9 research outputs found

    H∞ smith predictor design for time-delayed MIMO systems via convex optimization

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    A new method for robust fixed-order H∞ controller design for uncertain time-delayed MIMO systems is presented. It is shown that the H∞ robust performance condition can be represented by a set of convex constraints with respect to the parameters of a linearly parameterized primary controller in the Smith predictor structure. Therefore, the parameters of the primary controller can be obtained by convex optimization. The proposed method will be applied to stable MIMO models with uncertain dead-time and with multimodel and frequency-dependent uncertainty. The performance of this method is illustrated by simulation examples of industrial processes

    Robust Smith Predictor Design for Time-Delay Systems with H∞ Performance

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    A new method for robust fixed-order H∞ controller design for uncertain time-delay systems is presented. It is shown that the H∞ robust performance condition can be represented by a set of convex constraints with respect to the parameters of a linearly parameterized primary controller in the Smith predictor structure. Therefore, the parameters of the primary controller can be obtained by convex optimization. The proposed method can be applied to stable SISO and MIMO models with uncertain dead-time and with multimodel and frequency-dependent uncertainty. It is also shown that how the design method can be extended to unstable SISO models. The design of robust gain-scheduled dead-time compensators is also investigated. The performance of the method is illustrated for both SISO and MIMO systems by simulation examples

    Continuous-time self-tuning algorithms

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    This thesis proposes some new self-tuning algorithms. In contrast to the conventional discrete-time approach to self-tuning control, the continuous-time approach is used here, that is continuous-time design but digital implementation is used. The proposed underlying control methods are combined with a continuous-time version of the well-known discrete recursive least squares algorithms. The continuous-time estimation scheme is chosen to maintain the continuous-time nature of the algorithms. The first new algorithm proposed is emulator-based relay control (which has already been described in a paper by the author). The algorithm is based on the idea of constructing the switching surface by emulators; that is, unrealisable output derivatives are replaced by their emulated values. In particular, the relay is forced to operate in the sliding mode. In this case, it is shown that emulator-based control and its proposed relay version become equivalent in the sense that both give the same control law. The second new algorithm proposed is a continuous-time version of the discrete-time generalized predictive control (GPC) of Clarke et al (which has already been described in a paper by the author). The algorithm, continuous-time generalized predictive control (CGPC), is based on similar ideas to the GPC, however the formulation is very different. For example, the output prediction is accomplished by using the Taylor series expansion of the output and emulating the output derivatives involved. A detailed closed-loop analysis of this algorithm is also given. It is shown that the CGPC control law only changes the closed-loop pole locations leaving the open-loop zeros untouched (except one special case). It is also shown that LQ control can be considered in the CGPC framework. Further, the CGPC is extended to include some design polynomials so that the model-following and pole-placement control can be considered in the same framework. A third new algorithm, a relay version of the CGPC, is described. The method is based on the ideas of the emulator-based relay control and again it is shown that the CGPC and its relay version become equivalent when the relay operates in the sliding mode. Finally, the CGPC ideas are extended to the multivariable systems and the resulting closed-loop system is analysed in some detail. It is shown that some special choice of design parameters result in a decoupled closed-loop system for certain systems. In addition, it is shown that if the system is decouplable, it is possible to obtain model-following control. It is also shown that LQ control, as in the scalar case, can be considered in the same framework. An illustrative simulation study is also provided for all of the above methods throughout the thesis

    Modeling multivariable time series using regular and singular autoregressions

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    The primary aim of this thesis is to study the modeling of high-dimensional time series with periodic missing observations. This study is very important in different branches of science and technology such as: econometric modeling, signal processing and systems and control. For instance, in the field of econometric modeling, it is crucial to provide proper models for national economies to help policy makers with decision making and policy adjustments. These models are built upon available high-dimensional data sets, which are not usually collected at the same rate. For example, some data such as, the employment rate are available on a monthly basis while some others like the gross domestic product (GDP) are collected quarterly. Motivated by applications in econometric modeling, we mainly consider systems, which have two sets of measurement streams, one stream being available at all times and the other one is observed every N-th time. There are two major issues involved with modeling of high-dimensional time series with periodic missing observations, namely, the curse of dimensionality and missing observations. Generalized dynamic factor models (GDFMs), which have been recently introduced in the field of econometric modeling, are exploited to handle the curse of dimensionality phenomenon. Furthermore, the blocking technique from systems and control is used to tackle issues associated with the missing observations. In this thesis, we consider a class of GDFMs and assume that there exists an underlying linear time-invariant system operating at the highest sample rate and our task is to identify this model from the available mixed frequency measurements. To this end, we first provide a very detailed study about zeros of linear systems with alternate missing measurements. Zeros of this class of linear systems are examined when the parameter matrices of a minimal state space representation of a transfer function matrix corresponding to the underlying high frequency system assume generic values. Under this setting, we then illustrate situations under which linear systems with missing observations are completely zero-free. It is worthwhile noting that the obtained condition is very common in an econometric modeling context. Then we apply this result and assume that the underlying high frequency system has an autoregressive (AR) structure. Next, we study identifiability of AR systems from those population second order moments, which can be observed in principle. We propose the method of modified extended Yule-Walker equations to show that the set of identifiable AR systems is an open and dense subset of the associated parameter space i.e. AR systems are generically identifiable

    Controllability analysis of industrial processes : towards the industrial application

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    A Data-Driven Frequency-Domain Approach for Robust Controller Design via Convex Optimization

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    The objective of this dissertation is to develop data-driven frequency-domain methods for designing robust controllers through the use of convex optimization algorithms. Many of today's industrial processes are becoming more complex, and modeling accurate physical models for these plants using first principles may be impossible. With the increased developments in the computing world, large amounts of measured data can be easily collected and stored for processing purposes. Data can also be collected and used in an on-line fashion. Thus it would be very sensible to make full use of this data for controller design, performance evaluation, and stability analysis. The design methods imposed in this work ensure that the dynamics of a system are captured in an experiment and avoids the problem of unmodeled dynamics associated with parametric models. The devised methods consider robust designs for both linear-time-invariant (LTI) single-input-single-output (SISO) systems and certain classes of nonlinear systems. In this dissertation, a data-driven approach using the frequency response function of a system is proposed for designing robust controllers with H∞ performance. Necessary and sufficient conditions are derived for obtaining H∞ performance while guaranteeing the closed-loop stability of a system. A convex optimization algorithm is implemented to obtain the controller parameters which ensure system robustness; the controller is robust with respect to the frequency-dependent uncertainties of the frequency response function. For a certain class of nonlinearities, the proposed method can be used to obtain a best-linear-approximation with an associated frequency dependent uncertainty to guarantee the stability and performance for the underlying linear system that is subject to nonlinear distortions. The concepts behind these design methods are then used to devise necessary and sufficient conditions for ensuring the closed-loop stability of systems with sector-bounded nonlinearities. The conditions are simple convex feasibility constraints which can be used to stabilize systems with multi-model uncertainty. Additionally, a method is proposed for obtaining H∞ performance for an approximate model (i.e., describing function) of a sector-bounded nonlinearity. This work also proposes several data-driven methods for designing robust fixed-structure controllers with H∞ performance. One method considers the solution to a non-convex problem, while another method convexifies the problem and implements an iterative algorithm to obtain the local solution (which can also consider H2 performance). The effectiveness of the proposed method(s) is illustrated by considering several case studies that require robust controllers for achieving the desired performance. The main applicative work in this dissertation is with respect to a power converter control system at the European Organization for Nuclear Research (CERN) (which is used to control the current in a magnet to produce the desired field in controlling particle trajectories in accelerators). The proposed design methods are implemented in order to satisfy the challenging performance specifications set by the application while guaranteeing the system stability and robustness using data-driven design strategies

    System modelling and control

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    Multivariable Smith Predictors Design for Nonsquare Plants

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    Abstract: The goal of this paper is to provide a solution to the optimal design problem of optimal decoupled multivariable Smith predictor for general linear stable plants with multiple time delays. The design procedure is divided into three steps. In the first step, a nonsquare plant is factored into the "delay free" part and delay part and the "delay free" part is further factored into minimum phase part and nonminimum phase part. In the second step, the factorization is utilized to analytically derive the optimal multivariable Smith predictor based on only output feedback. Finally, the controller is shaped by a filter for specified inputs and a simple procedure is developed to quantitatively tune the closed-loop response expressed in time domain or frequency domain
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