Soft Computing Applications on SR-30 Turbojet Engine

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AIAA 2004-6444Figure 4, shows that the proposed controller gives apositive gain margin of 12.6 db and a positive phasemargin of 65.8 deg, which make the system stable.Since the system has a positive gain margin, there is atolerance of raising the proportional gain of the PIDcontroller.Cutoff frequency is the maximum frequency at whichthe output of a system will track an input sinusoid in asatisfactory manner.6.05.55.0Thrust [lbs]4.54.03.53.02.52.00 1 2 3 4 5 6Time [sec]Figure 7 Step Responses from SR-30 EngineFigure 4 Open-Loop Bode PlotsFigure 5 is the closed-loop Bode plots for thesystem. From the gain plot, the proposed closed-loopmodel has a cutoff frequency of about 3.01 rad/sec.Step input tests were conducted to test the designedPID controller. Figure 6 is the result from estimatedmodel using MATLAB. It shows a rise time of 0.65 secand a settling time of 1.15 sec. Figure 7 shows theexperimental results of step input tests using the SR-30engine. In the figure, three cases were plotted. For eachcase, a step command was issued at t = 1.0 sec. Thethrust values for the three cases were 3.5, 4.0, and 5.0lbs. For all cases the results show about 2 seconds ofsettling time with near zero steady-state errors.The large initial jump observed in the 3 to 5 lbincrease thrust run is undesirable and it is due tounforeseen nonlinear effects. This jump does not appearwhen using the fuzzy controller.IV. FUZZY LOGIC CONTROLLER DESIGN ANDAPPLICATION [2]Figures 5 Closed-Loop Bode PlotsThe employment of Bayesian and fuzzy techniquesderive from the “soft computing” family of algorithms.Here “soft computing” refers to computationalmechanisms that can determine suitable relationships(in a system data set) to assess and determine aquantitative opinion(s) based on future conditions.Since the scope of this paper is not on the depth ofunderstanding Bayesian and fuzzy techniques,application of them is presented. In short, withinMSFC, such computational mechanisms are viewed asa collection of algorithms that can achieve optimal ornear-optimal results in the presence of imprecise data,uncertainty [3], unknown physics, and probabilisticoutcomes. The central goal in soft computing is toattain more robust response.Figure 6 Simulated Unit Step Response4American Institute of Aeronautics and Astronautics
AIAA 2004-6444Similar to the PID design, for main-stage control, afuzzy logic controller was designed and implemented tocontrol the SR-30 engine and the response of the engineto a step input using the PID and Fuzzy controllers wascompared. The use of fuzzy logic was seen suitablesince it accommodates the uncertainties associated withcontroller architecture. Fuzzy logic is a branch ofmathematics that deals with approximate reasoning.Fuzzy logic, developed by Lotfi A. Zadeh of theUniversity of California at Berkely, combines the topicsof multi-valued logic, probability theory, and artificialintelligence for simulation of human thoughts by usingcomputer software as a medium. The technology offuzzy logic enables a computer to make decisions basedon vagueness or imprecision intrinsic in most physicalsystems. Fuzzy logic also provides a convenient way tointroduce useful nonlinearities into the control law toachieve specific effects, such as reducing largeovershoots. In depth details of fuzzy logic are outside toscope of this paper. A more detailed description onfuzzy logic can be found in [5].In the rest of this section the fuzzy logic controllerdesign and related programming process are discussed.A brief description of the design of the fuzzy logiccontrol algorithm is introduced. A simulation programwritten to test the fuzzy logic controller and the resultsof the simulation are discussed. Implementation of thefuzzy logic control algorithm on the SR-30 engineusing LabVIEW is detailed and the hardware-in-thelooptest results are discussed.IV-A.FUZZY LOGIC ALGORITHMDESCRIPTIONFuzzy Logic algorithm differs from the PID controlalgorithm since it can be used for non-linear-timevariantsystems. The algorithm intends to mimic humanthoughts in the sense that the relation between an inputand its output is assessed by a user, depending on theuser’s experience. In the fuzzy logic terminology,vague terms used such as hot, and cold are calledlinguistic terms and range of real numbers for the inputand the output is referred to as universe of discourse.Range of the input values divided into sections by itslinguistic terms is called antecedence and range ofoutput values divided into sections by its linguisticterms is called consequence.In a fuzzy logic control system, the fuzzificationprocess translates real input values to linguistic inputvalues, next the fuzzy inference system drives a5American Institute of Aeronautics and Astronauticsconclusion in a form of linguistic output valuesaccording to its rule base, which resembles IF-THENstructure used in many text-based programminglanguages. The final process called the defuzzificationprocess translates back the linguistic output values tocorresponding real output values for subsequent controlactions.IV-B. FUZZY LOGIC CONTROLLERARCHITECTUREThe NI LabVIEW Fuzzy Logic Controller Toolkitwas used to develop fuzzy logic controllers for the SR-30 engine control application. The toolkit allows theuser to interface with LabVIEW programs. The FuzzySet Editor specifies the details of the fuzzification step,and the details of defuzzification step. The Rule BaseEditor of the Fuzzy Logic Controller Toolkit enablesthe user to specify the details of the fuzzy inferencesystem. Before testing a fuzzy logic algorithm with theSR-30 engine, a LabVIEW-fuzzy simulation programwas developed using the plant model identified in thedesign process of the PID controller. The fuzzysimulation program had similar inputs to the ones of theLabVIEW-PID controller and the controller outputagain was the fuel-flow valve position. The fuzzysimulation program calculates appropriate valveposition in every loop execution for adjusting the fuelflowvalve opening to obtain desired thrust. A picture ofthe Labview fuzzy simulation program developed forthis purpose is shown in Figure 10. The input variablesused in the design of the PD part of the controller werethrust error calculated at node (1) and thrust error ratecalculated at node (2). As for the integral part of theprogram, the thrust error was the only input variable.The PD part and the integral part evaluate their outputsto the stepper motor separately from their inputs. Thesum of the angle outputs calculated at node (3) fromthe two parts is the total angle output to the steppermotor to control the fuel-flow valve position.The Figure 11-A shows the architectures of thefuzzy sets associated with the thrust error and the thrusterror rate as the controller inputs and the Figure 11-Bshows the architectures of the fuzzy sets associated withthe valve position and the valve position error (SeeTable 1 for the corresponding linguistic values for eachoutput). The use of the thrust error and thrust error rateeach with five linguistic terms results in 5 2 = 25 rulesfor the PD part. The use of the thrust error with fivelinguistic variables results in five more rules for theintegral part bringing the number of the total rules tothirty. The choice of using thirty rules gives areasonable number of rules and allows the user to
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