Switched Reluctance Machine Modeling Applied on a MRAC Scheme

Transcription

1 Switched Reluctance Machine Modeling Applied on a MRAC Scheme Arnaldo Matute a, Julio Viola b,c, José Restrepo a,b,c, José Manuel Aller a,b,c, Flavio Quizhpi c a Universidad Simón Bolívar. Caracas, Venezuela b Prometeo Project Researcher c Universidad Politécnica Salesiana. Cuenca, Ecuador

2 Introduction Switched Reluctance Machines (SRM) are of considerable interest on several applications: Automotive Traction. Coolant pump drives. Wind energy conversion. Aerospace systems. Advantages over other electrical motors: Easy to build. Higher fault tolerance due to independence of windings. Disadvantages Special power converter topology. Highly nonlinear equations for modeling.

3 Introduction Switched Reluctance Machines (SRM) are of considerable interest on several applications: Automotive Traction. Coolant pump drives. Wind energy conversion. Aerospace systems. Advantages over other electrical motors: Easy to build. Higher fault tolerance due to independence of windings. Disadvantages Special power converter topology. Highly nonlinear equations for modeling.

4 Introduction The idea of a soft computing model for the SRM would reduce processing times and computing costs for its execution on a MRAC (Model Reference Adaptive Control) Scheme. Fuzzy Inference Systems are universal approximators capable of adapting nonlinear input output relations whenever an appropiate and training is provided. FIS to adapt nonlinear relations in the SRM model are obtained through a training algorithm. Despite of behaving as nonlinear systems the internal mathematical operations remain linear and simple enough to be executed in low cost microprocessors Since Linear relations in the SRM model are simple enough for being executed by low cost microprocessors, they will remain unvaried.

5 SRM Modeling The state equations for a 6/4 SRM are:

6 SRM Modeling The state equations for a 6/4 SRM are: First Equation provides the relation between magnetic flux and, current and inductance.

7 SRM Modeling The state equations for a 6/4 SRM are: First Equation provides the relation between magnetic flux and, current and inductance.

8 SRM Modeling The state equations for a 6/4 SRM are: First Equation provides the relation between magnetic flux and, current and inductance. Neglecting saturation effects, it can be rewritten as a relation where flux and rotor position are inputs and current is the output.

9 SRM Modeling The state equations for a 6/4 SRM are: Remains as a linear relation between rotor position and angular speed.

10 SRM Modeling The state equations for a 6/4 SRM are: The third equation can be rewritten as two equations: The first one is linear The second one is the nonlinear relation where current and rotor position are inputs and Electrical Torque is the output.

11 SRM Modeling

12 SRM Modeling Nonlinear relations are replaced by two different FIS Inductive FIS Torque FIS

13 SRM Modeling Nonlinear relations are replaced by two different FIS Inductive FIS Torque FIS Linear relations remain crisp

14 SRM Modeling Nonlinear relations are replaced by two different FIS Inductive FIS Torque FIS Linear relations remain crisp

15 FIS Training To adapt the FIS to the nonlinear relations in the model, an ANFIS (Adaptive Neuro Fuzzy Inference System) algorithm is performed, where two sets of data are required: Training data: This set must contain data that is representative enough of dynamic features of the system under modeling. Checking data: This set must contain data corresponding to typical operation conditions for validating the model.

16 FIS Training To adapt the FIS to the nonlinear relations in the model, an ANFIS (Adaptive Neuro Fuzzy Inference System) algorithm is performed, where two sets of data are required: Data requirements can be accomplished using a stepped phase current reference, applied to a crisp model for the SRM, but the proposed modeling method can be applied also to data obtained from a real machine. With the recovered data two zero order Takagi Sugeno FIS were tuned.

17 Inductive FIS Input membership functions: Output Matrix of Rules:

18 Torque FIS Input membership functions: Output Matrix of Rules:

19 Simulations The obtained fuzzy model as well as the the previously available crisp corresponding model of the same SRM were executed for comparison on the following conditions.

20 Simulations Transient phase current Upper: Crisp Model. Lower: Fuzzy model

21 Simulations Permanent phase current Upper: Crisp Model. Lower: Fuzzy model

22 Simulations Transient rotor position Upper: Crisp Model. Lower: Fuzzy model

23 Simulations Permanent rotor position Upper: Crisp Model. Lower: Fuzzy model

24 Simulations Angular speed Upper: Crisp Model. Lower: Fuzzy model

25 Control Experiment MRAC (Model Reference Adaptive Control) scheme:

26 Control Experiment MRAC (Model Reference Adaptive Control) scheme: Real plant to be controlled by an adaptive Proportional Integral controller.

27 Control Experiment MRAC (Model Reference Adaptive Control) scheme: Reference model: Controlled by classical tunned Proportional Integral controller

28 Control Experiment MRAC (Model Reference Adaptive Control) scheme: Control rule: If error between reference model and real model is higher than 5%, the controler is Proportional Integral. Otherwise, the controller is just Proportional.

29 Control Experiment MRAC (Model Reference Adaptive Control) scheme: Since this experiment is simulated and the real plant s parameters are known, a random bias in a ±40% band around the nominal value is introduced to the SRM parameters so robustness of the control scheme can be assessed.

30 Control Experiment MRAC (Model Reference Adaptive Control) scheme: The reference model is the proposed fuzzy model

31 Control Experiment MRAC (Model Reference Adaptive Control) scheme: At t=0.2s a step is introduced to ω r setting its value to 300 rad/s

32 Control Experiment Angular speed Upper: Angular speed. Middle: Controler s integral component. Bottom: Error

33 Control Experiment The scheme accomplishes the speed control

34 Control Experiment Controller s integral component growing and switched response depicts how challenging the control experiment has been for the scheme.

35 Conclusion The proposed approach for obtaining fuzzy models for 6/4 SRM has been proved by simulations. The resulting models are suitable to act as reference on speed control schemes such as MRAC, that consider executing models in the algorithm. The developed method is a less expensive option from a computationally point of view, that may be implemented on less complex digital control architectures. Intentional random deviations were applied to the resistance and inductance parameters to test the robustness of the algorithm.

36 Thank You Questions? MSc. Ing. Arnaldo Matute