Application Of Fuzzy - Logic Controller In Gas Turbine Control On Transient Performance With Object Orientation Simulation

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1 Application Of Fuzzy - Logic Controller In Gas Turbine Control On Transient erformance With Object Orientation Simulation Alireza.A Torghabeh ; A.M Tousi Amirkabir university of technology, Tehran, Iran alireza @yahoo.com Abstract. This paper presents Fuzzy Logic approach to Gas Turbine Fuel schedules. Modeling and control of non-linear system by fuzzy logic controller using data generated by a simulated gas turbine program is introduced. Off-line fast simulations with Object Orientation rogramming are used for engine controller design for turbojet engine based on repeated simulation. The Mamdani and Sugeno models are used to expression the Fuzzy system. The linguistic Fuzzy rules and membership functions are presents and a Fuzzy controller will be proposed to provide an Open-Loop control for the gas turbine engine during acceleration and deceleration. MATLAB Simulink was used to apply the Fuzzy Logic analysis. Both systems were able to approximate functions characterizing the acceleration and deceleration schedules. Surge and Flame-out avoidance during acceleration and deceleration phases are then checked. This Fuzzy Logic Controllers output results are validated and evaluated by GS software. The validation results are used to evaluate the generalization ability of Fuzzy Logic controllers with Object Orientation rogramming simulation. 1. ITRODUCTIO The application of Fuzzy Logic to the control and modeling of gas turbine engines is a new area in the identification and control of non-linear dynamics systems. The ability of these technique to approximate any non-linear functions, by mapping an input vector to it s corresponding output vector, make theirs useful for modeling dynamics systems. Fuzzy Logic present the next step in computerizing the human thought processes. The work is motivated by the complexity in modeling and controlling gas turbine engines due to the non-linear nature of their behavior. The problem of non-linearity can be regarded as a root cause for control instability, the loss of smooth transient between operating points and reduced efficiency in the performance of gas turbine engine at off-design points.conventional rule based expert systems allow one to develop computer programs in an optimal manner by processing rules using Boolean or discrete Logic- only complete truth or false situations. Fuzzy Logic takes the next step by relating rules to Fuzzy or continuous Logic allowing operations on descriptors such as tall, short, big, heavy,medium, etc. This Fuzzy Logic attribute allows the capture of human thought processes in an optimal manner for automation. For example, if one is going too fast and finds it necessary to slow up, the braking consists of Fuzzy sets defined over a graded range of decelerating braking speeds. Fuzzy Logic provides the ability to handle control problems where there is uncertainty without developing or understanding the complex dynamics of an environment as long as insight exists about the behavior. These rule-base systems can provide basic advantages for gas turbine engine control. The potential advantage of fuzzy logic controller are the ease of implementation, an increase in the smooth transient between operating points. fuzzy logic applications can be widely employed in such fields where an accurate mathematical model of any process subject to control can not be developed. In summary, Fuzzy Logic provide the ability to address the mechanization in computer software and hardware very difficult control and pattern matching problems in a more natural and optimal manner. 2.SIMULATIO AALYSIS The simulation is based on one dimensional and determination of each off-design point requires iterations where different thermodynamic input variables are estimated for this purpose. For gas turbine engine performance analysis, a variety of simulation tools is available. In order to minimize model development and software maintenance costs, generic gas turbine system simulation tools are required for new modeling tasks. Many modeling aspects remain engine specific and still require large implementation efforts. Objectorientation offers an excellent mechanism for this problem. With Object orientation programming (OO), a generic object hierarchy using class types and inheritance has been defined for simulation program. A class is a structure consisting of a fixed number of components being fields, methods and properties. A class can inherit components from another class type. If B inherits from A, then B is a descendant of A, and A is an ancestor of B. Inheritance is transitive, implying that if C inherits from B and B inherits from A, then C also inherits from A. A descendant class implicitly contains all the components defined by its ancestor class. A descendent class can add new components to those it inherits, but it can not remove the definition of a component

2 defined in an ancestor class. The principle of object hierarchy is highly applicable to a gas turbine simulation program. Many gas turbine components have similarities in the model code and interface code, which can be concentrated in, and inherited from, a single abstract ancestor class. When a new component model is required or a small adaptation to an existing component model must be perform to obtain a custom component, a descendent class may be derived, requiring only a limited amount of new code. Many publications on object-oriented software design show the three basic principles of objectorientation: encapsulation, inheritance and polymorphism. These principles offer significant potential to efficient gas turbine simulation software development. Encapsulation enhances code maintainability and readability by concentrating all data declarations and procedures ( both for interface and simulation calculations ) in a single code unit. Inheritance is used to concentrate code common to multiple component types in component classes, preventing code duplication and enhancing code maintainability. olymorphism is the ability of parameters to represent different object classes.and is extensively applied in gas turbine program simulation. For example, the system model code has an abstract ( polymorph) identifier able to represent any component in the model.during simulation, the abstract identifier subsequently represents all components and runs their simulation codes. Most gas turbine cycle models calculate steady state or transient off-design operating point by solving sets of non-linear differential equations. The equations set represents the conservation laws that apply for the specific engine and solve these equations by ewton-raphson iteration and based on error minimizing technique. Really the mathematical model of the engine is produced by this iterative method. Engine models are applied both for off-line and on-line simulations. Off-line simulations are used for engine controller design methods based on repeated simulations ( Fuzzy Logic, eural etworks, etc). 3.The Fuzzy Logic rocess The notation of a fuzzy set was introduced in 1965 by rofessor Lotfi Zadeh [1], who was then a professor of Electrical Engineering at the university of California at Berkeley. His idea was to expand upon the general definition of a set in order to allow for the treatment of uncertainty in the classification of objects. A fuzzy set is a collection of objects. A fuzzy set is a collection of objects whose membership, unlike those in a crisp set, is a matter of degree. This is expressed in terms of a membership function that assigns a number between 0 and 1 to each object, where 1 denotes absolute membership in the set and 0 denotes exclusion from the set. An object assigned a value somewhere in between 0.6 is said to belong to the set with degree ( or membership) 0.6. This also implies that it is excluded from the set with degree 1-0.6=0.4.Thus, by virtue of this fuzzy classification, it is possible to deal with sets which are not (mathematically) well defined, but rather have been defined in linguistic terms, such as the set of numbers that are approximately equal to π, or the set of jet engines exhibiting low exhaust gas temperature margin. Inasmuch as ordinary set theory serves as a foundation for classical logic, fuzzy set theory has likewise aided the development of fuzzy logic([2]).fuzzy logic combines notions from ordinary Aristotelian logic and fuzzy set theory, in that the truth of a given proposition (like a fuzzy set) can be something between 0 (representing false) and 1 (representing true).logical operations and rules of inference have also been defined, which allows for the description (and analysis) of complex systems in a natural language setting. This process mimics the way humans convey and process information, and thus provides a mathematical vehicle for the representation of imprecise rules and heuristics. It wasn't long after Zadeh's introduction of fuzzy logic that applications arose in the area of dynamic control. Mamdani [2] demonstrate its ability by successfully constructing a fuzzy logic control system for a steam engine. Generally speaking, there are three major processes common to all fuzzy control systems : fuzzification, rulebase inference, and defuzzification. See Figure 1 Crisp input Fuzzification Fuzzy input Data generator Fuzzy Inference Rule evaluation Crisp Output Deffuzification Fuzzy Output Figure 1.Flowchart of Fuzzy Logic controller 1.Fuzzification is the process that converts a crisp input value to fuzzy set values, thereby forming the interface between the real world and the fuzzy inference process. 2.Rulebase inference is the application of a series of rules given in terms of fuzzy set values and producing for output variable(s), fuzzy set values for each rule fired. These rules usually take the form IF (X1 is big) AD (X2 is small), THE (Y is medium).

3 3.Defuzzification converts the fuzzy set values of the output variable(s)] back to a crisp value so that it may be utilized in the control. 4.rinciples Of Control A simple engine control system computes the amount of fuel needed for the engine to produce a desired power (or thrust), based on pilot s power request through a throttle (or a power lever); then it meters the right amount of fuel to the engine s combustion chamber(s); and it maintains the engine power at the desired level in the presence of air flow disturbance and changes in flight conditions. Figure2, illustrates this fuel control system and identifies the various components needed to make the system work. The valve is usually called an actuator, whose position changes with the fuel flow command, and the fuel flow is called a controlled variable. If we change power in Fig.3 to turbine temperature, then the process represents a temperature control system, or temperature governor. Likewise, if we change both power and fuel flow to inlet guide vane angle (IGV), then the diagram becomes an IGV control system. In-flight engine thrust measurements are not possible. Good indicators of thrust can, however, be obtained from either engine shaft rotational speed () or engine pressure ratio (ER) and these parameters have been used effectively in the engine control process. An aircraft engine is designed to operate in a wide operating envelope (to support aircraft mission profiles). Typically, the altitude can vary from sea level to 50,000 ft (or even higher), the air speed can go beyond Mach 3; furthermore, the air temperature at the same altitude and airspeed can vary from a hot summer day to a cold winter night. These ambient condition variations have imposed severe challenges on control system design. To a control engineer, these challenges are represented on a fuel flow (Wf) versus engine shaft speed () graph, or a fuel ratio unit (Wf/3, where 3 is the compressor exit static pressure) versus speed graph, as shown in Fig.4 After engine start, the engine operating envelope (shaded in light green) is bounded by the maximum flow limit, the minimum flow limit, the idle power governor and the maximum power governor. The max. flow limit prevents the engine from surge and over-temperature. The min. flow limit prevents the engine from flame-out. The idle power is typically set to produce a desirable ground thrust for taxiing the airplane, and the max. power produces the engine maximum-rated thrust. The max. and min. flow limits are also called the acceleration and deceleration schedules. These schedules change with the engine ambient condition. The figure also shows four straight lines intersecting the idle power point and the max. power point on the steady state operating curve. These lines are called droop lines, which represent the proportional control gains ( Wf/ ) at the two power points, respectively. In reality, the trajectories between a power set-point (e.g., idle or maximum) and a fuel control limit (either the max. limit or the min. limit) is not a straight line, because all engine fuel controls use at least one additional control law, the integral control, to improve control system robustness. Many modern engines use derivative control and complex control compensations to shape the transient performance. Figure 2: functional process diagram of a simple engine control system. Figure 3: Gas turbine engine fuel control system operating envelop. 5.Transient performance The transient performance or behavior of the gas turbine engine indicates the response of the engine to a change in the output ( Thrust or power demand ). The prediction of this performance is important for control purpose. A detail knowledge of the dynamic response at the design stage is becoming increasingly important for the design and development of control systems for advanced gas

4 turbines. The transient behavior calculations are determined from the off-design performance. These usually included the thermodynamic relations of the steady state gas turbine engine model, the polar moment of inertia and the control system. The polar moment of inertia has a different effect on the work balance between the compressor and turbine. Because of this, more power is needed from the turbine during transient acceleration than in steady state operation. The demand for power results in higher fuel flow for a given speed, a shift in the operating line towards the surge line, and in higher operating temperatures ( the TIT temperature increase before the turbine reaches its speed to supply adequate mass flow to the combustor. Hence the control system must be able to keep the fuel flow during transient operation between two limiting schedules : the acceleration schedule (AS) and the deceleration schedules (DS). Below figure shows a typical acceleration schedule on a generic compressor map, and typical Compressor map showing all relevant lines and schedules (for example SL, OL,AS,DS). As can be seen in the above figures when the fuel flow increase, the new operating line moves the acceleration schedule closer to the surge line. For control purpose these schedules must be mapped into a gas generator speed ( GG ) versus fuel flow ratio graph as shown in these figures.the fuel schedules are chosen as limits used in open loop control strategies to avoid surge and flame out of the gas turbine during transient operations.these schedules are depicted as running lines between the steady state operating fuel requirements and surge fuel margins. Figure 4: Transient acceleration schedule on a compressor map The modeling and simulation of the turbojet engine that discussed in this paper show in Figure5. that simulated with Object Orientation rogramming. W f/ Figure 5: Turbojet engine modeling 6. Fuel schedules The goal of choosing an acceleration schedule is to limit the fuel to the engine at each operating point to a safe value without the surge in compressor and overheating in turbine. One way to achieve a safe margin of operation is to map the limiting lines shown on the compressor map onto a gas generator speed versus fuel flow ratio graph,this process is shown in below figures, that the relation between the speed and Wf/3( where 3 is the compressor exit static pressure ) is then drown. The next step is to draw an acceleration schedule between the surge and operating lines. In the case presented here, the acceleration schedule was selected midway between the surge line and the operating line. This selection is reasonable since it secure a compromise between a fast acceleration safety.a similar procedure is applied to the selection of the deceleration schedule. However the choice of the deceleration schedule is somewhat arbitrary, but constrained by flame stability. In this report I selected a deceleration schedule at 20% below the operating line was chosen ( the 20 % will be revised if necessary when the combustor is tested and flame out line or flame stability defined. ow that the schedule have been marked analytically, a fuzzy logic approach is developed to map these fuel schedules Below figure 6, illustrate the fuel schedule of this system. Fuel flow schedule GG Operating Line Surge Line Acceleration Deceleration Figure6: Fuel schedule on a fuel flow ratio versus gas generator speed (GG) graph

5 7. inputs and outputs for the control scheme The linguistic fuzzy model, the Mamdani model, is employed. The advantage of this fuzzy model is that in easy implementation it s rule. The if-then rule is expressed in the general form : Wf If GG is Ai then is B i k i = 1,2,..., In the above statement K is the number of fuzzy logic rules.to explain how the fuzzy system process works, a brief description follows. After the input and output linguistic variables and rules are specified, the membership functions are defined. The combination if the database and the rule base creates the knowledge base in which all the information related to the fuzzy system is stored. Below Table.1 illustrate the linguistic variable GG with seven linguistic terms. For each linguistic term the membership functions overlap, in other words, each element is allocated to one or more fuzzy sets with a nonzero membership degree. Two linguistic variables are used, GG and c. One method of representing this antecedent-consequent relation (or rule base) is through a fuzzy matrix. Table1 shows onedimensional representation of the fuzzy sets implemented for the acceleration schedule to 14 S(positive small) to 14.5 B(positive big) Table 2: Table 4. Fuzzy output control value (deceleration schedule) Figure7: Membership function for GG input vector ( generated by Simulink Matlab) GG M S M B W f / c L S B Table 1: Rule base for fuel flow membership functions (acceleration schedule) The fuzzy membership function characterizing the consequent rules are shown in Table 2. The overlapping in the membership functions are intended to guarantee a smooth mapping and transient between the discrete and desired control actions. Figure8. Membership function for fuel ratio output vector ( generated by Simulink Matlab) For the design of the deceleration fuel schedule, a sugeno fuzzy system with constant consequent membership functions was employed.below Table 3. lists the rule base for the deceleration fuel schedule for GG and GG items. Shape Fuzzy Logic values interval for W f / c 11.5 to to to to to 3.85 Linguistic term description L (low egative) (negative) (negative small) (positive)

6 GG W f / c B B S S M Table 3: Rule base for fuel flow membership functions (deceleration schedule) B B The Fuzzy controller was modeling by Simulink Matlab software,this model for acceleration and deceleration control,was shown below : The fuzzy membership function for this deceleration phase shows in Table 4. Shape Fuzzy Logic values interval for W f / c Linguistic term description B ( negative big) (negative) (negative small) S(positive small) (positive ) B(positive big) Table 4. Fuzzy output control value (deceleration schedule) Figure 11. Simulink model for deceleration /deceleration schedule control Results Acceleration phase Deceleration phase Figure9: Membership function for GG input vector ( generated by Simulink Matlab) REFERECES Figure10. Membership function for fuel ratio output vector ( generated by Simulink Matlab) 1. Zadeh, L.A., (1965),Fuzzy sets, Inform. Control Vol Mamdani,E.H(1974) "fuzzy algorithms" IEEE,Vol.121,o.12.