identification of nonlinear systems using Volterra-Laguerre model is a method for estimating the dynamic coefficients of Volterra series. On base of experimental input-output data from carbamide production process, the estimation of coefficients will be using Laguerre filters and method of lest squares.Идентификация нелинейной системы с помощью модели Вольтера-Лагерра - это метод, который позволяет оценить динамические коэффициенты ряда Вольтерра, применяя свойства ортогональных функций Лагерра. На основе экспериментальных данных входа-выхода процесса производства карбамида, оцениваются коэффициенты рядов Вольтерра посредством фильтров Лагерра и метода наименьших квадратов

MODELLING OF NONLINEAR SYSTEMS USING INTEGRATED OBFARX PLUS NEURAL NETWORK MODELS

The objective of this project is to develop a new model, which is by combining OBFARX linear model with nonlinear NN model. The results obtained will be compared with the previous models to show performance improvement by the new model. The new model development is based on the model developed by (Zabiri et al 2011) which is OBF linear model combination with nonlinear NN model. The OBF-NN model cannot work efficiently on some problems due to the limitations of the OBF part of the equation. So it is important to analyze the new model which is OBFARX-NN with OBF-NN model. The scope for this project will be the development of the parallel OBFARX-NN model, methods for estimating the model parameter, simulation analysis using MATLAB and evaluation on OBFARX-NN model performance. The method for completing the project will be firstly, make sure all the necessary information about the individual model is available. Then develop a theoretically working OBFARX-NN model. After that, analysis of the performance of the created model is done and also alterations here and there for better clarification. All in all, the result are the improve performance of process control by OBFARX-NN model compared to OBF-NN model.The most important aspect of the model development is the extrapolation capabilities of the model itself. When a model is forced to perform prediction in regions beyond the space of original training, then it can be said that the model can function well even when the process parameter is changed. This aspect is very important because in practical plant, the process conditions are continually changing making extrapolation inevitable. Thus, by testing the extrapolation capabilities of the OBFARX-NN model, the project had come up with the subsequent RMSE value and compared with previous model. The RMSE value indicates superior performance in the extrapolation region