Electric Vehicles Modelling and Simulations Part 15 pdf

Sugeno Inference Perturbation Analysis for Electric Aerial Vehicles 409 Fig. 8. UAV EPS Model at variable exogenous conditions with Sugeno (fuzzy-hybrid system) and Sugeno parameter perturbations. The inputs of Figure 5 are shown next in Figure 9 (top, centre graphs) while the resulting thruster’s input electrical power is also shown (lower graph). The quasi-static approach shows that the armature input electrical power does vary in order to balance the UAV flight requirements for altitude and overcome the atmospheric air moisture conditions. Clearly, Figure 10, shows a realisable UAV test scenario. Initially the UAV starts at ground (sea level) and gradually gains altitude with a realisable climb rate. During its mission the UAV remains at a fixed altitude and then gains altitude again reaching before its 6 km requirement, where it remains for a given time (25 min) until it starts to descend back to sea level. Meanwhile, the air moisture varies between two fuzzy logic extremes of “1” and “0.5” each representing a different condition, “dry air” and “saturated moist air” respectively. The moist air affects the temperature variation as the UAV altitude varies and hence was modelled utilising the Sugeno FIS topology. Based on the chapter hypothesis, the armature resistance will affect the propeller shaft angular velocity for given conditions. Therefore, the next step is to observe the armature resistance during the UAV mission and compare this to the nominal (sea level) conditions. Figure 11, successfully demonstrates the nominal “blue line” armature resistance at sea level and the variable resistance due to the altitude and air moisture conditions. In Figure 11, the dotted upper and lower lines demonstrate the injected ±10% perturbation in the Sugeno consequent. Both the effects of altitude, air moisture and the sensor SIEB type of perturbations affect the thruster’s armature resistance and therefore it is expected to observe this variation to cascade also to the thruster’s variables such as the propeller shaft angular velocity. Electric Vehicles – Modelling and Simulations 410 Figure 12, shows more clearly the injected ±10% perturbations in the Sugeno consequent and the effect of these. Typically, the boundaries (upper and lower) indicate the line for instantaneous measurements where the sensor measurement is used rather than the exact value of the sensor. Fig. 9. UAV thruster armature voltage, current and input electrical power. Fig. 10. UAV operational scenario, indicating altitude and air moisture conditions. Sugeno Inference Perturbation Analysis for Electric Aerial Vehicles 411 Fig. 11. Thruster armature resistance for nominal conditions (blue) and altitude based conditions (red). Normally, UAV propulsion pack designs have a limited maximum rated electrical power which is available for use, including the propeller power requirements and thruster’s power losses. Figure 12, shows the armature resistance related copper losses for the given UAV test scenario. Clearly, the power copper losses relating to the nominal (sea level) when compared to the variable altitude and air moisture conditions result in different losses. In particular the variable altitude scenario power losses are less than the sea level equivalent, hence resulting in a gain in net power available for thrust for the same power pack. Fig. 12. Nominal (blue) and altitude based copper losses and propeller shaft powers. Electric Vehicles – Modelling and Simulations 412 Figure 12, (lower graph), shows the propeller shaft available power for the test scenario shown earlier. During time intervals (0,1500)s and (2200,3000)s the UAV requires its maximum rated power in order to climb to the desired altitudes of 3000 m and 6000 m. Fig. 13. Geared shaft RPM for nominal (blue) and altitude based (red), second graph showing the percent variation in the shaft RPM. Figure 13, shows (top graph) the propeller geared shaft RPM for the nominal (in blue) and the altitude varied angular velocity (in red). As expected because the power pack has a maximum rated power capability and the armature resistance losses reduce, the propeller shaft mechanical power increases for the same rated input power. Hence, while the propeller loading remains as shown in the previous profiles the angular velocity at the propeller shaft is expected to increase as shown from the analysis. Figure 13, also shows a zoomed version (lower graph) clearly showing the implications of the added phenomenon of speed changing due to an example injected ±10% perturbations in the Sugeno sensor. It appears that this specific injected perturbation does not cause a substantial change compared to the altitude based angular velocities. Figure 14. shows the armature resistance percentage error when compared to the sea level conditions. Clearly the expected error (top graph) exceeds 20% from nominal, therefore demonstrating the importance of the Sugeno fuzzy inference modelling within the context of the fuzzy-hybrid modelling process. The armature resistance percentage error for both the upper and lower boundaries (centre graph), are approximately 2.5 % for the upper/lower boundary or 5% for both boundaries. This indicates that the Sugeno perturbation based on SIEB-type errors can indeed affect the model behaviour. The (last graph), shows the SIEB errors with reference to the sea level equivalent. These are expected to be high and exceeding 20% due to the inclusion of the fuzzy-hybrid model which includes the altitude/moisture and perturbation effects. Figure 15 shows the thruster’s angular velocity error comparing the sea level and altitude based models. Clearly the error (top graph) is nearly 5% and variant throughout the UAV flight scenario. The centre graph shows the thruster’s upper and lower injected ±10% perturbations in the Sugeno FIS and compared to the non-perturbation model. The error resulting from this test run is less than 1%, thus shown some influence of the armature Sugeno Inference Perturbation Analysis for Electric Aerial Vehicles 413 resistance variations cascading and affecting the propeller shaft angular velocity. However, (last graph), when the perturbation model is compared to the sea level model the error increased by approximately 10 times reaching a percentage error of up to 6%. Fig. 14. Altitude-based armature resistance error with respect to the nominal (top graph); altitude-based armature resistance error wrt ± 10% FIS Consequent perturbation (Centre graph); the lower graph is showing the error due to ± 10% FIS Consequent perturbation wrt the nominal armature resistance. Fig. 15. Altitude-based shaft angular velocity error with respect to the nominal (top graph); altitude-based angular velocity error wrt ± 10% FIS Consequent perturbation (Centre graph); the lower graph is showing the error due to ± 10% FIS Consequent perturbation wrt the nominal angular velocity. Electric Vehicles – Modelling and Simulations 414 3. Conclusion In this chapter we have learned how to incorporate sensor perturbations via the Sugeno fuzzy logic inference for electrical thruster systems which are propelling a class of electrically-powered unmanned aerial vehicles. Therefore, design considerations have included the UAV altitude variation and atmospheric moisture via the fuzzy logic Sugeno design framework. Furthermore the necessity of the fuzzy-hybrid modelling topology became apparent for the electrical thruster system. While the thruster was modelled utilising an ordinary differential equation form, the additional UAV operational conditions such as altitude and atmospheric moisture required the inclusion of the Sugeno-based fuzzy inference system thus amalgamating the two topologies into a single fuzzy-hybrid topology. 4. Nomenclature Nomenclature (Units are in SI) n Rule number n max Maximum number of rules j Number of Sensors j max Maximum number of sensors z j j-th sensor variable j n Z Membership function for the n h n-th rule function 123 (,,) n fzzz Linear polynomial in terms of z 1 ,z 2 , ,z j j c Centre for Gaussian type membership function for the j-th sensor j d Dispersion for Gaussian type membership function for the j-sensor η Horizontal shift operator n b Rule consequent offset j n  n-th rule j-th sensor polynomial coefficients * h Sugeno FIS output at time  . n  n-th rule rule firing j  j-th sensor error j  j-th sensor error upper boundary j  j-th sensor error lower boundary () a Vt PMDC Armature thruster voltage ()t Thruster angular velocity () a it Thruster Armature Current a K Thruster back emf constant a R Thruster armature resistance a R  Sugeno upper bound for armature resistance for different altitudes Sugeno Inference Perturbation Analysis for Electric Aerial Vehicles 415 a R  Sugeno lower bound for armature resistance for different altitudes L Thruster inductance a E Thruster equivalent back emf voltage ()t Shaft angle T K Thruster torque constant m T Thruster produced torque a J Thruster armature inertia L J Load inertia a B Thruster armature viscous angular damping L B Load viscous angular damping 1 N Thruster side gear teeth 2 N Load side gear teeth m P Thruster mechanical power  Constant in W re f R Reference resistance for thrusters armature at temperature re f T c a Coefficient of thermal expansion for copper  UAV Altitude in m  Air moisture condition T Temperature at altitude  re f T Reference temperature 5. References Kladis, G.P.; Economou, J.T.; Knowles, K.; Lauber, J. & Guerra T.M. (2010). Energy conservation based fuzzy tracking for unmanned aerial vehicle missions under a priori known wind information, Journal of Engineering Applications of Artificial Intelligence, Vol. 24, Issue 2, pp. 278-294. Karunarathne, L.; Economou J.T. & Knowles, K. (2007). Adaptive neuro fuzzy inference system-based intelligent power management strategies for fuel cell/battery driven unmanned aerial vehicles, Journal of Aerospace Engineering, Vol/ 224, No. G1, pp 77 – 88. Sugeno, M. (1999). On stability of fuzzy systems expressed by fuzzy rules with singleton consequents, IEEE Transactions on Fuzzy Systems, Vol. 7, Issue 2, pp 201-224. Economou, J.T. & Colyer, R.E. (2005). Fuzzy-hybrid modelling of an Ackerman steered electric vehicle, International Journal of Approximate Reasoning, Vol.41, No.3, pp. 343-368. Ehsani, M.; Gao, Y.; Gay, S.E. & Emadi, A., (2005). Modern Electric, Hybrid Electric, and Fuel Cell Vehicles, CRC Press, ISBN 0 8493 3154 4, USA. Economou, J.T.; Tsourdos, A. & White B.A. (2007). Fuzzy logic consequent perturbation analysis for electric vehicles , Journal of Automobile Engineering, Proceedings of the IMech E PART D., Vol. 221, No D7, pp 757-765. Electric Vehicles – Modelling and Simulations 416 Miller, J.M., (2004). Propulsion Systems for Hybrid Vehicles, IEE Power & Energy Series 45, ISBN 0 86341 336 6, UK. 19 Extended Simulation of an Embedded Brushless Motor Drive (BLMD) System for Adjustable Speed Control Inclusive of a Novel Impedance Angle Compensation Technique for Improved Torque Control in Electric Vehicle Propulsion Systems Richard A. Guinee Cork Institute of Technology Ireland 1. Introduction As already stated for the reasons given in a previous chapter a good continuous time model, of low complexity, of a BLMD system is essential to adequately describe mathematically the PWM inverter switching process with dead time and subsequent binary waveform generation in terms of the switching instant occurrences for accurate computer aided design (CAD) of embedded BLMD model simulation in proposed electric vehicle (EV) propulsion systems. In this chapter a complete software model of the BLMD system as a set of difference equations representing subsystem functionality, the organization of these subsystem activities into flowchart form and the processing details of these modular activities as software function calls in C-language for simulation purposes (Guinee, 2003) is presented. Furthermore in this the second chapter, concerning BLMD model fidelity for EV applications, BLMD model simulation accuracy for embedded EV CAD is next checked for a range of restraining shaft load torques via numerical simulation and then extensively compared and benchmarked for accuracy against theoretical estimates using known manufacturer’s catalogued specifications and motor drive constants (Guinee, 2003). Model simulation accuracy is further substantiated and validated through evaluation of the shaft velocity step response rise time when cross checked against (i) experimental test data and (ii) that evaluated from the catalogued performance index relating to the brushless motor dynamic factor (Guinee, 2003). Numerical simulation with outer velocity loop closure is used to demonstrate the accuracy of the completed BLMD reference model, based on established model confidence in torque control mode, in ASD configuration when compared with experimental test data. In addition to the BLMD model structure presented in the previous chapter for actual drive emulation two innovative measures which relate to increased drive performance are also provided. These novel techniques (Guinee, 2003), which include Electric Vehicles – Modelling and Simulations 418 i. inverter dead time cancellation and ii. motor stator winding impedance angle compensation, are encapsulated within the BLMD model framework and simulated for validation purposes and prediction of enhanced drive performance in EV systems. An approximate analysis is given to support the approach taken and verify the performance outcome in each case. In the first of these BLMD performance enhancements a novel compensation method has already been presented in the first chapter to offset the torque reduction effects of inverter delay during BLMD operation. This simple expedient relies on the zener diode clamping of the triangular carrier voltage during the carrier waveform comparison with the modulating current control signal in the comparator modulator to nullify power transistor turnon delay. This approach obviates the need for separate compensation timing circuitry in each phase as required in other schemes. The accuracy of this methodology is supported by current feedback, EM torque generation and shaft velocity trace simulation when compared with similar traces from the BLMD benchmark reference model with the effects of the inverter basedrive trigger delay neglected. The second proposed innovative improvement, presented in this chapter, relates to the progressive introduction of commutation phase lead with increased shaft speed as BLMD impedance angle compensation which forces the impedance angle to the same value as the internal power factor angle. This effect maintains zero load angle between the stator winding terminal voltage and the back emf. It also results in rated load torque delivery at lower shaft speeds with minimal rise time, overshoot and settling time in the generated torque for a range of torque demand input values. This novel technique greatly enhances the dynamic performance of the embedded BLMD prime mover in EV applications without overstressing mechanical assembly components during periods of rapid acceleration and deceleration. The incorporation of this novel impedance angle compensation technique thus minimizes component wear-out such as gear boxes, transmission shafts and wheel velocity joints and consequently enhances overall EV reliability improvement. BLMD simulation is provided in torque control mode at rated torque load conditions, for the actual drive system represented, with and without impedance angle compensation to gauge model performance accuracy over a range of torque demand step input values. 2. BLMD model structure and program sequence of activities The BLMD model structure is composed of interconnected subsystems with feedback as shown in Figure 1, of varying complexity according to physical principles. Consequently it can be described by a discrete time configuration of first order digital filter realizations for linear elements cascaded with difference equations representing nonlinear PWM inverter behaviour into a complete software model for simulation purposes as illustrated in Figure 2. The BLMD model program is organized into a sequence of software activities, coded in C-language as function calls, representing the functionality of various subsystem modules shown as the flowchart in Figure 3. All subsystem output (o/p) variable quantities in the cascaded activity chain are assumed to remain constant, once computed irrespective of feedback linkage, throughout the remainder of the time step interval t k based on the simulation sampling rates (1/t k ) chosen from considerations given in section 3.1 of the previous chapter. The essential features of the BLMD model program in Figure 3 can be explained by means of the linked modular software configuration encoded as the functional block sequence in Figure 2 along with the appropriate C-language code segments illustrated in Figure 4. [...]... 419 420 Electric Vehicles – Modelling and Simulations Fig 2-A Software Functional Block Diagram (Guinee, 2003) of a BLMD System Extended Simulation of an Embedded Brushless Motor Drive (BLMD) System for Adjustable Speed Control Inclusive of a Novel Impedance Angle Compensation Technique Fig 2-B Software Functional Block Diagram of a BLMD System 421 422 Electric Vehicles – Modelling and Simulations. .. back_emfk[j] // Motor back EMF vke[j] ph_curk[j] // Stator winding Phase current iks[j]  init_vars ( )  // Function initializes all global variables and arrays to 0.0 Fig 4-1 Declaration and Initialization (Guinee, 2003) 426 Electric Vehicles – Modelling and Simulations Fig 5 Network Structure (Guinee, 1999) of a Typical Brushless Motor Drive System Extended Simulation of an Embedded Brushless Motor Drive... in the execution of the carrier function dither ( ) and rerun of the call sequence run_to_pwmsw ( ) followed by the block function call run_post_pwmsw ( ) The post PWM 432 Electric Vehicles – Modelling and Simulations simulation call list contains the additional BLMD model basedrive switching features as an embedded layer in the nested base_drive ( ) and associated switch event signalling test_drk_xover... consequence of its dependency on torque demand input The corresponding generated torque step response family of characteristics 438 e Electric Vehicles – Modelling and Simulations  4v  d  9 v & d  1v for the specified variation in torque demand inputs are shown in Figures 8 and 9 r Motor Speed Step Response Characteristics r Rads.sec-1 400 S h a f t S p e e d 0 Rads.sec-1 400 S h a f t T res  d =6v... (pslp*temp-Ad); // Pos going ramp else return (Ad-(temp-period/2)*pslp);} //Neg going ramp 430 Electric Vehicles – Modelling and Simulations The o/p status of the comparator modulator is examined by comparing the trapped value cpwmtrk[j] at the beginning of the time step tk-1 with the new o/p pwmtrk[j] at tk for each phase j and signalling any change via the pwm_test_flag in the function call test_pwm_xover (... if (drk_sw_flag>0) // interrogate basedrive turn ON and OFF // times with subsequent inverter operation inter_base_drk_sim (&drk_sw_flag); else // No basedrive switching - proceed with // remaining BLMD model simulation run_post_drksw ( ); 1 Fig 3-A Program Flow Diagram (Guinee, 2003) for BLMD Model Simulation 424 Electric Vehicles – Modelling and Simulations 1 inter_base_drk_sim (&drk_sw_flag); restore_filt_out... -1.0; discrete.d1=bt-temp.d1; } discrete.k=temp.k; return discrete; } return discrete;} Fig 4-2 Linear Subsystem Discretization 428 Electric Vehicles – Modelling and Simulations Before proceeding with model program execution in the kth time step (tk-1  tk) all global variables and arrays are captured in the function call capture_filt_out ( ) for later reinstatement, during accurate resolution of the width... ph_htk[test_flag]=back_emfk[test_flag]; for(j=1;j . perturbation analysis for electric vehicles , Journal of Automobile Engineering, Proceedings of the IMech E PART D., Vol. 221, No D7, pp 757-765. Electric Vehicles – Modelling and Simulations 416. same power pack. Fig. 12. Nominal (blue) and altitude based copper losses and propeller shaft powers. Electric Vehicles – Modelling and Simulations 412 Figure 12, (lower graph), shows. velocity. Electric Vehicles – Modelling and Simulations 414 3. Conclusion In this chapter we have learned how to incorporate sensor perturbations via the Sugeno fuzzy logic inference for electrical