Design of PID Controllers Satisfying Gain Margin and Sensitivity Constraints on a Set of Plants

This paper presents a method for the design of PID-type controllers, including those augmented by a filter on the D element, satisfying a required gain margin and an upper bound on the (complementary) sensitivity for a finite set of plants. Important properties of the method are: (i) it can be applied to plants of any order including non-minimum phase plants, plants with delay, plants characterized by quasi-polynomials, unstable plants and plants described by measured data, (ii) the sensors associated with the PI terms and the D term can be different (i.e., they can have different transfer function models), (iii) the algorithm relies on explicit equations that can be solved efficiently, (iv) the algorithm can be used in near real-time to determine a controller for on-line modification of a plant accounting for its uncertainty and closed-loop specifications, (v) a single plot can be generated that graphically highlights tradeoffs among the gain margin, (complementary) sensitivity bound, low-frequency sensitivity and high-frequency sensor noise amplification, and (vi) the optimal controller for a practical definition of optimality can readily be identified

Robust PI Controller Design Satisfying Gain and Phase Margin Constraints

This paper presents a control design algorithm for determining PI-type controllers satisfying specifications on gain margin, phase margin, and an upper bound on the (complementary) sensitivity for a finite set of plants. Important properties of the algorithm are: (i) it can be applied to plants of any order including plants with delay, unstable plants, and plants given by measured data, (ii) it is efficient and fast, and as such can be used in near real-time to determine controller parameters (for on-line modification of the plant model including its uncertainty and/or the specifications), (iii) it can be used to identify the optimal controller for a practical definition of optimality, and (iv) it enables graphical portrayal of design tradeoffs in a single plot (highlighting tradeoffs among the gain margin, complementary sensitivity bound, low frequency sensitivity and high frequency sensor noise amplification)

Feedback Control of Human Stress with Music Modulation

Mental stress has known detrimental effects on human health, however few algorithmic methods of reducing mental stress have been widely explored. While the act of listening to music has been shown to have beneficial effects for stress reduction, and furthermore, audio players have been designed to selectively choose music and other inputs with the intent of stress reduction, limited work has been conducted for real-time stress reduction with feedback control using physiological input signals such as heart rate or Heart Rate Variability (HRV). This thesis proposes a feedback controller that uses HRV signals from wearable sensors to perform real-time (< 1 second) modulations to music through tempo changes with the goal to regulate and reduce stress levels. A standardized, stress inducing test based on the popular Stroop test is also introduced, which has been shown to induce acute stress in subjects and can be used as a testing benchmark for controller design. Ultimately, a controller is presented that when used is not only able to maintain stress levels during stress-inducing inputs to a human but even provides de-stressing effects beyond baseline performance.No embargoAcademic Major: Electrical and Computer Engineerin

Design of Nonlinear PID Controllers and Their Application to a Heat Exchanger System for LNG-fuelled Marine Engines

Excessive use of fossil fuels resources is adding several types of greenhouse gases which make the earth warmer. Emissions from ship's exhausts contribute to global climate change, too. The International Maritime Organization (IMO) has adopted regulations to reduce the emission of air pollutants from international shipping, such as major air pollutants, carbon dioxide (CO2), nitrogen oxides (NOx), and sulphur oxides (SOx) under Annex VI of the 1997 MARPOL protocol. Likewise, as regulations on the emission of major air pollutants have become internationally strict, the development of environmentally friendly vessels and engines is required. One of the globally accepted means of reducing emission gases is the use of more eco-friendly fuel, LNG (Liquefied Natural Gas). LNG as a marine fuel reduces air pollutants as referred compared to traditional heavy fuel oil (HFO). Recently, large engine manufacturers are developing LNG-fuelled marine engines. In order to use this cryogenic LNG as a fuel, it is necessary to change it back to a gaseous state. A heat exchanger is used to regasify LNG. The heat exchange takes place between LNG and glycol on the primary loop, and heat exchange occurs between glycol and steam on the secondary loop. These series of processes are called LNG regasification. To control the temperature of the heat exchanger, it is necessary to model the heat exchanger. However, it is not easy to obtain an accurate mathematical model because the heat exchanger has non-linearity and time-varying characteristics. In addition, a fixed-gain controller is bound to have a limitation in its function if parameters of the heat exchanger are changed. Thus, various techniques have been studied to improve the adaptability and robustness of the controller. Recently, there has been using nonlinear PID (NPID) controller for the controlled system which have highly nonlinear and time-varying characteristics during operation. Therefore, this thesis proposes two types of the nonlinear proportional, integral, derivative (NPID) controllers to control the glycol temperature of the regasification system for LNG-fuelled marine engines. The Fully-Nonlinear PID (F-NPID) controller has a structure that the error between the set-point (or reference input) and output (or the measured output) is scaled nonlinearly, and input into the controller to derive proportional, integral, and derivative controllers. The Partial-Nonlinear PID (P-NPID) controller uses the conventional linear PD controller and only I controller uses the method of F-NPID controller. In this case, the nonlinear functions are implemented by the Fuzzy model of Takagi-Sugeno (T-S) type. In addition, the error is continuously scaled so that outstanding control performance can be maintained even when the operating environment is changed, thereby improving the swiftness and the closeness of responses. Also, the parameters of the two proposed controllers are optimally tuned in terms of minimizing the integral of the absolute error (IAE) objective function based on the genetic algorithm (GA). Meanwhile, it is necessary to examine the stability of overall feedback system that can be caused by introducing nonlinear functions during controller design. For this, the stability of the overall feedback system is analyzed by applying the circle stability theorems, which is often used for stability analysis of nonlinear problems. The proposed controllers are verified their performances which are the set-point tracking, robustness against noise and parameter changes, disturbance rejection performances by comparing with two conventional PID controllers and a conventional NPID controller.Chapter 1. Introduction 1 1.1 Research background and trends 1 1.2 Research content and composition 6 Chapter 2. LNG-fuelled Marine Engines 8 2.1 Changes of LNG-fuelled marine engines 8 2.2 Fuel injection of LNG-fuelled marine engines 10 2.3 Fuel supply system of LNG-fuelled marine engines 13 Chapter 3. Modeling of LNG Regasification System 17 3.1 Heat exchanger 17 3.2 LNG regasification system 18 3.3 Modeling of the secondary loop heat exchanger of LNG regasification system 19 3.3.1 Model of an I/P converter 19 3.3.2 Model of a pneumatic control valve 20 3.3.3 Model of a heat exchanger 23 3.3.4 Model of a disturbance 27 3.3.5 Model of a RTD sensor 28 3.3.6 Model of a time delay 29 3.3.7 Open-loop control system 30 Chapter 4. Surveys of Existing PID Controllers 32 4.1 Linear PID controller 32 4.1.1 Structure of the conventional PID controller 32 4.1.2 Characteristics of control actions 33 4.1.3 Effects of PID controller gains 36 4.2 Gain tuning of the conventional PID controller 37 4.2.1 Ziegler-Nichols tuning method 37 4.2.2 Tyreus-Luyben tuning method 40 4.3 Practical PID controller 41 4.4 Existing nonlinear PID controllers 44 4.4.1 Seraji’s NPID controller 45 4.4.2 Korkmaz’s NPID controller 48 Chapter 5. Suggestion of the Proposed Nonlinear PID Controllers 52 5.1 Fully-nonlinear PID controller 52 5.1.1 Nonlinear P block 53 5.1.2 Nonlinear D block 57 5.1.3 Nonlinear I block 57 5.1.4 Relationship between and 60 5.2 Partially-nonlinear PID controller 62 5.2.1 Linear PD block 63 5.2.2 Nonlinear I block 63 5.3 Feedback control systems 63 5.3.1 Modified F-NPID control system 63 5.3.2 P-NPID control system 66 5.4 Tuning of the controller parameters 68 5.4.1 Genetic algorithm 68 5.4.2 Optimal tuning of the controller parameters 73 Chapter 6. Stability Analysis 75 6.1 System description 75 6.2 Basic definitions and theorems 76 6.3 Stability of the NPID control systems 86 6.3.1 Sector condition of nonlinear block 86 6.3.2 Stability analysis of F-NPID control system 87 6.3.3 Stability analysis of P-NPID control system 88 Chapter 7. Simulation and Discussion of Results 90 7.1 Controller parameter tuning 90 7.2 Reponses to set-point changes 91 7.3 Reponses to noise rejection 94 7.4 Reponses to system parameter changes 95 7.5 Reponses to disturbance changes 97 Chapter 8. Conclusion 99 References 101Docto

Gain tuning of proportional integral controller based on multiobjective optimization and controller hardware-in-loop microgrid setup

Proportional integral (PI) control is a commonly used industrial controller framework. This PI controller needs to be tuned to obtain desired response from the process under control. Tuning methods available in literature by and large need sophisticated mathematical modelling, and simplifications in the plant model to perform gain tuning. The process of obtaining approximate plant model conceivably become time consuming and produce less accurate results. This is due to the simplifications desired by the power system applications especially when power electronics based inverters are used in it. Optimal gain selection for PI controllers becomes crucial for microgrid application. Because of the presence of inverter based distributed energy resources. In the proposed approach, a multi-objective genetic algorithm is used to tune the controller to obtain expected step response characteristics. The proposed approach do not need simplified mathematical models. This prevents the need for obtaining unfailing plant models to maintain the fidelity of modelling. Microgrid system and the PI controller are modelled in different software, hardware platform and tuned using the proposed approach. Gain values for PI controller in these different platform are tuned using the same objective function and multi-objective optimization. This proves the re-usability, scalability, and modularity of the proposed tuning algorithm. Three different combination of software, hardware platform are proposed. First, the process and the PI controller are modelled in a computer based hardware. In order to increase the speed of the multi-objective optimization in the computer based hardware parallel computing is employed. This is a natural fit for paralleling the GA based optimization. Second, both the plant and control representation are modelled in the real time digital simulator (RTDS). Finally, a controller hardware in loop platform is used. In this platform, the plant will be modelled in RTDS and the PI controller will be modelled in an FPGA based hardware platform. Results indicate that the proposed approach has promising potentials since it does not need to simplify the switching model and can effectively solve the complicated tuning procedure using parallel computing. Similar advantage could be said for RTDS based tuning because RTDS simulates the models in real time

Tuning of resonant controllers based on the frequency response

Resonant controllers are introduced to fulfil the increased demand for controllers capable to follow or reject periodic signals with superior performance than conventional PID ones. The main characteristic of these controllers is the infinite gain in the frequency of interest, which can lead to stability problems and makes their tuning more complex. This work presents the computation of resonant controllers parameters based on a frequency response method, using stability margins and sensitivity functions as indicators of performance and stability for the controlled system. In addition, the combination with a phase-lead compensator is proposed to allow better performance in an augmented bandwidth. The method is extended for multiple frequency modes in order to deal with higher harmonic content, resulting in the multi-resonant controller. The proposed method is tested using different classes of processes found in typical control problems in order to illustrate its wide applicability.Controladores ressonantes são introduzidos para atender à demanda crescente por controladores capazes de seguir ou rejeitar sinais periódicos com desempenho superior ao dos controladores PID convencionais. A principal característica destes controladores é o ganho infinito na frequência de interesse, o que pode levar a problemas de estabilidade e torna o seu projeto e sintonia mais complexos. Este trabalho apresenta um método para a sintonia dos parâmetros de controladores ressonantes baseada em um método de resposta em frequência, usando as margens de estabilidade e as funções sensibilidade como indicadores de desempenho e estabilidade para o sistema controlado. Além disso, a combinação com um compensador de avanço de fase é proposta para possibilitar desempenho superior em uma maior largura de banda. O método é então estendido para múltiplos modos de frequência a fim de considerar sinais de referência ou perturbação com maior conteúdo harmônico, resultando no controlador multirressonante. O método proposto é testado usando diferentes classes de processos encontrados em problemas típicos de controle para demonstrar sua vasta aplicabilidade

Proportional-Integral-Plus Control Strategy of an Intelligent Excavator

This article considers the application of Proportional-Integral-Plus (PIP) control to the Lancaster University Computerised Intelligent Excavator (LUCIE), which is being developed to dig foundation trenches on a building site. Previous work using LUCIE was based on the ubiquitous PI/PID control algorithm, tuned on-line, and implemented in a rather ad hoc manner. By contrast, the present research utilizes new hardware and advanced model-based control system design methods to improve the joint control and so provide smoother, more accurate movement of the excavator arm. In this article, a novel nonlinear simulation model of the system is developed for MATLAB/SIMULINK, allowing for straightforward refinement of the control algorithm and initial evaluation. The PIP controller is compared with a conventionally tuned PID algorithm, with the final designs implemented on-line for the control of dipper angle. The simulated responses and preliminary implementation results demonstrate the feasibility of the approach