Algebraic robust control of a closed circuit heating-cooling system with a heat exchanger and internal loop delays

This study demonstrates the use of a simple algebraic controller design for a cooling-heating plant with a through-flow air-water heat exchanger that evinces long internal delays with respect to the robustness to plant model uncertainties and variable ambient temperature conditions during the season. The advantage of the proposed design method consists in that the delays are not approximated but fully considered. Moreover, the reduction of sensitivity to model parameters’ variations yields the better applicability regardless modeling errors or environmental fluctuations. The infinite-dimensional mathematical model of the plant has been obtained by using anisochronic modeling principles. The key tool for the design is the ring special of quasipolynomial meromorphic functions (RQM). The Two-Feedback-Controllers (TFC) rather than the simple negative control feedback loop is utilized, which enables to solve the reference tracking and disturbance rejection independently and more efficiently. The eventual controller is then tuned such that robust stability and robust performance requirements are fulfilled. The tuning procedure is supported by a performance optimization idea. Since the originally obtained controller is of the infinite-dimensional nature, a possible way how to substitute it by a simplified finite-dimensional one is proposed for engineering practice. The functionality of both the controllers is compared and verified by simulations as well as by real measurements which prove a very good performance. © 2016 Elsevier LtdEuropean Regional Development Fund under the project CEBIA-Tech Instrumentation [CZ.1.05/2.1.00/19.0376

Sampled-data sliding mode observer for robust fault reconstruction: A time-delay approach

A sliding mode observer in the presence of sampled output information and its application to robust fault reconstruction is studied. The observer is designed by using the delayed continuous-time representation of the sampled-data system, for which sufficient conditions are given in the form of linear matrix inequalities (LMIs) to guarantee the ultimate boundedness of the error dynamics. Though an ideal sliding motion cannot be achieved in the observer when the outputs are sampled, ultimately bounded solutions can be obtained provided the sampling frequency is fast enough. The bound on the solution is proportional to the sampling interval and the magnitude of the switching gain. The proposed observer design is applied to the problem of fault reconstruction under sampled outputs and system uncertainties. It is shown that actuator or sensor faults can be reconstructed reliably from the output error dynamics. An example of observer design for an inverted pendulum system is used to demonstrate the merit of the proposed methodology compared to existing sliding mode observer design approaches

Observer-based H∞ control for systems with repeated scalar nonlinearities and multiple packet losses

This paper is concerned with the H∞ control problem for a class of systems with repeated scalar nonlinearities and multiple missing measurements. The nonlinear system is described by a discrete-time state equation involving a repeated scalar nonlinearity, which typically appears in recurrent neural networks. The measurement missing phenomenon is assumed to occur, simultaneously, in the communication channels from the sensor to the controller and from the controller to the actuator, where the missing probability for each sensor/actuator is governed by an individual random variable satisfying a certain probabilistic distribution in the interval [0 1]. Attention is focused on the analysis and design of an observer-based feedback controller such that the closed-loop control system is stochastically stable and preserves a guaranteed H∞ performance. Sufficient conditions are obtained for the existence of admissible controllers. It is shown that the controller design problem under consideration is solvable if certain linear matrix inequalities (LMIs) are feasible. Three examples are provided to illustrate the effectiveness of the developed theoretical result

Control and operation of a spinning disc reactor

PhD ThesisThe aim of the present research is to assess the control and operation of a Spinning Disc Reactor (SDR), carried out via four separate investigations. Firstly, the effect of equipment size reduction on control is studied by comparing the performance of a PID controller applied to simulated intensified and conventional processes. It was found that superior control performance in terms of Integral of Absolute Error (IAE) is achieved for the simulated intensified system. However, the results showed that intensified systems are more susceptible to disturbances and the controlled variable exhibits larger overshoots. Furthermore, the frequency response analysis of the two systems showed that the simulated intensified system has reduced stability margins. The second part of the research investigates the task of pH control in a SDR using a PID controller by means of simulation and experimental studies. The effectiveness of a disturbance observer (DO) and a pH characteriser to compensate for the severe pH system nonlinearity is also explored in detail. The experimental studies showed that a PID controller provides adequate setpoint tracking and disturbance rejection performances. However, sluggish transient responses prevailed and the effluent pH limit cycled around the setpoint. There were indications of unstable behaviour at lower flowrates, which implied more advanced control schemas may be required to adapt to various operating regions dictated by the complex thin film hydrodynamics. The addition of the DO scheme improved the control performance by reducing the limit cycles. In the third segment of the investigations, the potential of exploiting the disc rotational speed as a manipulated variable is assessed for the process of barium sulphate precipitation. A PI controller is successfully used to regulate the conductivity of the effluent stream by adjusting the disc rotational speed. The results are immensely encouraging and show that the disc speed may be used as an extra degree of freedom in control system design. Finally, the flow regimes and wave characteristics of thin liquid films produced in a SDR are investigated by means of a thermal imaging camera. The film hydrodynamics strongly affect the heat and mass transfer processes within the processing films, and thus the intensification aspects of SDRs. Therefore, effective control and operation of such units is significantly dependent on the knowledge of film hydrodynamics and the underlying impact of the operating parameters and the manipulated variables on a given process. The results provided an interesting insight and unveiled promising potentials for characterisation of thin liquid film flow and temperature profiles across the disc by means of thermographic techniques. The present study reveals both challenges and opportunities regarding the control aspects of SDRs. It is recommended that equipment design and process control need to be considered simultaneously during the early stages of the future developments. Furthermore, intensified sensors and advanced controllers may be required to achieve an optimum control capability. Currently, the control performance is inhibited by the lack of sufficient considerations during the SDR design and manufacturing stages, and also by the characteristics of the commercially available instrumentation.EPSRC Doctoral Training Awar

High performance position control for permanent magnet synchronous drives

In the design and test of electric drive control systems, computer simulations provide a useful way to verify the correctness and efficiency of various schemes and control algorithms before the final system is actually constructed, therefore, development time and associated costs are reduced. Nevertheless, the transition from the simulation stage to the actual implementation has to be as straightforward as possible. This document presents the design and implementation of a position control system for permanent magnet synchronous drives, including a review and comparison of various related works about non-linear control systems applied to this type of machine. The overall electric drive control system is simulated and tested in Proteus VSM software which is able to simulate the interaction between the firmware running on a microcontroller and analogue circuits connected to it. The dsPIC33FJ32MC204 is used as the target processor to implement the control algorithms. The electric drive model is developed using elements existing in the Proteus VSM library. As in any high performance electric drive system, field oriented control is applied to achieve accurate torque control. The complete control system is distributed in three control loops, namely torque, speed and position. A standard PID control system, and a hybrid control system based on fuzzy logic are implemented and tested. The natural variation of motor parameters, such as winding resistance and magnetic flux are also simulated. Comparisons between the two control schemes are carried out for speed and position using different error measurements, such as, integral square error, integral absolute error and root mean squared error. Comparison results show a superior performance of the hybrid fuzzy-logic-based controller when coping with parameter variations, and by reducing torque ripple, but the results are reversed when periodical torque disturbances are present. Finally, the speed controllers are implemented and evaluated physically in a testbed based on a brushless DC motor, with the control algorithms implemented on a dsPIC30F2010. The comparisons carried out for the speed controllers are consistent for both simulation and physical implementation

Hypertracking and Hyperrejection: Control of Signals beyond the Nyquist Frequency

This paper studies the problem of signal tracking and disturbance rejection for sampled-data control systems, where the pertinent signals can reside beyond the so-called Nyquist frequency. In light of the sampling theorem, it is generally understood that manipulating signals beyond the Nyquist frequency is either impossible or at least very difficult. On the other hand, such control objectives often arise in practice, and control of such signals is much desired. This paper examines the basic underlying assumptions in the sampling theorem and pertinent sampled-data control schemes, and shows that the limitation above can be removed by assuming a suitable analog signal generator model. Detailed analysis of multirate closed-loop systems, zeros and poles are given, which gives rise to tracking or rejection conditions. Robustness of the new scheme is fully characterized; it is shown that there is a close relationship between tracking/rejection frequencies and the delay length introduced for allowing better performance. Examples are discussed to illustrate the effectiveness of the proposed method here

Robust control strategies for unstable systems with input/output delays

Los sistemas con retardo temporal aparecen con frecuencia en el ámbito de la ingeniería, por ejemplo en transmisiones hidráulicas o mecánicas, procesos metalúrgicos o sistemas de control en red. Los retardos temporales han despertado el interés de los investigadores en el ámbito del control desde finales de los años 50. Se ha desarrollado una amplia gama de herramientas para el análisis de su estabilidad y prestaciones, especialmente durante las dos últimas décadas. Esta tesis se centra en la estabilización de sistemas afectados por retardos temporales en la actuación y/o la medida. Concretamente, las contribuciones que aquí se incluyen tienen por objetivo mejorar las prestaciones de los controladores existentes en presencia de perturbaciones. Los retardos temporales degradan, inevitablemente, el desempeño de un bucle de control. No es de extrañar que el rechazo de perturbaciones haya sido motivo de estudio desde que emergieron los primeros controladores predictivos para sistemas con retardo. Las estrategias presentadas en esta tesis se basan en la combinación de controladores predictivos y observadores de perturbaciones. Estos últimos han sido aplicados con éxito para mejorar el rechazo de perturbaciones de controladores convencionales. Sin embargo, la aplicación de esta metodología a sistemas con retardo es poco frecuente en la literatura, la cual se investiga exhaustivamente en esta tesis. Otro inconveniente de los controladores predictivos está relacionado con su implementación, que puede llevar a la inestabilidad si no se realiza cuidadosamente. Este fenómeno está relacionado con el hecho de que las leyes de control predictivas se expresan mediante una ecuación integral. En esta tesis se presenta una estructura de control alternativa que evita este problema, la cual utiliza un observador de dimensión infinita, gobernado por una ecuación en derivadas parciales de tipo hiperbólico.Time-delay systems are ubiquitous in many engineering applications, such as mechanical or fluid transmissions, metallurgical processes or networked control systems. Time-delay systems have attracted the interest of control researchers since the late 50's. A wide variety of tools for stability and performance analysis has been developed, specially over the past two decades. This thesis is focused on the problem of stabilizing systems that are affected by delays on the actuator and/or sensing paths. More specifically, the contributions herein reported aim at improving the performance of existing controllers in the presence of external disturbances. Time delays unavoidably degrade the control loop performance. Disturbance rejection has been a matter of concern since the first predictive controllers for time-delay systems emerged. The key idea of the strategies presented in this thesis is the combination of predictive controllers and disturbance observers. The latter have been successfully applied to improve the disturbance rejection capabilities of conventional controllers. However, the application of this methodology to time-delay systems is rarely found in the literature. This combination is extensively investigated in this thesis. Another handicap of predictive controllers has to do with their implementation, which can induce instability if not done carefully. This issue is related to the fact that predictive control laws take the form of integral equations. An alternative control structure that avoids this problem is also reported in this thesis, which employs an infinite-dimensional observer, governed by a hyperbolic partial differential equation.Sanz Díaz, R. (2018). Robust control strategies for unstable systems with input/output delays [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/111830TESI

플라즈마 식각 장치를 위한 적응모델예측제어기의 설계

학위논문 (박사)-- 서울대학교 대학원 : 공과대학 화학생물공학부(에너지환경 화학융합기술전공), 2019. 2. 이윤우.The semiconductor etching process, which is one of the most critical processes in the manufacturing of semiconductors and one that comprises numerous steps, requires higher sophistication as 10 nm semiconductors are mass produced. Currently, the semiconductor etching process is mostly done by physical and/or chemical etching with plasma. In addition, the plasma etching is getting increasingly popular with the miniaturization of the process to a scale of less than 10 nm. The result of a plasma etching process is represented in the form of an etch profile which is determined by the plasma variables. Therefore, the performance of the process depends on these variables, and it is essential to measure and control them in real time. Although research on the control of plasma etching processes has been actively carried out, the plasma etching process strongly relies on the experience and skill level of seasoned engineers at the industry level. This is because a plasma-based system is very complicated and sensitive, and has a time-varying characteristics. However, even though previous studies show excellent results, they employed invasive diagnostic tools, and have single variable control schemes where a counter change of another plasma variable during control actions for other variables might occur due to the highly interactive plasma characteristics. Moreover, they did not consider the time-varying characteristics of plasma-based systems. Therefore, this thesis proposes a multivariable control strategy which can cope with interaction effects and a design of an adaptive model predictive controller which maintains its performance wherein systems vary with time. At first, the plasma variables which are considered as controlled variables were selected as the electron density and the electron temperature. This is because one of the etch profile, especially etch rate, can be expressed as functions of those plasma variables and the variables can be measured by the optical emission spectroscopy which is a non-invasive diagnostic tool. The plasma variables were paired with instrumental variables through singular value decomposition and relative gain array for constructing the optimal multivariable system model. Two parallel proportional integral derivative (PID) controllers were designed based on the output errors then conducted plasma variable control simulations. Through the simulations, the exist of interaction between the variables was obviously verified. For resolving the interaction effectively, decoupler controllers were applied to the PID controllers. As it performed the control experiment of the Ar plasma electron density and electron temperature excellently, the possibility of multivariable control of plasma-based system is demonstrated. In spite of the meaningful control results using the PID controllers, there are obvious limitations in relation to the exquisiteness and to the characteristics of decoupler controllers as it highly dependent to the accuracy of the system model. In order to maintain performance even in the case of a system change, an advanced control strategy is required and model predictive control can be an alternative. Therefore, a model predictive controller was designed where the Bayesian optimization is used as tuning method for the maximization of the exquisiteness. The controller verified its capability as it conducted Ar plasma electron density control in a drift-free system. However, the performance of it deteriorated in control simulations of time-varying systems and in a control experiment performed in a system where O2 plasma was injected into an Ar plasma system inducing the high nonlinearity. Therefore, a more advanced control strategy which can overcome the difficulty was required. In an adaptive control method, once the information from the system is entered into the adjustment mechanism part, the part makes a decision to deliver it to the controller. Then the controller is modified in accordance with the decision and releases the optimal control action. The typical adaptive control algorithm, which is the recursive least squares algorithm, was used in this thesis. Using the algorithm with Kalman filter interpretation, the time-delay effect which comes from the plasma etching reactor can be considered. The recursive model parameter estimator utilizing this algorithm was tuned by Bayesian optimization. When the recursive model parameter estimator detects changes of the system model parameters in real time and transmits it to the model predictive controller, the controller calculates the optimal manipulated variable based on the modified model. The adaptive model predictive controller performed the same simulations and experiment as those performed by the model predictive controller. Unlike the model predictive controller, the proposed controller performed control excellently even when the system changes over time. Numerically, it showed the improved control ability by 24.7% and 30.4% in terms of the mean absolute percentage error and the number of deviated sample, respectively compared to the conventional model predictive controller. These results demonstrate that the adaptive model predictive controller designed in this theses is invaluable for plasma-based system control and is the effective controller for the plasma etching reactor. It is expected to make a significant contribution to plasma-based processes that require high sophistication and flexibility.수 많은 공정으로 이루어진 반도체 제조 공정 내에서 가장 큰 비중을 차지하고 있는 반도체 식각 공정은 최근 10 nm급 반도체의 양산이 이뤄짐에 따라 식각의 높은 정교성이 요구되고 있다. 반도체 식각 공정은 현재 산업계에선 플라즈마를 이용하여 물리적, 화학적 식각을 일으키는 방법을 통해 이루어지고 있으며, 공정이 10 nm 급 이하 스케일로 미세화된 후로 이 방법이 더욱 각광 받고 있다. 공정의 결과는 식각 프로필을 기준으로 결정되는 데 이 식각 프로필이 플라즈마 변수들에 크게 의존함이 입증됨에 따라 이 변수들을 실시간으로 측정하고 제어하는 것이 공정의 핵심이 되었다. 그동안 플라즈마 변수 제어에 관한 연구들이 활발히 진행되어 왔으나 아직까지 산업계에선 그 이론들을 바로 활용하지 못하고 경험 많은 엔지니어의 감에 의존하고 있다. 그 이유는 근본적으로 시스템이 매우 복잡하고 예민할 뿐 아니라 시간에 따라 변하는 특성을 갖고 있기 때문이다. 그러나 이전의 연구들은 훌륭한 결과를 보였음에도 불구하고, 플라즈마 시스템에 직접적으로 영향을 미치는 침투성 센서를 이용했거나, 플라즈마 변수들과 장치 변수들이 서로 복잡하게 얽혀 있어 야기되는 상호작용을 간과할 수밖에 없는 단변수 제어를 수행한 데에 그치고 있다. 게다가 외란 때문에 발생되는 시간에 따라 변하는 특성을 고려하지 못하고 있다. 따라서, 본 학위논문에서는 변수간 상호작용을 최소화하는 다변수 제어 전략과 시스템이 시간에 따라 변하는 상황에서도 성능이 악화되지 않는 적응모델예측제어기의 설계를 제안한다. 먼저, 전자 밀도와 전자 온도가 제어 대상이 되는 플라즈마 변수로 선정되었다. 이는 식각 프로필, 특히 식각률이 이 변수들에 대한 함수로 표현될 수 있으며, 이 변수들은 침투성 센서인 광학적 발광 분광법을 통해 측정될 수 있기 때문이다. 그 다음에, 최적의 다변수 시스템 정의를 위해 특이치 분석과 상대이득배열을 이용하여 가장 효과적으로 제어를 수행할 수 있는 장치 변수 선정이 이루어졌다. 이를 바탕으로 두 개의 병렬로 연결된 비례적분미분제어기를 설계, 아르곤 플라즈마 전자 밀도와 전자 온도의 제어 시뮬레이션을 수행하였다. 해당 시뮬레이션에서 변수들 간 상호 작용이 확연함을 입증하였으며 이를 효과적으로 해결하기 위해 디커플러 제어기가 비례적분미분제어기에 결합되었다. 이 제어기는 아르곤 플라즈마의 전자 밀도와 전자 온도 제어를 훌륭하게 수행함으로써 다변수 플라즈마 시스템의 제어 가능성을 분명하게 입증하였다. 다변수 플라즈마 시스템의 제어 가능성이 입증 됐음에도 불구하고, 이 제어 전략은 비례적분미분제어기의 정교성 측면에서의 한계와 디커플러 제어기의 시스템 모델에 대한 높은 의존도 특성으로 인한 한계가 존재한다. 시스템이 변하는 상황에서도 성능을 유지하기 위해선 더욱 수준 높은 제어 전략이 요구되며, 모델예측제어가 그 대안이 될 수 있다. 모델예측제어기의 설계는 제어의 정교성을 극대화 시키기 위해 베이시안 최적화 기법을 통해 이루어졌다. 이 모델예측제어기는 인위적인 외란이 적용되지 않은 순수 아르곤 플라즈마 시스템에서의 전자 밀도 제어를 훌륭하게 수행함으로써 그 성능을 입증하였다. 하지만, 시스템이 시간에 따라 변하는 상황을 모사한 시뮬레이션과 산소 플라즈마가 아르곤 플라즈마 시스템에 주입되어 시스템 변화를 야기시키는 상황에서 수행된 제어 실험에서 제어기의 성능이 확연히 악화됨을 확인할 수 있었다. 따라서 이를 극복할 수 있는 더욱 발전된 제어 전략이 요구되었다. 적응 제어 기법은 시스템에서 얻어진 정보를 조절 메커니즘 부분으로 보내 실시간으로 제어기의 수정 사항을 결정하여 이를 바탕으로 제어를 수행하는 기법이다. 본 학위논문에서는 대표적인 적응 제어 알고리즘인 순환형 최소자승법 알고리즘을 활용하였다. 이 알고리즘에 칼만 필터 해석을 접목시킴에 따라, 플라즈마 식각 장치로부터 비롯되는 시간 지연의 효과를 고려할 수 있게 하였다. 이 알고리즘이 탑재된 순환형 모델 파라미터 추정기는 베이시안 최적화 기법을 통해 튜닝되었다. 순환형 모델 파라미터 추정기가 실시간으로 감지하는 모델 파라미터의 변화를 모델예측제어기에 전달하면 수정된 모델을 기반으로 제어기는 최적의 조절 변수를 계산한다. 이렇게 설계된 적응모델예측제어기는 앞서 모델예측제어기가 수행한 것과 동일한 시뮬레이션과 실험을 수행하였다. 모델예측제어기와 달리 적응모델예측제어기는 시간에 따라 시스템이 변하는 상황에서도 훌륭한 제어를 수행하였으며, 평균절대오차율을 기준으로 했을 때 기존의 모델예측제어기보다 24.7%의 향상된 제어 성능을 보여주었다. 이 결과는 본 학위논문에서 제안하고 있는 적응모델예측제어기가 시스템의 변화가 빈번한 플라즈마 시스템에서의 제어에 매우 가치 있음과 더불어 플라즈마 식각 장치에 유효한 제어기라는 것을 반증한다. 이 결과가 플라즈마 기반 시스템을 대상으로 하는 모든 제어 공정의 발전에 크게 이바지할 것을 기대하는 바이다.Abstract i Contents v List of Figures viii List of Tables xii CHAPTER 1. Introduction 1 1.1. Research motivation 1 1.2. Research objectives 4 1.3. Description of the equipment used in this thesis 5 1.4. Outline of the thesis 9 CHAPTER 2. Design of Multi-Input Multi-Output Controller for Plasma-based System 10 2.1. Introduction 10 2.2. Theoretical backgrounds 13 2.2.1. Estimation of plasma variables from optical emission spectroscopy 13 2.2.2. The influence of oxygen in plasma etching reactor 16 2.2.3. Singular value decomposition and condition number 18 2.2.4. Relative gain array method 21 2.2.5. Multi-loop control system 23 2.3. MIMO control results in the Ar plasma system 31 2.3.1. Variable selection and pairing 31 2.3.2. Disturbance rejection control results for SISO systems 37 2.3.3. Simulation of multi-loop control scheme and decoupling control scheme 41 2.3.4. Set-point tracking control experiment of multi-loop controller with decoupler controllers 58 2.4. Concluding remarks 62 CHAPTER 3. Disturbance Rejection Control of Plasma Electron Density by Model Predictive Controller 64 3.1. Introduction 64 3.2. Model predictive control 68 3.2.1. Concept of model predictive control 68 3.2.2. Description of model predictive control algorithm 71 3.2.2.1. State estimation algorithm 71 3.2.2.2. Optimization algorithm 76 3.3. Design of model predictive controller for Ar plasma system 78 3.3.1. System identification of Ar plasma system 78 3.3.2. Optimal MPC weight parameters from integral squared error based Bayesian optimization 80 3.3.3. Experimental results of Ar plasma electron density control 84 3.4. Disturbance rejection control using model predictive controller 86 3.4.1. Development of time-varying system model for control simulation 86 3.4.2. Design of model predictive controller for disturbance rejection control 91 3.4.3. Experimental result of disturbance rejection control in Ar/O2 plasma system 101 3.5. Concluding remarks 104 CHAPTER 4. Design of Adaptive Model Predictive Controller for Plasma Etching Reactor 106 4.1. Introduction 106 4.2. Recursive model parameter estimation 112 4.2.1. Recursive least squares algorithm with forgetting factor 113 4.2.2. Recursive least squares algorithm with Kalman filter interpretation 116 4.3. Adaptive model predictive control algorithm 119 4.4. Time-varying system control using adaptive model predictive controller 123 4.4.1. Initial system identification (Scaling method) 123 4.4.2. Design of adaptive model predictive controller for time-varying system 125 4.4.3. Set-point tracking control results in drifted system 143 4.5. Concluding remarks 152 CHAPTER 5. Conclusion 154 5.1. Summary of contributions 154 5.2. Future work 157 Nomenclature 159 References 167 Abstract in Korean (국문초록) 174Docto

Integrated design of chemical waste water treatment systems.

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