Design of Low-Order Controllers using Optimization Techniques

In many applications, especially in the process industry, low-level controllers are the workhorses of the automated production lines. The aim of this study has been to provide simple tuning procedures, either optimization-based methods or tuning rules, for design of low-order controllers. The first part of this thesis deals with PID tuning. Design methods or both SISO and MIMO PID controllers based on convex optimization are presented. The methods consist of solving a nonconvex optimization problem by deriving convex approximations of the original problem and solving these iteratively until convergence. The algorithms are fast because of the convex approximations. The controllers obtained minimize low-frequency sensitivity subject to constraints that ensure robustness to process variations and limitations of control signal effort. The second part of this thesis deals with tuning of feedforward controllers. Tuning rules that minimize the integrated-squared-error arising from measurable step disturbances are derived for a controller that can be interpreted as a filtered and possibly time-delayed PD controller. Using a controller structure that decouples the effects of the feedforward and feedback controllers, the controller is optimal both in open and closed loop settings. To improve the high-frequency noise behavior of the feedforward controller, it is proposed that the optimal controller is augmented with a second-order filter. Several aspects on the tuning of this filter are discussed. For systems with PID controllers, the response to step changes in the reference can be improved by introducing set-point weighting. This can be interpreted as feedforward from the reference signal to the control signal. It is shown how these weights can be found by solving a convex optimization problem. Proportional set-point weight that minimizes the integrated-absolute-error was obtained for a batch of over 130 different processes. From these weights, simple tuning rules were derived and the performance was evaluated on all processes in the batch using five different feedback controller tuning methods. The proposed tuning rules could improve the performance by up to 45% with a modest increase in actuation

Control of Multiple Remote Servers for Quality-Fair Delivery of Multimedia Contents

This paper proposes a control scheme for the quality-fair delivery of several encoded video streams to mobile users sharing a common wireless resource. Video quality fairness, as well as similar delivery delays are targeted among streams. The proposed controller is implemented within some aggregator located near the bottleneck of the network. The transmission rate among streams is adapted based on the quality of the already encoded and buffered packets in the aggregator. Encoding rate targets are evaluated by the aggregator and fed back to each remote video server (fully centralized solution), or directly evaluated by each server in a distributed way (partially distributed solution). Each encoding rate target is adjusted for each stream independently based on the corresponding buffer level or buffering delay in the aggregator. Communication delays between the servers and the aggregator are taken into account. The transmission and encoding rate control problems are studied with a control-theoretic perspective. The system is described with a multi-input multi-output model. Proportional Integral (PI) controllers are used to adjust the video quality and control the aggregator buffer levels. The system equilibrium and stability properties are studied. This provides guidelines for choosing the parameters of the PI controllers. Experimental results show the convergence of the proposed control system and demonstrate the improvement in video quality fairness compared to a classical transmission rate fair streaming solution and to a utility max-min fair approach

An automatic tuner with short experiment and probabilistic plant parameterization

A novel automatic tuning strategy is proposed. It is based on an experiment of very short duration, followed by simultaneous identification of LTI model parameters and an estimate of their error covariance. The parametric uncertainty model is subsequently exploited to design linear controllers with magnitude bounds on some closed-loop transfer function of interest, such as the sensitivity function. The method is demonstrated through industrially relevant examples. Robustness is enforced through probabilistic constraints on the H∞ norms of the sensitivity function, while minimizing load disturbance integral error (IE) to ensure performance. To demonstrate the strength of the proposed method, identification for the mentioned examples is carried out under a high level of measurement noise

Further results on fractional order control of a mechatronic system

Ovaj rad predstavlja jedan novi algoritam PID upravljanja necelobrojnog reda zasnovani na genetskim algoritmima (GA) u zadatku pozicioniranja robotskog sistema sa tri stepena slobode pogonjen jednosmernim motorima. Urađena su optimalna podešavanja parametara FOPID kontrolera kao i IOPID kontrolera, primenom GA pristupa za date FOPID/IOPID kontrolere na uporedni način. Efektivnost predloženog optimalnog FOPID upravljanja je demonstrirano na datom robotskom sistemu kao jednim ilustrativnim primerom. Takođe, u preostalom delu rada prezentovano je projektovanje naprednog algoritma FOPID upravljanja podešavanog primenom GA i primena u upravljanju proizvodnjom tehničkih gasova, tj. kriogenog procesa separacije vazduha. Zatim je izvedeni model linearizovan i raspregnut i gde su zatim primenjeni IOPID i FOPID kontroleri. Na sličan način, skup optimalnih parametara datih kontrolera su dobijeni primenom GA optimizacione procedure minimizujući predloženi kriterijum optimalnosti. Konačno, koristeći rezultate simulacije u vremenskom domenu pokazano je da FOPID kontroler poboljšava odgovor sistema u prelaznom režimu i obezbeđuje više robusnosti u poređenju sa klasičnim IOPID kontrolerom.This paper presents a new algorithm of the fractional order PID (FOPID) control based on genetic algorithms (GA) in the position control of a 3 DOF's robotic system driven by DC motors. The optimal settings for a FOPID controller as well as an integer order PID controller (IOPID) are done, applying the GA tuning approach and their extension for FOPID-IOPID controllers in a comparative manner. The effectiveness of the suggested optimal FOPID control is demonstrated with a given robotic system as an illustrative example. The rest of the paper presents the design of an advanced algorithm of the FOPID control tuned by GA and the application in the control of the production of technical gases, i.e. in the cryogenic air separation process. Then, the obtained model is linearized and decoupled and consequently IOPID and FOPID controllers are applied. In the same manner, a set of optimal parameters of these controllers is achieved through the GA optimization procedure through minimizing the proposed cost function. Finally, the use of the simulation results in the time domain has shown that the FOPID controller improves a transient response and provides more robustness than a conventional IOPID

Multi-objective Optimization of Multi-loop Control Systems

Cascade Control systems are composed of inner and outer control loops. Compared to the traditional single feedback controls, the structure of cascade controls is more complex. As a result, the implementation of these control methods is costly because extra sensors are needed to measure the inner process states. On the other side, cascade control algorithms can significantly improve the controlled system performance if they are designed properly. For instance, cascade control strategies can act faster than single feedback methods to prevent undesired disturbances, which can drive the controlled system’s output away from its target value, from spreading through the process. As a result, cascade control techniques have received much attention recently. In this thesis, we present a multi-objective optimal design of linear cascade control systems using a multi-objective algorithm called the non-dominated sorting genetic algorithm (NSGA-II), which is one of the widely used algorithms in solving multi-objective optimization problems (MOPs). Two case studies have been considered. In the first case, a multi-objective optimal design of a cascade control system for an underactuated mechanical system consisting of a rotary servo motor, and a ball and beam is introduced. The setup parameters of the inner and outer control loops are tuned by the NSGA-II to achieve four objectives: 1) the closed-loop system should be robust against inevitable internal and outer disturbances, 2) the controlled system is insensitive to inescapable measurement noise affecting the feedback sensors, 3) the control signal driving the mechanical system is optimum, and 4) the dynamics of the inner closed-loop system has to be faster than that of the outer feedback system. By using the NSGAII algorithm, four design parameters and four conflicting objective functions are obtained. The second case study investigates a multi-objective optimal design of an aeroelastic cascade controller applied to an aircraft wing with a leading and trailing control surface. The dynamics of the actuators driving the control surfaces are considered in the design. Similarly, the NSGA-II is used to optimally adjust the parameters of the control algorithm. Ten design parameters and three conflicting objectives are considered in the design: the controlled system’s tracking error to an external gust load should be minimal, the actuators should be driven by minimum energy, and the dynamics of the closed-loop comprising the actuators and inner control algorithm should be faster than that of the aeroelastic structure and the outer control loop. Computer simulations show that the presented case studies may become the basis for multi-objective optimal design of multi-loop control systems

A survey of recent advances in fractional order control for time delay systems

Several papers reviewing fractional order calculus in control applications have been published recently. These papers focus on general tuning procedures, especially for the fractional order proportional integral derivative controller. However, not all these tuning procedures are applicable to all kinds of processes, such as the delicate time delay systems. This motivates the need for synthesizing fractional order control applications, problems, and advances completely dedicated to time delay processes. The purpose of this paper is to provide a state of the art that can be easily used as a basis to familiarize oneself with fractional order tuning strategies targeted for time delayed processes. Solely, the most recent advances, dating from the last decade, are included in this review

Real time observer and control scheme for a wind turbine system based on a high order sliding modes

The introduction of advanced control algorithms may improve considerably the efficiency of wind turbine systems. This work proposes a high order sliding mode (HOSM) control scheme based on the super twisting algorithm for regulating the wind turbine speed in order to obtain the maximum power from the wind. A robust aerodynamic torque observer, also based on the super twisting algorithm, is included in the control scheme in order to avoid the use of wind speed sensors. The presented robust control scheme ensures good performance under system uncertainties avoiding the chattering problem, which may appear in traditional sliding mode control schemes. The stability analysis of the proposed HOSM observer is provided by means of the Lyapunov stability theory. Experimental results show that the proposed control scheme, based on HOSM controller and observer, provides good performance and that this scheme is robust with respect to system uncertainties and external disturbances.The authors are very grateful to the Basque Government by its support through the project EKOHEGAZ (ELKARTEK KK-2021/00092), to the Diputacion Foral de Alava (DFA) by its support through the project CONAVANTER, to Gipuzkoako Foru Aldundia by its support through the project Etorkizuna Eraikiz 2019, and to the UPV/EHU by its support through the project GIU20/063

Controller Tuning Using System Identification

In the industries today, less attention has been put on the development of a unified tuning approach for Proportional-Integral-Derivative (PID) controller of Single Input Single Output (SISO) system and Multiple Input Multiple Output (MIMO) system. The current tuning methods are limited and specific to particular systems. This paper focuses on the development of a unified controller tuning method based on Internal Model Control (IMC) method and system identification using software Matlab Simulink. The controller tuning performance of the proposed method tested on SISO and MIMO systems are being compared with the performance shown by the existing tuning methods; Ziegler-Nichols (ZN) and Simple Internal Model Control (SIMC). The evaluation of performance measurement is done based on Integral Absolute Error (IAE), Integral Square Error (ISE), Integral Time-weighted Absolute Error (ITAE) and Total Input Variation (TV). It is observed that the proposed unified tuning method is effective for tuning on SISO and MIMO systems and gives better performance than ZN and SIMC in terms of IAE, ISE, ITAE and TV in both set point tracking and disturbance rejection