A project report submitted to the Faculty of Engineering, University of the Witwatersrand, Johannesburg, in partial fulfilment of the requirements for the degree of Master of Science in Engineering. / Up to now the benefits and problems with fuzzy control have not been fully identified and its role in the control domain needs investigation. The past trend has been to show that a fuzzy controller can provide better control than classical control, without examining what is actually being achieved. The aim in this project report is to give a fair comparison between classical and fuzzy control. Robustness, disturbance rejection, noise suppression" nonminimurn phase and dead time are examined for both controllers. The comparison is performed through computer simulation of classical and fuzzy controlled plant models. Fuzzy control has the advantage of non-linear performance and the ability to capture linguistic information. Translating quantitative information into the fuzzy domain is difficult; therefore when the system is easily mathematically modelled and linear, classical control is usually better. Which controller should be used depends on the application, control designer and information available. / Andrew Chakane 2018

by Lee Wai Man. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1995. / Includes bibliographical references (leaves 118-[124]). / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Introduction --- p.1 / Chapter 1.2 --- Review of Previous Work --- p.3 / Chapter 1.3 --- Scope of the Thesis --- p.4 / Chapter 2 --- Background Knowledge of Fuzzy Control System --- p.7 / Chapter 2.1 --- Introduction --- p.7 / Chapter 2.2 --- Fuzzy Sets --- p.7 / Chapter 2.2.1 --- Properties of Fuzzy Sets --- p.10 / Chapter 2.2.2 --- Operations on Fuzzy Sets --- p.13 / Chapter 2.3 --- Fuzzy Models --- p.14 / Chapter 2.3.1 --- Linguistic Model --- p.15 / Chapter 2.3.2 --- Takagi-Sugeno-Kang (TSK) Fuzzy Model --- p.16 / Chapter 2.4 --- Fuzzy Inference System --- p.17 / Chapter 2.4.1 --- Fuzzifier --- p.18 / Chapter 2.4.2 --- Knowledge Base --- p.19 / Chapter 2.4.3 --- Inference Engine --- p.19 / Chapter 2.4.4 --- Defuzzifier --- p.20 / Chapter 2.4.5 --- Product-Sum-Gravity Inference --- p.21 / Chapter 3 --- Decomposition of Fuzzy Rules --- p.25 / Chapter 3.1 --- Introduction --- p.25 / Chapter 3.2 --- Decomposability of Fuzzy Inference System --- p.26 / Chapter 3.3 --- The Decomposability condition --- p.29 / Chapter 3.4 --- Determining Decomposed Parameters --- p.32 / Chapter 3.5 --- Decomposable Approximation --- p.35 / Chapter 3.5.1 --- Linear Approximation --- p.38 / Chapter 3.5.2 --- Case Study --- p.40 / Chapter 3.6 --- Limitation of Decomposable Approximation --- p.42 / Chapter 3.7 --- Approximation Index --- p.44 / Chapter 3.7.1 --- Case Study --- p.48 / Chapter 3.8 --- Decomposable TSK Model --- p.52 / Chapter 3.8.1 --- Case Study --- p.54 / Chapter 3.9 --- Conclusion --- p.56 / Chapter 4 --- Fuzzy Identification --- p.58 / Chapter 4.1 --- Introduction --- p.58 / Chapter 4.2 --- Least-squares Estimation --- p.59 / Chapter 4.3 --- LSE Formulation of Various Fuzzy Models --- p.63 / Chapter 4.3.1 --- Linguistic Model --- p.63 / Chapter 4.3.2 --- TSK Model --- p.69 / Chapter 4.3.3 --- Decomposable System --- p.75 / Chapter 4.3.4 --- Comparative Case Study --- p.79 / Chapter 4.4 --- Fuzzy Regional System Identification --- p.81 / Chapter 4.4.1 --- Case Study --- p.86 / Chapter 4.5 --- Recursive Estimation --- p.86 / Chapter 4.5.1 --- Case Study --- p.90 / Chapter 4.6 --- Conclusion --- p.90 / Chapter 5 --- Performance-Based Fuzzy Gain Controller --- p.92 / Chapter 5.1 --- Introduction --- p.92 / Chapter 5.2 --- Conventional Fuzzy Control --- p.93 / Chapter 5.3 --- Fuzzy Gain Control --- p.95 / Chapter 5.4 --- Design Algorithm --- p.97 / Chapter 5.5 --- Stability Design Approach --- p.98 / Chapter 5.6 --- Simulation Case Study --- p.102 / Chapter 5.7 --- Conclusion --- p.106 / Chapter 6 --- Identification/Control Design Example --- p.107 / Chapter 7 --- Conclusion --- p.115 / Bibliography --- p.118

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<p>The aim of the thesis is to develop and describe WRAP’s capabilities in handling the WiMAX standard as defined in IEEE 802.16e related to traffic capacity calculations. WRAP International has developed the software WRAP for spectrum management and radio network planning. WRAP includes various technical calculation functions that are applied for design and analysis tasks with the purpose of achieving the desired quality of service within radio communication networks, navigation and radar systems. WRAP already includes functions for radio wave calculations to establish for instance coverage; best server maps etc, as well as traffic calculations for cellular networks (2G) using channel-orientated calculations that are modeled by Erlang B and Erlang C formulas. Since WiMAX supports multiple broadband data services including voice, video, web data, interactive network gaming and streaming media so there is a need to build a tool for the estimation of WiMAX traffic capacity calculations. Some methods and algorithms are analyzed and a tool has been built to ease the network planner’s job. It works based upon the calculations and algorithm presented in the report. Total number of users and data rate supported by a base station is calculated and total number of base stations, required for the coverage of a specific area is determined. This new tool is compatible with WRAP’s current functions.</p>

<p>Från Sjövärnskåren division syd, underavdelning Blekinge, inkom en förfrågan om att göra en undersökning och projektering till ett digitalt maskinövervakningssystem.</p><p>Syftet med maskinövervakningssystemet är att det ska vara lättare för de som tränas ombord att ta till sig maskineriets kondition. Detta kommer att bidra till att minska underhållskostnaderna genom att förbättra övervakningen under drift, för att undvika oönskade driftfall, och dels att förbättra driftsdokumentationen som underlag för beslut om underhållsåtgärder/-intervaller.</p><p>Projektet innebar en föreberedande undersökning av vilken utrustning som behövs till det nya systemet samt för att få en kostnadsram åt Sjövärnskåren.</p><p>Vi träffades i Karlskrona för att komma överens om vilka maskinparametrar som skulle presenteras. Därefter påbörjades förundersökning och dokumentationsgenomgång för att ta reda på vilka givare det var samt vad för signal de gav till det befintliga övervakningssystemet. Detta visade sig bli en stor del av projektet som tog mycket tid. Vi var och mätte signalerna från givarna på fartyget utan att komma fram till slutsats. Efter att ha pratat med varv och underhållsenheter som fartyget varit i kontakt med under sin tid i försvaret, hittade vi en källa som var mycket kunnig i området. Denne uppgav muntligen information som innebar att givarna skulle ge standardsignal, 4-20 mA.</p><p>Projektet fortskred med denna information och offertunderlag gjordes och skickades ut till olika företag som hade produkter som kunde klara av uppgiften.</p><p>Det inkom tre system som skulle klara av uppgiften. Alla dessa innebär omfattande programmeringsarbete för att få controllern att hantera och presentera informationen som det är tänkt. Samtliga system programmeras med funktionsblock (FB) eller strukturerad text, (ST). Även för den insatte i dessa språk kommer det att bli en ansenlig mängd programmeringstimmar.</p> / <p>This exam work was initiated by a request from Sjövärnskåren division Syd. They wanted to implement a newer, computer based system with graphical display, an engine monitoring system which was ment to provide the engineer on watch with data from the engines. The object for this is to reduce the maintenance costs through improved monitoring while running and to improve documentation which later on the maintenance measures is based on.</p><p>The project was an initial study which conclusions and recommendations on systems suited for the task is to give Sjövärnskåren an economical frame.</p><p>We met up in Karlskrona on the ship and had a discussion about which parameters that should be presented. After that we started to go through the documentation and perform onsite surveys to conclude what signals the transmitters put out to the existing monitoring system.</p><p>This was a delicate task, information about the transmitters was lacking in the documentation.</p><p>The onsite measures gave no vital information. We talked to the shipyards and maintenance units that the ship had been in contact with during its time in the navy. We came in contact with a man that had been working with this ship, and he gave us information that told us that the transmitters were of standard type, 4-20 mA.</p><p>With this information, the project pursued and we invited tenders to give us systems that could cope with the task.</p><p>We had three tenders thar supplied us with systems. All of theese meant considerable programmingwork to get the monitoring system up and running.</p>

Efficient drive cycle simulation of longitudinal vehicle propulsion models is an important aid for design and analysis of power trains. Tools on the market today mainly use two different methods for such simulations, forward dynamic or quasi-static inverse simulation. Here known theory for stable inversion of non linear systems is used in order to combine the fast simulation times of the quasi-static inverse simulation with the ability of including transient dynamics as in the forward dynamic simulation. The stable inversion technique with a new implicit driver model together forms a new concept, inverse dynamic simulation. This technique is demonstrated feasible for vehicle propulsion simulation and specifically on three powertrain applications that include important dynamics that can not be handled using quasi-static inverse simulation. The extensions are engine dynamics, drive line dynamics, and gas flow dynamics for diesel engines, which also are selected to represent important properties such as zero dynamics, resonances, and non-minimum phase systems. It is shown that inverse dynamic simulation is easy to set up, gives short simulation times, and gives consistent results for design space exploration. This makes inverse dynamic simulation a suitable method to use for drive cycle simulation, especially in situations requiring many simulations, such as optimization over design space, powertrain configuration optimization, or development of powertrain control strategies. Optimal vehicle propulsion control is developed with special focus on heavy trucks used for long haulage. The power to mass ratio for a typical heavy duty truck makes even moderate road slopes significant in the sense that it is impossible to keep a constant cruising speed. This gives an interesting problem how to control vehicle speed such that fuel consumption is minimized. Todays telematic systems together with three dimensional roadmaps can provide the vehicle control system with information of the road topography. This enables intelligent cruise controllers that utilize this information to control engine fueling and gear shifting such that an optimal speed trajectory is obtained. First the optimal control problem is solved numerically by dynamic programming, giving a controller with real time capabilities that can be used on-line in the vehicles control system. Simulations of such a system on authentic road profiles show that it has potential for significant fuel savings. To achieve knowledge about the underlying physics that affects the optimal solution, the optimal control problem is solved in detail and analytical expressions for the conditions of optimality are derived. Those expressions are then used to find optimal solutions on constructed test road profiles. Such test cases point out the typical behavior of an optimal solution and also which parameters that are decisive for the fuel minimization problem, and also how they quantitatively influence the behavior. It is for example shown that small non-linearities in the engine torque characteristics have significant effect on the optimal control strategy. The solutions for the non linear engine model have a smoother character but also require longer prediction horizons. For optimal gear ratio control it is shown that the maximum fueling function is essential for the solution. For example, in the case of a continuously variable transmission it is shown that the gear ratio never is chosen such that engine speed exceeds the speed of maximum engine power. For a discrete step transmission the gear shifting losses are essential for the optimal shift positions, but over all the solutions are close to continuous solutions.

Legislators steadily increase the demands on lowered emissions from heavy duty vehicles. To meet these demands it is necessary to integrate technologies like Exhaust Gas Recirculation (EGR) and Variable Geometry Turbochargers (VGT) together with advanced control systems. Control structures are proposed and investigated for coordinated control of EGR valve and VGT position in heavy duty diesel engines. Main control goals are to fulfill the legislated emission levels, to reduce the fuel consumption, and to fulfill safe operation of the turbocharger. These goals are achieved through regulation of normalized oxygen/fuel ratio and intake manifold EGR-fraction. These are chosen as main performance variables since they are strongly coupled to the emissions. To design successful control structures, a mean value model of a diesel engine is developed and validated. The intended applications of the model are system analysis, simulation, and development of model-based control systems. Dynamic validations show that the proposed model captures the essential system properties, i.e. non-minimum phase behaviors and sign reversals. A first control structure consisting of PID controllers and min/max-selectors is developed based on a system analysis of the model. A key characteristic behind this structure is that oxygen/fuel ratio is controlled by the EGR-valve and EGR-fraction by the VGT-position, in order to handle a sign reversal in the system from VGT to oxygen/fuel ratio. This structure also minimizes the pumping work by opening the EGR-valve and the VGT as much as possible while achieving the control objectives for oxygen/fuel ratio and EGR-fraction. For efficient calibration an automatic controller tuning method is developed. The controller objectives are captured by a cost function, that is evaluated utilizing a method choosing representative transients. Experiments in an engine test cell show that the controller achieves all the control objectives and that the current production controller has at least 26% higher pumping losses compared to the proposed controller. In a second control structure, a non-linear compensator is used in an inner loop for handling non-linear effects. This compensator is a non-linear state dependent input transformation. PID controllers and selectors are used in an outer loop similar to the first control structure. Experimental validations of the second control structure show that it handles nonlinear effects, and that it reduces EGR-errors but increases the pumping losses compared to the first control structure. Substantial experimental evaluations in engine test cells show that both these structures are good controller candidates. In conclusion, validated modeling, system analysis, tuning methodology, experimental evaluation of transient response, and complete ETC-cycles give a firm foundation for deployment of these controllers in the important area of coordinated EGR and VGT control.

System identification is about constructing and validating modelsfrom measured data. When designing system identificationexperiments in control applications, there are many aspects toconsider. One important aspect is the choice of model structure.Another crucial issue is the design of input signals. Once a modelof the system has been estimated, it is essential to validate theclosed loop performance if the feedback controller is based onthis model. In this thesis we consider the prediction-erroridentification method. We study model structure complexity issues,input design and model validation for control. To describe real-life systems with high accuracy, models of veryhigh complexity are typically needed. However, the variance of themodel estimate usually increases with the model order. In thisthesis we investigate why system identification, despite thisrather pessimistic observation, is successfully applied in theindustrial practise as a reliable modelling tool. It is shown thatby designing suitable input signals for the identificationexperiment, we obtain accurate estimates of the frequency functionalso for very complex systems. The input power spectrum can beused to shape the model quality. A key tool in input design is tointroduce a linear parametrization of the spectrum. With thisparametrization, several optimal input design problems can berewritten as convex optimization problems. Another problem considered is to design controllers withguaranteed robust stability and prescribed robust performanceusing models identified from experimental data. These models areuncertain due to process noise, measurement noise and unmodelleddynamics. In this thesis we only consider errors due tomeasurement noise. The model uncertainty is represented byellipsoidal confidence regions in the model parameter space. Wedevelop tools to cope with these ellipsoids for scalar andmultivariable models. These tools are used for designing robustcontrollers, for validating the closed loop performance and forimproving the model with input design. Therefore this thesis ispart of the research effort to connect prediction-erroridentification methods and robust control theory. The stability of the closed loop system can be validated using thesmall gain theorem. A critical issue is thus to have an accurateestimate of the L2-gain of the system. The key tosolve this problem is to find the input signal that maximizes thegain. One approach is to use a model of the system to design theinput signal. An alternative approach is to let the system itselfdetermine a suitable input sequence in repeated experiments. Insuch an approach no model of the system is required. Proceduresfor gain estimation of linear and nonlinear systems are discussedand compared. / QC 20100702