COMPREHENSIVE STUDY ON FUZZY LOGIC BASED DTC OF THREE-PHASE INDUCTION MOTOR دراسة شاملة لمنظومة التحكم المباشر بالعزم باستخدام التحكم المضبب لمحرك حثي ثالثي الطور
Direct Torque Control + - + - E ψ E T State Selector θ s Three phase inverter IM Voltage and current feedba ck Flux and Torque Estimator Fig. ( 1.2) Block diagram of the DTC scheme.
Thesis structrure Chapter one General introduction Chapter two control methods for three phase induction motor Chapter three : Background Theory of Fuzzy System and Genetic Algorithm
Chapter four : Fuzzy Logic Based DTC with Torque Ripple Minimization Fuzzy Duty Ratio Controller Duty ratio control for direct torque control with genetic fuzzy algorithm Angle Correction Method
Chapter Five: Fuzzy Logic Based Speed Control of I.M. Structure of Fuzzy PI-Controller Based DTC with simulation results Optimization of Proportional KP and Integral KI Factors Using Genetic Algorithm
Chapter Six : Fuzzy Logic Based Stator Resistance Estimator For DTC of I.M.
Fuzzy Duty Ratio Controller Block diagram of fuzzy duty ratio control V d sign Eψ Duty Ratio Fuzzy Controller θ ψ E Te Direct Torque Control (DTC) δ Switchi ng State VSI Induction Motor Stator Currents Stator voltages
Design of The Duty Ratio Fuzzy Controller Selection of input variables : E te, E flux, theta Selection of output variables : delta Number of fuzzy controllers : two Selection of the membership function : triang. Selection of the defuzzification: centroid
Design of The Duty Ratio Fuzzy Controller Table (4.4) Fuzzy Control Linguistic Rules for duty ratio control Flux is great er than Ref. flux E ψ E Te S M L S S S M M S M L L S M L Flux is less than Ref. flux S S M L M S M L L M L L
Implemented simulink model of the modified (FDR) control scheme
Implemented simulink model of the (DTC) with (FDR) control Valpha vsalphaisalpha Vbeta ialpha flux Torque refrence vsbeta cr isbeta w ibeta Flux estimator. Refrence speed 1.2 stator resistance Rs cem Induction Motor Model.. PID Relay Sa Flux error Vsalpha Vsabc Vsbetha T.Clarke va vb vc sa sb sc 3 phase inverter Sa1 Sa Sb1 Sb Sc1 Sc Delta Multiplier Sb Sc Torque error phalpha phbeta direct torque controller 1 flux ref Demux fluxerrror segma alphaflux betaaflux 1 Terror Proposed fuzzy system
Electromagnetic Torque (N.m) Electromagnetic torque (N.m.) 8 6 Load step change 5 N.m. at 2 second 8 6 Load step change 5 N.m. at 2 second 4 4 2 2-2 -2-4 -4.5 1 1.5 2 2.5 3 3.5 Electromagnetic torque responce with a stepchange of 5 N.m. at 2 second for classical DTC -6.5 1 1.5 2 2.5 3 3.5 Electromagnetic torque responce for the proposed controller with a step change of 5 N.m. at 2 second
Speed (rpm) Speed (rpm) 15 14 15 14 12 12 1 1 8 8 6 6 4 4 2 2.5 1 1.5 2 2.5 3 3.5 Speed response for classical DTC with a stepchange of 5 N.m. at 2 second.5 1 1.5 2 2.5 3 3.5 Speed response for the proposed controller with a step change of 5 N.m. at 2 second
Stator current magnitude (Amp.) Stator current magnitude (Amp.) Stator current magnitude for three phase I.M. with a step change of 5 N.m. at 2 second for classical DTC Stator current magnitude for three phase I.M. with a step change of 5 N.m. at 2 second for proposed controller 9 8 7 5 45 4 6 5 4 3 2 1.5 1 1.5 2 2.5 3 3.5 35 3 25 2 15 1 5.5 1 1.5 2 2.5 3 3.5
Electromagnetic torque (N.m.) Electromagnetic Torque (N.m.) Two load applied at two instants Electromagnetic torque responce for the classical DTC with a step change of 5 N.m. at 2 second 1 N.m. at 3 second Electromagnetic torque responce for the proposed controller with a step change of 5 N.m. at 2 second 1 N.m. at 3 second 8 6 Load step change 5 N.m. at 2 second Load step change 1 N.m. at 3 second 3 2 Load step change 5 N.m. at 2 second Load step change 1 N.m. at 3 second 4 1 2-1 -2-2 -4.5 1 1.5 2 2.5 3 3.5-3.5 1 1.5 2 2.5 3 3.5
Speed (rpm) Speed (rpm) Speed response for classical DTC with a step change of 5 N.m. at 2 second 1 N.m. at 3 second 15 14 Speed response for the proposed controller with a step change of 5 N.m. at 2 second 1 N.m. at 3 second 15 14 12 1 8 Load step change 5 N.m. at 2 second Load step change 1 N.m. at 3 second second 12 1 8 Load step change 5 N.m. at 2 second Load step change 1 N.m. at 3 second 6 6 4 4 2 2.5 1 1.5 2 2.5 3 3.5.5 1 1.5 2 2.5 3 3.5
Comparison of The Modified (FDRC) With Original (FDRC) the modification occur in two places, first one in changing some rule of the inference engine; the second is a conversion of the input of the FIS variable from three fuzzy variables to two fuzzy variable plus one crisp.
Comparison of The Modified (FDRC) With Original (FDRC) the torque ripple reduction obtained from (FDRC) are 7% of it is value in (CDTC), while torque ripple reduction in the modified (FDRC) is about 4% of that using classical DTC. While the stator current in this modified (FDRC) have been reduced up to 43% of the value using classical version.
Tuning of Membership Functions Using Genetic Algorithm Alternative membership function distribution
Fitness function Duty ratio control for direct torque control with genetic fuzzy algorithm 45 4 35 3 25 2 15 2 4 6 8 1 12 14 16 18 2 Generation
Tuning of the input membership functions using GA (b) (b) 1 S M L 1 S M L.5.5-25 -15 5 15 25 (a) E T -25-15 5 1 25 (a) E T (b) S 1 (b) M L S 1 M L.5.5 -.2.5 1.2 θ ψ.6 1.1 1.2 θ ψ (b) (b )
Developed electromagnetic torque (N.m.) Developed electromgnetic torque (N.m.) Developed electromagnetic torque for the three phase I.M. drived by DTC with fuzzy duty ratio 8 Developed electromagnetic torque for the three phase I.M. drived by DTC with fuzzy genetic duty ratio 7 7 6 5 4 3 2 1-1 -2.1.2.3.4.5.6.7.8.9 1 6 5 4 3 2 1-1 -2.1.2.3.4.5.6.7.8.9 1
Stator current magnitude(amp.) Stator current magnitude (Amp.) Stator current magnitude for the three phase I.M. drived by DTC with fuzzy duty ratio 1 9 Stator current magnitude for the three phase I.M. drived by DTC with fuzzy genetic duty ratio 1 9 8 8 7 6 5 4 3 2 1.1.2.3.4.5.6.7.8.9 1 7 6 5 4 3 2 1.1.2.3.4.5.6.7.8.9 1
Angle Correction Method
Block diagram of the DTC with angle corrector fuzzy logic estimator. + - + - E ψ E T State Selector Fuzzy Logic Corrector θ ξ + θ s Three phase inverter IM Voltage and current feedba ck Flux and Torque Estimator
Electromagnetic torque (N.m.) Electromagnetic torque (N.m.) Electromagnetic torque for the classical DTC for a load step change 5 N.m. at 2 second Electromagnetic torque for the proposed controller for a load step change 5 N.m. at 2 second 8 6 4 Load step change 5 N.m. at 2 second 9 8 7 6 2 5-2 -4 4 3 2 1 Load step change 5 N.m. at 2 second -6.5 1 1.5 2 2.5 3 3.5-1.5 1 1.5 2 2.5 3 3.5
Stator current magnitude (amp.) Stator current magnitude (amp.) Stator current magnitude for three phase I.M. with a step change of 5 N.m. at 2 second for classical DTC 1 9 8 7 Stator current magnitude for three phase I.M. with a step change of 5 N.m. at 2 second for the proposed controller 8 7 6 6 5 4 3 2 5 4 3 2 1.5 1 1.5 2 2.5 3 3.5 4 4.5 1.5 1 1.5 2 2.5 3 3.5
Conclusion two fuzzy schemes were introduced to minimize the torque ripples, the first scheme is (FDRC), this method is modified by reducing the number of input variables from three to two inputs.
Conclusion A fuzzy genetic algorithm is used to tune the parameters of membership functions in the (MFDRC) to have good performance for this modified scheme such as torque ripple minimization, swift speed response, and reduced the stator current magnitude.
Conclusion The second proposed method which is the angle correction, which is used to correct the defection of stator flux angle results from torque and flux errors, which lead to the optimal switching state.
Chapter Five Fuzzy Logic Based Speed Control of I.M. W ref W + - Speed PI Controller + - + - Switch State Selector 3-Phase Inverter IM K i K p Fuzzy Controller Stator and Torque Observation d/dt Adaptive Controller Fuzzy PI controller based DTC
Start Read speed error, change of speed error Calculate proportional and integral gains change of PI controller from linear transformation If speed error <desired speed error value no yes Set the proportional and integral gains changes Set the proportional and integral gains changes from FLC + K=K+1 Fig.(5.8 ) Proportional and integral fuzzy gains evaluator flow
Electromagnetic torque (N.m.) Electromagnetic Torque(N.m.) 3 3 2 2 1 1-1 -1-2 -2-3 -3-4.5 1 1.5 2 2.5 3 3.5 4-4.5 1 1.5 2 2.5 3 3.5 4 Time(second) Fig. (5.13 ) Electromagnetic torque response for the classical direct torque control by using conventional PI controller with a step change of speed from to 143 r.p.m Fig. (5.14) Electromagnetic torque response for modified fuzzy controller based DTC, with a step change of speed from to 143 r.p.m.
Statorcurrent magnitude (Amp.) Stator current magnitude (Amp.) Stator current magnitude for classical direct torque control by using conventional PI controller with a step change of speed from to 143 r.p.m. Stator current magnitude for modified fuzzy PI- controller based DTC, with a step change of speed from to 143 r.p.m. 9 8 7 9 8 7 6 5 4 3 2 1.5 1 1.5 2 2.5 3 3.5 4 6 5 4 3 2 1.5 1 1.5 2 2.5 3 3.5 4 4.5
Electromagnetic Torque (N.m.) Electromagnetic torque (N.m.) Electromagnetic torque response for the classical DTC by using conventional PI controller with a step change of speed from to 48 and then to 96 r.p.m.respectively Electromagnetic torque response for modified fuzzy PI-controller based DTC with a step change of speed from to 48 and then to 96 r.p.m.respectively 6 6 4 4 2 2-2 -2-4 -4-6.5 1 1.5 2 2.5 3-6.5 1 1.5 2 2.5 3
Stator current magnitude Stator current magnitude (Amp.) Stator current magnitude for classical direct torque control by using conventional PI controller with a step change of speed from to 48 and then to 96 r.p.m.respectively 6 Stator current magnitude for modified fuzzy PI- controller based DTC, with a step change of speed from to 48 and then to 96 r.p.m.respectively 6 5 5 4 4 3 3 2 2 1 1.5 1 1.5 2 2.5 3 3.5.5 1 1.5 2 2.5 3
Electromagnetic torque (N.m.) Electromagnetic torque (N.m.) Electromagnetic torque response for the classical DTC by using conventional PI controller with a step change of load torque from to 5 (N.m.) at 2 sec 3 Electromagnetic torque response for modified fuzzy PI-controller based DTC with a step change of load torque from to 5 (N.m.) at 2 sec 3 2 2 1 1-1 -1-2 -2-3 -3-4.5 1 1.5 2 2.5 3-4.5 1 1.5 2 2.5 3
Stator current magnitude (Amp.) Stator current magnitude (Amp.) Stator current magnitude for classical direct torque control by using conventional PI controller with a step change of load torque from to 5 (N.m.) at 2 sec Stator current magnitude for modified fuzzy PI- controller based DTC, with a step change of load torque from to 5 (N.m.) at 2 sec 9 8 9 8 7 7 6 6 5 5 4 4 3 3 2 2 1 1.5 1 1.5 2 2.5 3.5 1 1.5 2 2.5 3 time (second)
Optimization of Proportional KP and Integral KI Factors Using Genetic Algorithm os OS rt RT F j 1 2 3 OS RT se SE SE
Conclusion In this chapter a modified fuzzy PI-controller is presented to overcome the disadvantages of conventional PI-controller. The proposed scheme has satisfactory performances ( dynamically adjusts the gains KP and KI to ensure the stability of the system over a wide torque-speed range, smooth speed response, no overshoot, minimal rise-time, and extermaly small steady state errors of the speed).
Conclusion This modified fuzzy controller is compared with the old version of this fuzzy controller and the results gave first a good progress in controller performance mentioned above, and second is simplicity in implementing of the fuzzy controller by reducing the dimensions of fuzzy inference rules.
Conclusion A genetic algorithm is presented to evaluate the gains values of the PIcontroller ( proportional gain, integral gain) and this algorithm allows to have a good performance for the PI-controller as those obtained from fuzzy PI-controller.
Chapter Six Fuzzy Logic Based Stator Resistance Estimator For DTC of I.M.
Change in stator resistance Change in stator current Estimation error in torque and flux Deterioration in torque and flux control Fig.(6.1) Flow chart for the effect of stator resistance variation on a DTC drive system
+ - + - E ψ E T State Selector Fuzzy Stator resistance Estimator θ s Three phase inverter IM Voltage and current feedbac k Flux and Torque Estimator Block diagram of the DTC with fuzzy logic based stator resistance estimator. F uz zi fi ca ti on Fuzzy Inference Engine Knowledge Base Fuzzy Set Rule Base D ef uz zi fi ca ti on Stator resistance Proposed fuzzy logic based stator resistance estimator
Input and output memberships functions f 1 f 2 f 3 f 4 f 5 f 6 f 7 f 8 f 9 f 1 f 11 f 12 R 1 R 2 R 3 R 4 R 5 R 6 R 7 R 8 flu x Resistanc e Membership functions for phase error of stator flux Stator resistance membership functions
Estimated flux phase Actual flux phase _ + rms value of phase error Fuzzy Logic Estimator Stator resistance Fig. (6.7) Block diagram of the fuzzy logic based stator resistance estimator
resistance value (ohm) Phase error of stator flux (rad.) 2.4.7 2.2.6 2.5 1.8.4 1.6.3 1.4.2 1.2.1 1 1 2 3 4 5 6 1 1.2 1.4 1.6 1.8 2 2.2 2.4 Stator resistance variation (Ohm) Expected ramp change of stator resistance during the operation of three phase I.M. Error in phase of stator flux for a ramp change of stator resistance
Resistance (Ohm) Resistance (Ohm) 1.45 Actual Resistance Estimated Resistance 1.7 Actual Resistance Estimated Resistance 1.4 1.6 1.35 1.5 1.3 1.4 1.25 1.3 1.2 1 2 3 4 5 6 7 8 Actual and the estimated stator resistance for a ramp change from 1.2Ω to 1.4Ω 1.2.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Time (Second) Actual and estimated stator resistance for a ramp change from 1.2Ω to 1.6Ω
Resistance (Ohm) 2.2 Actual Resistance Estimated Resistance 2 1.8 1.6 1.4 1.2 1 2 3 4 5 6 7 8 9 Time(second) Actual and estimated stator resistance for a ramp change from 1.2Ω to 2Ω
Electromagnetic Torque (N.m.) Speed (rad./sec.) Electromagnetic Torque (N.m.) Speed (rad/sec.) 5 25 4 3 2 2 1 15 1-1 -2 5-3 -4 1 2 3 4 5 6 Time(second) Electromagnetic torque with no stator resistance estimation for a ramp change of stator resistance from 1.2Ω to 2.2Ω 5 1 2 3 4 5 6 time (second) 25 4 2 3 2 15 1 1-1 -2 5-3 -4 1 2 3 4 5 6 Electromagnetic torque with fuzzy stator resistance estimation for a ramp change of stator resistance from 1.2Ω to 2.2Ω 1 2 3 4 5 6 7