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Tot i la seva senzillesa, la idea de la realimentació negativa (o "feedback" en anglès) és extremadament poderosa i ha tingut un gran impacte en la societat des de la revolució industrial ençà. En l'actualitat, els sistemes de control estan a tot arreu. A la indústria de processos, per exemple, s'encarreguen de mantenir les variables d'interès aprop dels valors de consigna. Encara més, els sistemes de control han de garantir aquests objectius tot i la presència d'incertesa en el procés i l'existència de pertorbacions. En aquest sentit, la realimentació representa un mecanisme essencial alhora de millorar tant la qualitat com l'eficiència energètica en molts processos de fabricació. El tema cabdal d'aquesta tesi consisteix en el disseny analític de compensadors (també anomenats controladors) fent servir l'esquema convencial en realimentació unitària. El marc adoptat és del control lineal i invariant en el temps (LTI). Encara que la realitat és de naturalesa no lineal, la simplificació al cas lineal no suposa una restricció greu ja que, localment, sempre podem considerar l'aproximació lineal del procés sota control. Posteriorment, el rang d'operació del compensador es pot extendre fent servir algun procediment de control adaptatiu. Des del punt de vista del disseny del controlador, l'escenari considerat planteja, entre d’altres, dos compromisos fonamentals. D'una banda, el controlador haurà de sel·leccionar-se per tal d'assolir un bon balanç entre rendiment i robustesa de modelat. D'altra banda, existeix també un conflicte entre el rendiment tipus "regulatori" (rebuig de pertorbacions) i el rendiment tipus "servo" (seguiment de la consigna), essent de vegades convenient trobar-ne un equilibri entre aquests dos modes de funcionament. L'objectiu d'aquesta tesi és proporcionar procediments de disseny analítics basats en un model de la planta i els compromisos de robustesa/rendiment i servo/regulació. A diferència d'altres mètodes, els procediments presentats eximeixen el dissenyador d'haver de pensar pesos o models de referència adients. A més, els paràmetres de sintonia tenen un significat intuitiu per tal de simplificar l'ajustament dels paràmetres del controlador. Com que els controladors de tipus Proporcional-Integral-Derivatiu (PID) continuen sent els més emprats en la pràctica, s'ha considerat l'aplicació a aquest tipus particular de controlador. Per últim, val a dir que l'apropament analític d'aquesta tesi permet determinar, de manera explícita, com els diferents compromisos considerats afecten l'el·lecció final del controlador. Aquesta característica, creiem, és també valuosa des del punt de vista docent. / La idea de la realimentación negativa (o "feedback" en inglés), si bien sencilla, es extremadamente poderosa y ha tenido un gran impacto en la sociedad desde la revolución industrial. En la actualidad, los sistemas de control están en todas partes. En la industria de procesos, por ejemplo, son los encargados de mantener las variables de interés próximas a los valores de consigna, todo ello pese a la incerteza en el proceso y las perturbaciones externas. En este sentido, la realimentación es la única manera de estabilizar una planta inestable, y se presenta así como un mecanismo esencial en procesos de fabricación con el fin de mejorar la calidad del producto final y la eficiencia energética. El tema central de esta tesis es el diseño analítico de compensadores (también llamados controladores) en realimentación. El marco de control adoptado es del control lineal e invariante en el tiempo (LTI). Aunque la realidad raramente es de naturaleza lineal, la restricción al caso LTI obedece a su simplicidad y al hecho de que, localmente, es siempre posible aproximar un proceso no lineal por otro lineal. Desde este punto de vista, el rango de operación del compensador puede extenderse posteriormente mediante planificación de ganancia o control adaptable. Respecto a la configuración de control, esta tesis considera el esquema convencional en realimentación unitaria. En el escenario considerado, tenemos por un lado que el controlador debe diseñarse para proporcionar un buen compromiso entre el rendimiento y la robustez ante incerteza en el proceso. Por otro lado, también existe un conflicto entre el rendimiento tipo "servo" (seguimiento de la referencia o consigna) y el rendimiento tipo "regulatorio" (rechazo de las perturbaciones), siendo a veces deseable encontrar un equilibrio entre ambos modos de funcionamiento. El objetivo de esta tesis es proporcionar procedimientos de diseño analíticos basados en un modelo del proceso y los compromisos de robustez/rendimiento y servo/regulación. En los métodos propuestos no es necesario que el diseñador seleccione pesos o modelos de referencia como pasa con otros enfoques. Además, los parámetros de sintonía tienen un significado intuitivo con el fin de simplificar el ajuste de los parámetros del controlador. Debido a que los controladores de tipo Proporcional-Integral-Derivativo (PID) son ampliamente utilizados en la industria, se ha considerado la aplicación a este tipo de controladores. Por último, mencionar que el enfoque analítico de la tesis permite plasmar, de forma explícita, cómo los diferentes compromisos considerados influyen en la elección final del compensador. Esta característica es también valiosa desde el punto de vista de la docencia del control automático. / The concept of (negative) feedback, albeit simple, is extremely powerful, and has since the Industrial Revolution changed our world dramatically. Nowadays, control systems are everywhere. In process industry, for example, they keep the manipulated variables close to the set-points in spite of disturbances and changes in the plant. Moreover, feedback provides the only means to stabilize unstable processes. This way, the feedback mechanism reveals essential for improving product quality and energy efficiency, which yields better (sustainable) economy. The theme of this thesis is on analytical design of feedback compensators through linear control theory. The restriction to the Linear Time Invariant (LTI) case is not severe in the sense that most processes are well modeled locally by LTI systems. The operating range of the controller can then be extended using gain scheduling or adaptation. Within this work, the standard single-loop feedback configuration is assumed. Among the control objectives, stability and robustness are important considerations because of the presence of uncertainty in practice. Apart from that, the controller faces servo (set-point tracking) and regulation (disturbance rejection) objectives. In the considered scenario, it is well-known that there is an inherent compromise between robustness and performance. In general, the servo and regulation objectives are also conflicting and sometimes a balance is desirable. An example is in cascade configurations: the inner loop should be tuned based on tracking as it receives the set-points from the master loop. However, the inner loop may also need acceptable load disturbance suppression capabilities. Another good example is found in Model Predictive Control (MPC) applications due to frequent changes of set-points by the server. Finally, there may be a trade-off between the response to disturbances entering at the input and at the output of the plant, which can be understood as a servo/regulator trade-off too. The goal of this thesis is to provide model-based design procedures in terms of the Robustness/Performance and Servo/Regulator trade-offs, and give insight into how the tuning depends on the process parameters. In the presented methods, the designer is not required to choose weighting functions nor reference models as in other approaches, and the involved parameters have a clear meaning to facilitate the tuning process. Because PID controllers are prevalent in industry, application to PID tuning is considered most of the times. Although numerical methods for controller derivation may yield superior performance than analytical ones, the latter category has been preferred for several reasons. First, analytical procedures help understand the problem at hand. Second, when applied to low-order models, well-motivated tuning rules which are simple and easy to memorize can be obtained. These features are very desirable from the operator's point of view as well as for teaching purposes.

In some turbochargers, boost pressure is reduced by opening the wastegate valve. In a modern turbo charged car, the most common way for opening the wastegate is with a pneumatic actuator and an air control solenoid, controlled by the ECU. In the control systems studied the ECU utilizes a static feedforward and a PID controller, for the purpose of making the boost pressure follow its reference value. With no systematic method for tuning the controller, this can be time consuming, and a set of well defined experiments to determine PID parameters are desired.When test time in a real engine is limited or expensive, it is advantageousto work in a simulation environment before doing live tests. A model for thewastegate actuator and air control solenoid is developed in the thesis. This is used to simulate controller performance before any tests in a real car is performed.In the thesis a tuning method for the PID controller based on step responsesis proposed. The tuning method evaluated is the IMC-choice of controller fora second order system, and it has a single design parameter not given by theexperiments. The controller is shown to give desired behavior when the staticfeedforward is correct or has small error.

Control of a diesel engine equipped with Variable Geometry Turbine (VGT) and Exhaust Gas Recirculation (EGR) requires a multivariable control method. One problem is that the engine system is non-linear. Furthermore there are strong cross-connections between inputs and outputs and the inputs have alsoboundaries. To be able to manage these control problems, MPC has been used that is a multivariable method. The MPC-controller consists of an optimization problem and therefore MPC can find the optimum control signals in an easy way. Furthermore the boundaries of the control signals can be handled with by-conditions in the optimization. The disadvantage with MPC is that it requires a lot of amount of calculations and memory, which are important factors when a control system should be implemented. Therefore it has been chosen to compare MPC with PID, that is a common and simpler method. The results from this thesis are that MPC is a method that gives more optimal and faster control. Furthermore MPC can handle different control cases much better, without changing the settings. On the other hand PID requires considerable fewer amounts of calculations and memory. In one case that has been examined, MPC requires 40 times more amounts of calculations than PID. To be able to control a non-linear system, both MPC and PID must be implemented in several different working points. Furthermore decoupling must be used in the PID-controller to be able to manage cross-connections that seems to be a very important problem.

This thesis aims to cover some aspects of synthesis and design of Proportional- Integral-Derivative (PID) controllers. The topics include computer aided design of discrete time controllers, data-based design of discrete PID controllers and data- robust design of PID controllers. These topics are of paramount in control systems literature where a lot of stress is laid upon identification of plant and robust design. The computer aided design of discrete time controllers introduces a Graphical User Interface (GUI) based software. The controllers are: Proportional (P), Proportional-Derivative (PD),Proportional-Integral (PI) and Proportional-Integral- Derivative (PID) controllers. Different performance based design methods with these controllers have been introduced. The user can either explore the performance by interactively choosing controllers one by one from the entire set and visualizing its performance or specify some performance constraints and obtaining the resulting set. In data-based design, the thesis presents a way of designing PID controllers based on input-output data. Thus, the intermediate step of identification of model from data is removed, saving considerable effort. Moreover, the data required is step response data which is easier to obtain in case of discrete time system than frequency response data. Further, a GUI developed for interactive design is also described. In data-robust design, the problem of uncertainty in data is explored. The design method developed finds the stabilizing set which can robustly stabilize the plant with uncertainty. It has been put forward as an application to interval linear programming. The main results of this research include a new way of designing discrete time PID controllers directly from the data. The simulations further confirm the results. Robust design of PID controllers with data uncertainty has also been established. Additionally, as a part of this research, a GUI based software has been developed which is expected to be very beneficial to the designers in manufacturing, aerospace and petrochemical industries. PID controllers are widely used in the industry. Any progress in this field is well acknowledged both in the industry and the academia alike. This thesis attempts a small step further in this direction.

Since uncertainty exists inevitably in control systems, it is questionable whether the controller, designed to compensate a nominal plant well, still guarantees the criteria of robust stability and robust H¡Û performance for the perturbed plant. In this thesis, controller parameters tuning based on the sensitivity concept of structured singular value, called £g-sensitivity, will be adopted to do the parameter adjustment so that, when the influence of uncertainty is considered, the robust stability and robust performance properties of the nominal closed-loop system will be preserved. In view of the time consuming effect of numerical computation and the misjudgment due to discontinuity problem involved in the £g-sensitivity analysis, this thesis proposes the sensitivity concept of skewed structured singular value, called £h-sensitivity, to remedy these drawbacks. Finally, the feasibility of the £h-sensitivity based controller parameters tuning technique is verified by the simulation results of two examples.

controllers for discrete-time systems and time-delayed systems. By using bilinear transformation and orthogonal transformation, earlier research results obtained in the continuous-time case are extended to discrete-time situation. The complete set of stabilizing PID controllers for the discrete-time systems is thus obtained. Moreover, this set remains to be a union of convex sets when one particular parameter is fixed. Thus a method to design robust and non-fragile digital PID controllers is proposed by following a similar design procedure for the continuous-time systems. In order to find the stabilizing controller set for systems with time-delays, the relationship between the Nyquist Criterion and Pontryagin’s theory is investigated. The conditions under which one can correctly apply the Nyquist Criterion to time-delayed systems are derived. Then, the complete set of stabilizing PID controllers for arbitrary order LTI systems with time-delay up to a given value is obtained. Furthermore, the stability issue of a system with fixed-delay is also studied and a formula which provides complete knowledge of the distribution of the closed-loop poles is presented. Based on this formula, stabilizing P and PI controller sets for the system with fixed-delay can be computed.

This thesis proposes an interactive software tool that can be used to compute complete sets of Proportional Integral Derivative (PID) Controllers from knowledge of the plant transfer function/frequency response data. This is based on research results and algorithms developed by Bhattacharyya and others. Until these research results were published, it was not known if a nominal system could be stabilized using PID Controllers, and current PID Controller designs are carried out using ad hoc tuning rules. By using simulations, engineers can best plan for and observe the stabilizing effect each of the variables has on system performance in a realistic environment. The software application developed calculates and optimizes complete stabilizing sets of PID Controllers for a rational Linear Time Invariant (LTI) system, and has been developed for analytical models of plants with and without time delay. Further, these PID Controller sets are optimized to project subsets simultaneously satisfying multiple performance index specifications. Sets of PID Controllers that stabilize a system are also calculated automatically from knowledge of the frequency response of the plant. It allows the user ease of design and the ability to customize the final solution while permitting full control over source parameters. This thesis includes an introduction to the algorithms that have been developed for plant stabilization, a complete description of the graphical user interface, the simulation of the algorithms performed using LabVIEW, and a summary of future work.

This thesis aims to cover some aspects of synthesis and design of Proportional- Integral-Derivative (PID) controllers. The topics include computer aided design of discrete time controllers, data-based design of discrete PID controllers and data- robust design of PID controllers. These topics are of paramount in control systems literature where a lot of stress is laid upon identification of plant and robust design. The computer aided design of discrete time controllers introduces a Graphical User Interface (GUI) based software. The controllers are: Proportional (P), Proportional-Derivative (PD),Proportional-Integral (PI) and Proportional-Integral- Derivative (PID) controllers. Different performance based design methods with these controllers have been introduced. The user can either explore the performance by interactively choosing controllers one by one from the entire set and visualizing its performance or specify some performance constraints and obtaining the resulting set. In data-based design, the thesis presents a way of designing PID controllers based on input-output data. Thus, the intermediate step of identification of model from data is removed, saving considerable effort. Moreover, the data required is step response data which is easier to obtain in case of discrete time system than frequency response data. Further, a GUI developed for interactive design is also described. In data-robust design, the problem of uncertainty in data is explored. The design method developed finds the stabilizing set which can robustly stabilize the plant with uncertainty. It has been put forward as an application to interval linear programming. The main results of this research include a new way of designing discrete time PID controllers directly from the data. The simulations further confirm the results. Robust design of PID controllers with data uncertainty has also been established. Additionally, as a part of this research, a GUI based software has been developed which is expected to be very beneficial to the designers in manufacturing, aerospace and petrochemical industries. PID controllers are widely used in the industry. Any progress in this field is well acknowledged both in the industry and the academia alike. This thesis attempts a small step further in this direction.

<p>Control of a diesel engine equipped with Variable Geometry Turbine (VGT) and Exhaust Gas Recirculation (EGR) requires a multivariable control method. One problem is that the engine system is non-linear. Furthermore there are strong cross-connections between inputs and outputs and the inputs have alsoboundaries. To be able to manage these control problems, MPC has been used that is a multivariable method. The MPC-controller consists of an optimization problem and therefore MPC can find the optimum control signals in an easy way. Furthermore the boundaries of the control signals can be handled with by-conditions in the optimization. The disadvantage with MPC is that it requires a lot of amount of calculations and memory, which are important factors when a control system should be implemented. Therefore it has been chosen to compare MPC with PID, that is a common and simpler method. </p><p>The results from this thesis are that MPC is a method that gives more optimal and faster control. Furthermore MPC can handle different control cases much better, without changing the settings. On the other hand PID requires considerable fewer amounts of calculations and memory. In one case that has been examined, MPC requires 40 times more amounts of calculations than PID. To be able to control a non-linear system, both MPC and PID must be implemented in several different working points. Furthermore decoupling must be used in the PID-controller to be able to manage cross-connections that seems to be a very important problem.</p>