Closed-loop system identification and validation are important components in dynamic system modelling. In this dissertation, a comprehensive literature survey is compiled on system identification with a specific focus on closed-loop system identification and issues of identification experiment design and model validation. This is followed by simulated experiments on known linear and non-linear systems and experiments on a pilot scale distillation column. The aim of these experiments is to study several sensitivities between identification experiment variables and the consequent accuracy of identified models and discrimination capacity of validation sets given open and closed-loop conditions. The identified model structure was limited to an ARX structure and the parameter estimation method to the prediction error method. The identification and validation experiments provided the following findings regarding the effects of different feedback conditions: <ul> <li>Models obtained from open-loop experiments produced the most accurate responses when approximating the linear system. When approximating the non-linear system, models obtained from closed-loop experiments were found to produce the most accurate responses.</li> <li>Validation sets obtained from open-loop experiments were found to be most effective in discriminating between models approximating the linear system while the same may be said of validation sets obtained from closed-loop experiments for the nonlinear system.</li> </ul> These finding were mostly attributed to the condition that open-loop experiments produce more informative data than closed-loop experiments given no constraints are imposed on system outputs. In the case that system output constraints are imposed, closed-loop experiments produce the more informative data of the two. In identifying the non-linear system and the distillation column it was established that defining a clear output range, and consequently a region of dynamics to be identified, is very important when identifying linear approximations of non-linear systems. Thus, since closed-loop experiments produce more informative data given output constraints, the closed-loop experiments were more effective on the non-liner systems. Assessment into other identification experiment variables revealed the following: <ul> <li>Pseudo-random binary signals were the most persistently exciting signals as they were most consistent in producing models with accurate responses.</li> <li>Dither signals with frequency characteristics based on the system’s dominant dynamics produced models with more accurate responses.</li> <li>Setpoint changes were found to be very important in maximising the generation of informative data for closed-loop experiments</li></ul> Studying the literature surveyed and the results obtained from the identification and validation experiments it is recommended that, when identifying linear models approximating a linear system and validating such models, open-loop experiments should be used to produce data for identification and cross-validation. When identifying linear approximations of a non-linear system, defining a clear output range and region of dynamics is essential and should be coupled with closed-loop experiments to generate data for identification and cross-validation. / Dissertation (MEng)--University of Pretoria, 2009. / Chemical Engineering / unrestricted

Predictive control relies on predictions of the future behaviour of the system to be controlled. These predictions are calculated from a model of this system, thus making the model the cornerstone of the predictive controller. Furthermore predictive control is the only advanced control methodology that has managed to become widely used in the industry. The necessity of good models in the predictive control context can thus be motivated both from the very nature of predictive control and from its widespread use in industry. This thesis is concerned with examining the use of multiple models in the predictive controller. In order to do this the standard predictive control formulation has been extended to incorporate the use of multiple models. The most general case of this new formulation allows the use of an individual model for each prediction horizon. The models are estimated using measurements of the input and output sequences from the true system. When using this data to find a good model of the system it is important to remember the intended purpose of the model. In this case the model is going to be used in a predictive controller and the most important feature of the models is to deliver good k-step ahead predictions. The identification algorithms used to estimate the models thus strives for estimating models good at calculating these predictions. Finally this thesis presents some complete simulations of these ideas showing the potential of using multiple models in the predictive control framework.

<p>Predictive control relies on predictions of the future behaviour of the system to be controlled. These predictions are calculated from a model of this system, thus making the model the cornerstone of the predictive controller. Furthermore predictive control is the only advanced control methodology that has managed to become widely used in the industry. The necessity of good models in the predictive control context can thus be motivated both from the very nature of predictive control and from its widespread use in industry. </p><p>This thesis is concerned with examining the use of multiple models in the predictive controller. In order to do this the standard predictive control formulation has been extended to incorporate the use of multiple models. The most general case of this new formulation allows the use of an individual model for each prediction horizon. </p><p>The models are estimated using measurements of the input and output sequences from the true system. When using this data to find a good model of the system it is important to remember the intended purpose of the model. In this case the model is going to be used in a predictive controller and the most important feature of the models is to deliver good k-step ahead predictions. The identification algorithms used to estimate the models thus strives for estimating models good at calculating these predictions. </p><p>Finally this thesis presents some complete simulations of these ideas showing the potential of using multiple models in the predictive control framework.</p>

The stringent regulations of emission levels from heavy duty vehicles create a demand for new methods for reducing harmful emissions from diesel engines. This thesis deals with the modelling of the nitrogen oxide (NOx) emissions from heavy duty vehicles using a selective catalyst as an aftertreatment system, utilising ammonia (NH3) for its reduction. The process of the selective catalytic reduction (SCR) is nonlinear, since the result of the chemical reactions involved depends on the load operating point and the temperature. The purpose of this thesis is to investigate different methods for nonlinear system identification of SCR systems with control applications in mind. The main focus of the thesis is on finding suitable techniques for effective NOx reduction without the need of over dosage of ammonia. By using data collected from a simulator together with real measured data, new black-box identification techniques are developed. Scaling and convergence properties of the proposed algorithms are analysed theoretically. Some of the resulting models are used for controller development using e.g. feedback linearisation techniques, followed by validation in a simulator environment. The benefits of nonlinear modelling and control of the SCR system are highlighted in a comparison with control based on linear models of the system. Further, a multiple model approach is investigated for simultaneous control of NOx and tailpipe ammonia. The results indicate an improvement in terms of ammonia slip reduction in comparison with models that do not take the ammonia slip into account. Another approach to NOx reduction is achieved by controlling the SCR temperature using techniques developed for LPV systems. The results indicate a reduction of the accumulated NOx.

With the rising popularity of ROVs and other UV solutions, more robust and high performance controllers have become a necessity. A model of the ROV or UV can be a valuable tool during control synthesis. The main objective of this thesis was to use a model in design and development of controllers for an ROV. In this thesis, an ROV from Blue Robotics was used. The ROV was equipped with 6 thrusters placed such that the ROV was capable of moving in 6-DOFs. The ROV was further equipped with an IMU, two pressure sensors and a magnetometer. The ROV platform was further developed with EKF-based sensor fusion, a control system and manual control capabilities. To model the ROV, the framework of Fossen (2011) was used. The model was estimated using two different methods, the prediction-error method and an EKF-based method. Using the prediction-error method, it was found that the initial states of the quaternions had a large impact on the estimated parameters and the overall fit to validation data. A Kalman smoother was used to estimate the initial states. To circumvent the problems with the initial quaternions, an \abbrEKF was implemented to estimate the model parameters. The EKF estimator was less sensitive to deviations in the initial states and produced a better result than the prediction-error method. The resulting model was compared to validation data and described the angular velocities well with around 70 % fit. The estimated model was used to implement feedback linearisation which was used in conjunction with an attitude controller and an angular velocity controller. Furthermore, a depth controller was developed and tuned without the use of the model. Performance of the controllers was tested both in real tests and simulations. The angular velocity controller using feedback linearisation achieved good reference tracking. However, the attitude controller could not stabilise the system while using feedback linearisation. Both controllers' performance could be improved further by tuning the controllers' parameters during tests. The fact that the feedback linearisation made the ROV unstable, indicates that the attitude model is not good enough for use in feedback linearisation. To achieve stability, the magnitude of the parameters in the feedback linearisation were scaled down. The assumption that the ROV's center of rotation coincides with the placement of the ROV's center of gravity was presented as a possible source of error. In conclusion, good performance was achieved using the angular velocity controller. The ROV was easier to control with the angular velocity controller engaged compared to controlling it in open loop. More work is needed with the model to get acceptable performance from the attitude controller. Experiments to estimate the center of rotation and the center of gravity of the ROV may be helpful when further improving the model.

The estimation problem of stochastic nonlinear parametric models is recognized to be very challenging due to the intractability of the likelihood function. Recently, several methods have been developed to approximate the maximum likelihood estimator and the optimal mean-square error predictor using Monte Carlo methods. Albeit asymptotically optimal, these methods come with several computational challenges and fundamental limitations. The contributions of this thesis can be divided into two main parts. In the first part, approximate solutions to the maximum likelihood problem are explored. Both analytical and numerical approaches, based on the expectation-maximization algorithm and the quasi-Newton algorithm, are considered. While analytic approximations are difficult to analyze, asymptotic guarantees can be established for methods based on Monte Carlo approximations. Yet, Monte Carlo methods come with their own computational difficulties; sampling in high-dimensional spaces requires an efficient proposal distribution to reduce the number of required samples to a reasonable value. In the second part, relatively simple prediction error method estimators are proposed. They are based on non-stationary one-step ahead predictors which are linear in the observed outputs, but are nonlinear in the (assumed known) input. These predictors rely only on the first two moments of the model and the computation of the likelihood function is not required. Consequently, the resulting estimators are defined via analytically tractable objective functions in several relevant cases. It is shown that, under mild assumptions, the estimators are consistent and asymptotically normal. In cases where the first two moments are analytically intractable due to the complexity of the model, it is possible to resort to vanilla Monte Carlo approximations. Several numerical examples demonstrate a good performance of the suggested estimators in several cases that are usually considered challenging. / <p>QC 20171128</p>