Fuzzy Control Of Ac Induction
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Fuzzy Application Library/Technical Applications/AC Induction Motor Fuzzy Logic Enhanced Control of an AC Induction Motor with a DSP S. Beierke; Texas Instruments, Germany, [email protected] -- C. von Altrock; INFORM GmbH, Aachen, Germany, [email protected] -- R. Hemmerlein, Inform Software Corp., Chicago, U.S.A., [email protected] Citation Reference: This paper was published at the Fifth IEEE International Conference on Fuzzy Systems, held in New Orleans September 1996. The Fuzzy Logic Application Note series is published by Inform Software Corporation on its Internet server to promote the use of fuzzy logic technologies in applications. Fuzzy logic is a new and innovative technology being used to enhance control engineering solutions. It allows complex system design directly from engineering experience and experimental results, thus quickly rendering efficient solutions. In a joint application project, Texas Instruments and Inform Software have used fuzzy logic to improve AC induction motor control. The results were intriguing: control performance has been improved while design effort has been significantly reduced.
1. Introduction Market analysis shows that 90% of all industrial motor applications use AC induction type motors. The reasons for this are high robustness, reliability, low cost, and high efficiency. The drawback of using an AC induction type motor is its difficult controllability, which is due to a strong nonlinear behavior stemming from magnetic saturation effects and a strong temperature dependency of electrical motor parameters. For example, the rotor time constant of an induction motor can change up to 70% over the temperature range of the motor. These factors make mathematical modeling of motor control systems difficult. In real applications, only simplified models are used. The commonly used control methods are: • • •
voltage/frequency control (U/f) stator current flux control (Is/f2) field oriented control
Of these approaches, the field-oriented control method has become the de-facto standard for speed and position control of AC induction motors. It delivers the best dynamic behavior and a high robustness under sudden momentum changes. Alas, the optimization and parameterization of a field oriented controller is laborious and must be performed specifically for each motor. Also, due to the strong dependency of the motor's parameters, a controller optimized for one temperature may not perform well if the temperature changes. To avoid the undesirable characteristics of the field oriented control approach, the companies Texas Instruments and Inform Software have developed new alternative control methods, and compared them with the field oriented control approach. The alternative methods involved two types of flux controllers enhanced by fuzzy logic and NeuroFuzzy
techniques, respectively. The goal was to use fuzzy logic to improve the dynamic behavior of the flux control approach such that the robust behavior of the flux controller and the desirable dynamic properties of the field oriented controller are achieved simultaneously. For a practical introduction to fuzzy logic and NeuroFuzzy technologies, see [1]. Figure 1: Demonstration of the Test Motor at the Embedded Systems Conference, San Jose 1995 (large)
2. Field Oriented Control Method Figure 2 shows the principle of field oriented control. It allows for control of the AC induction motor in the same way a separately exited DC motor is controlled. The flux model computes the "phase shift" between rotor flux field and stator field from the stator currents iu and iv, and the rotor angle position n. The field oriented variables of the two independent controller units are subsequently computed by the transformation of the stator currents using this "phase shift". The actual control model consists of two components of cascaded standard PI controllers. The upper component comprises outer magnetizing current (imR) controller and inner isd current controller. The lower component comprises a speed controller and momentum controller. The input of the speed controller is computed as the difference between set speed nref and filtered measured speed n. To optimize the field oriented control model, all controllers must be parameterized and optimized individually. In this application project, the method of optimized amplitude adaptation was used to tune the current controller, and the method of the symmetrical optimum was used for the velocity controller. Implementation effort for the field oriented controller was 3 person months, including parameterization and design of the flux model. The computation time for the inner current controllers, the flux model, and the coordinate transformation is 100µs on a TMS320C31-40MHz digital signal processor. The resulting performance is shown in Figure 6. When switching the set speed from -1000 rmp to +1000 rpm, the new set speed is reached within only 0.25 seconds without any overshoot. However, this excellent performance is not always available. When the motor heats up the control performance drops significantly, and a motor with slightly different characteristics will achieve only mediocre results utilizing the same controller.
Figure 2: Field-Oriented Control of AC Induction Motors (large)
3. Fuzzy Flux Control Method The conventional flux control model has been enhanced by fuzzy logic in two steps. In the first step, the non-linear relation between slip frequency and stator current was described by a fuzzy logic system (Fuzzy Block #1). Figure 3 shows the principle of the resulting fuzzy flux controller. The control model consists of three inner control loops and one outer control loop. The inner control loops control the three stator phase currents using standard PI controllers. The outer control loop determines the slip frequency n2, also using a standard PI controller. The slip frequency is the input to Fuzzy Block #1, which outputs the set value of the stator current. The primary objective for Fuzzy Block #1 is to keep the magnetizing current constant in all operating modes. The magnetizing current is a nonlinear function of the slip frequency, the rotor time constant, the rotor leakage factor, and a non-constant offset current. Figure 3: Principle of a Fuzzy Flux Controller (large)
The stator frequency n1 is the sum of the measured rotor frequency n and the slip frequency n2. The reference position is determined by integration of the stator frequency n1. Modulated by sin/cos, the reference position is multiplied with the set value of the stator current, and split back into a 3 phase system of the stator current set values. The rules of the fuzzy block were not manually designed, but rather generated from existing sample data by the NeuroFuzzy add-on module of the fuzzyTECH design software. NeuroFuzzy utilizes neural network techniques to automatically generate rule bases and membership functions from sample data. The benefit of the NeuroFuzzy approach over the neural net approach is that the result of NeuroFuzzy training is a transparent fuzzy logic system that can be explicitly optimized and verified. In contrast, the result of a neural net training is a rather non-transparent black box [1].
4. Comparison with Field Oriented Control Figure 6 shows the performance of the fuzzy flux controller in comparison with the field oriented controller. The overshoot performance is almost as good as that provided by the field oriented control, however, it takes the fuzzy flux controller almost twice as long to reach the new set speed (curve Fuzzy_1). On the other hand, parameterization and optimization of the fuzzy flux controller only required 4 person days. The computation time for the entire controller is 150µs on the TMS320C31-40MHz digital signal processor.
To improve the performance of the fuzzy flux controller, in a second step, the standard PI controller for the outer control loop was replaced by a fuzzy PI controller (Fuzzy Block #2 in Figure 4). This fuzzy PI controller does not use the proportional (P) and integral (I) component of the error signal, but rather the differential (D) and proportional (P) component then integrates the output. This type of fuzzy PI controller has been used very successfully in a number of recent applications, especially in the area of speed and temperature control [1]. In contrast to the standard PI controller, the fuzzy PI controller implements a highly non-linear transfer characteristic. The sub-window in the lower left part of Figure 5 shows the transfer characteristics for the fuzzy PI controller implemented in this application. Figure 4: Enhanced Fuzzy Flux Controller (large)
The enhanced fuzzy flux controller reveals a much improved dynamic performance. Figure 6 shows the performance of the enhanced fuzzy flux controller (curve Fuzzy_2) in comparison to the fuzzy flux controller with only one fuzzy block. The enhanced fuzzy flux controller reaches the new set speed as fast as the field oriented controller and shows no overshoot at all. Initial analysis has also shown that the enhanced fuzzy flux controller is significantly more robust with regards to variances in motor parameters than the field oriented controller. The good performance attained in this case hinges on the non-linear behavior of the fuzzy PI controller. In contrast to the conventional linear PI controller, the non-linearity of the fuzzy PI controller produces stronger control action for a large speed error, and a smoother control action for a small speed error. This also results a higher robustness of the enhanced fuzzy flux controller against parameter changes. The implementation of the second fuzzy block with the fuzzy flux controller only required an additional day for the fuzzy logic system itself, and two additional days for the optimization of the total system. Hence, the total development effort for the enhanced fuzzy flux controller was 7 person days in comparison to 3 person month for the field oriented controller. The computation time for the entire controller is 200µs on the used TMS320C31-40MHz digital signal processor.
5. System Simulation Using Matlab/Simulink and fuzzyTECH The initial design of the system was implemented in a software simulation. The fuzzyTECH® fuzzy-system development software was used together with the Matlab™/Simulink™ control-system simulation software. fuzzyTECH allows using fuzzy blocks in Simulink's control diagrams [4]. This tool combination allows for the design of simulations combining conventional and fuzzy logic control engineering technologies in the same software environment. Figure 5 shows the development of the fuzzy blocks with fuzzyTECH/Simulink. The differential equation model used for the simulation of the AC induction motor is discussed in [3].
Figure 5: Simulation of the Enhanced Fuzzy Flux Controller Using the Software Products fuzzyTECH and Matlab/Simulink (large)
6. Fuzzy Logic on Digital Signal Processors Because of the increasing number of successful of applications of fuzzy logic in both control engineering and signal processing, DSP market leader Texas Instruments was looking for a software partner to implement fuzzy logic on DSP. In 1992, a formal partnership was formed with Inform Software Corp., a company specializing in fuzzy logic. One product of the partnership was the design of dedicated versions of fuzzyTECH that allow the implementation of fuzzy logic systems on standard TI-DSPs. The primary objective was to reach an acceptable computing performance level for fuzzy logic on DSPs, a quality previously unknown to software implementations of fuzzy logic. Using the fuzzyTECH assembly kernel for 16 bit resolution, 2.98 million fuzzy rules per second can be computed on the TMS230C52 (25ns instruction cycle DSP), including fuzzification and defuzzification. For comparison: the most recent dedicated fuzzy processor of VLSI (VY86C500/20) only computes 0.87 million fuzzy rules per second (not including fuzzification and defuzzification) with just 12 bit resolution (VLSI data sheet). While the referenced DSP only costs a few dollars in large quantities, the fuzzy processor is quoted at $75 each. This comparison shows that in most applications, the use of dedicated fuzzy processors is not necessary.
7. Result Discussion The application project discussed in this paper shows that even in areas where traditional control engineering already offers comprehensive solutions, fuzzy logic can deliver substantial benefits. The authors were astounded by the dramatically shorter design time for the fuzzy approach which delivered similar performance and higher robustness than the traditional approach. While the traditional approach required three (3) people months by a known expert in the area, the enhanced fuzzy flux controller only took seven (7) people days to implement. The fuzzyTECH assembly kernel for DSPs developed by Texas Instruments and Inform Software Corp. allows for the integration of fuzzy logic systems together with conventional algorithms on the same chip, even when control loop times of a fraction of a millisecond are required. Texas Instruments and Inform Software Corp. now work on further enhancements of the fuzzy flux controller. The companies are currently striving for even better dynamic performance by adding a fuzzy air-gap flux observer to the system.
Figure 6: Set Speed Response Comparison of the two Fuzzy Flux Control Approaches with the Field Oriented Control Approach (large)
8. Literature [1] v. Altrock, C.: "Fuzzy Logic and NeuroFuzzy Applications Explained"; Prentice Hall; ISBN 0-13-368465-2; 1995. [2] S. Beierke, R. Konigbauer, B. Krause, and C. v. Altrock: "Fuzzy Logic Enhanced Control of AC Motor Using DSP"; Embedded Systems Conference California; 1995. [3] D. Naunin, S. Beierke, and P. Heidrich: "Transputer Control of Asynchronous Servo Drives"; EPE Florence; 1991. [4] "fuzzyTECH User's Manual"; INFORM Software Corp., 2001 Midwest Rd., Oak Brook, IL60521, U.S.A.; 1995. [5] "TMS320C3X User's Guide; Texas Instruments; 1994.
1. Introduction Market analysis shows that 90% of all industrial motor applications use AC induction type motors. The reasons for this are high robustness, reliability, low cost, and high efficiency. The drawback of using an AC induction type motor is its difficult controllability, which is due to a strong nonlinear behavior stemming from magnetic saturation effects and a strong temperature dependency of electrical motor parameters. For example, the rotor time constant of an induction motor can change up to 70% over the temperature range of the motor. These factors make mathematical modeling of motor control systems difficult. In real applications, only simplified models are used. The commonly used control methods are: • • •
voltage/frequency control (U/f) stator current flux control (Is/f2) field oriented control
Of these approaches, the field-oriented control method has become the de-facto standard for speed and position control of AC induction motors. It delivers the best dynamic behavior and a high robustness under sudden momentum changes. Alas, the optimization and parameterization of a field oriented controller is laborious and must be performed specifically for each motor. Also, due to the strong dependency of the motor's parameters, a controller optimized for one temperature may not perform well if the temperature changes. To avoid the undesirable characteristics of the field oriented control approach, the companies Texas Instruments and Inform Software have developed new alternative control methods, and compared them with the field oriented control approach. The alternative methods involved two types of flux controllers enhanced by fuzzy logic and NeuroFuzzy
techniques, respectively. The goal was to use fuzzy logic to improve the dynamic behavior of the flux control approach such that the robust behavior of the flux controller and the desirable dynamic properties of the field oriented controller are achieved simultaneously. For a practical introduction to fuzzy logic and NeuroFuzzy technologies, see [1]. Figure 1: Demonstration of the Test Motor at the Embedded Systems Conference, San Jose 1995 (large)
2. Field Oriented Control Method Figure 2 shows the principle of field oriented control. It allows for control of the AC induction motor in the same way a separately exited DC motor is controlled. The flux model computes the "phase shift" between rotor flux field and stator field from the stator currents iu and iv, and the rotor angle position n. The field oriented variables of the two independent controller units are subsequently computed by the transformation of the stator currents using this "phase shift". The actual control model consists of two components of cascaded standard PI controllers. The upper component comprises outer magnetizing current (imR) controller and inner isd current controller. The lower component comprises a speed controller and momentum controller. The input of the speed controller is computed as the difference between set speed nref and filtered measured speed n. To optimize the field oriented control model, all controllers must be parameterized and optimized individually. In this application project, the method of optimized amplitude adaptation was used to tune the current controller, and the method of the symmetrical optimum was used for the velocity controller. Implementation effort for the field oriented controller was 3 person months, including parameterization and design of the flux model. The computation time for the inner current controllers, the flux model, and the coordinate transformation is 100µs on a TMS320C31-40MHz digital signal processor. The resulting performance is shown in Figure 6. When switching the set speed from -1000 rmp to +1000 rpm, the new set speed is reached within only 0.25 seconds without any overshoot. However, this excellent performance is not always available. When the motor heats up the control performance drops significantly, and a motor with slightly different characteristics will achieve only mediocre results utilizing the same controller.
Figure 2: Field-Oriented Control of AC Induction Motors (large)
3. Fuzzy Flux Control Method The conventional flux control model has been enhanced by fuzzy logic in two steps. In the first step, the non-linear relation between slip frequency and stator current was described by a fuzzy logic system (Fuzzy Block #1). Figure 3 shows the principle of the resulting fuzzy flux controller. The control model consists of three inner control loops and one outer control loop. The inner control loops control the three stator phase currents using standard PI controllers. The outer control loop determines the slip frequency n2, also using a standard PI controller. The slip frequency is the input to Fuzzy Block #1, which outputs the set value of the stator current. The primary objective for Fuzzy Block #1 is to keep the magnetizing current constant in all operating modes. The magnetizing current is a nonlinear function of the slip frequency, the rotor time constant, the rotor leakage factor, and a non-constant offset current. Figure 3: Principle of a Fuzzy Flux Controller (large)
The stator frequency n1 is the sum of the measured rotor frequency n and the slip frequency n2. The reference position is determined by integration of the stator frequency n1. Modulated by sin/cos, the reference position is multiplied with the set value of the stator current, and split back into a 3 phase system of the stator current set values. The rules of the fuzzy block were not manually designed, but rather generated from existing sample data by the NeuroFuzzy add-on module of the fuzzyTECH design software. NeuroFuzzy utilizes neural network techniques to automatically generate rule bases and membership functions from sample data. The benefit of the NeuroFuzzy approach over the neural net approach is that the result of NeuroFuzzy training is a transparent fuzzy logic system that can be explicitly optimized and verified. In contrast, the result of a neural net training is a rather non-transparent black box [1].
4. Comparison with Field Oriented Control Figure 6 shows the performance of the fuzzy flux controller in comparison with the field oriented controller. The overshoot performance is almost as good as that provided by the field oriented control, however, it takes the fuzzy flux controller almost twice as long to reach the new set speed (curve Fuzzy_1). On the other hand, parameterization and optimization of the fuzzy flux controller only required 4 person days. The computation time for the entire controller is 150µs on the TMS320C31-40MHz digital signal processor.
To improve the performance of the fuzzy flux controller, in a second step, the standard PI controller for the outer control loop was replaced by a fuzzy PI controller (Fuzzy Block #2 in Figure 4). This fuzzy PI controller does not use the proportional (P) and integral (I) component of the error signal, but rather the differential (D) and proportional (P) component then integrates the output. This type of fuzzy PI controller has been used very successfully in a number of recent applications, especially in the area of speed and temperature control [1]. In contrast to the standard PI controller, the fuzzy PI controller implements a highly non-linear transfer characteristic. The sub-window in the lower left part of Figure 5 shows the transfer characteristics for the fuzzy PI controller implemented in this application. Figure 4: Enhanced Fuzzy Flux Controller (large)
The enhanced fuzzy flux controller reveals a much improved dynamic performance. Figure 6 shows the performance of the enhanced fuzzy flux controller (curve Fuzzy_2) in comparison to the fuzzy flux controller with only one fuzzy block. The enhanced fuzzy flux controller reaches the new set speed as fast as the field oriented controller and shows no overshoot at all. Initial analysis has also shown that the enhanced fuzzy flux controller is significantly more robust with regards to variances in motor parameters than the field oriented controller. The good performance attained in this case hinges on the non-linear behavior of the fuzzy PI controller. In contrast to the conventional linear PI controller, the non-linearity of the fuzzy PI controller produces stronger control action for a large speed error, and a smoother control action for a small speed error. This also results a higher robustness of the enhanced fuzzy flux controller against parameter changes. The implementation of the second fuzzy block with the fuzzy flux controller only required an additional day for the fuzzy logic system itself, and two additional days for the optimization of the total system. Hence, the total development effort for the enhanced fuzzy flux controller was 7 person days in comparison to 3 person month for the field oriented controller. The computation time for the entire controller is 200µs on the used TMS320C31-40MHz digital signal processor.
5. System Simulation Using Matlab/Simulink and fuzzyTECH The initial design of the system was implemented in a software simulation. The fuzzyTECH® fuzzy-system development software was used together with the Matlab™/Simulink™ control-system simulation software. fuzzyTECH allows using fuzzy blocks in Simulink's control diagrams [4]. This tool combination allows for the design of simulations combining conventional and fuzzy logic control engineering technologies in the same software environment. Figure 5 shows the development of the fuzzy blocks with fuzzyTECH/Simulink. The differential equation model used for the simulation of the AC induction motor is discussed in [3].
Figure 5: Simulation of the Enhanced Fuzzy Flux Controller Using the Software Products fuzzyTECH and Matlab/Simulink (large)
6. Fuzzy Logic on Digital Signal Processors Because of the increasing number of successful of applications of fuzzy logic in both control engineering and signal processing, DSP market leader Texas Instruments was looking for a software partner to implement fuzzy logic on DSP. In 1992, a formal partnership was formed with Inform Software Corp., a company specializing in fuzzy logic. One product of the partnership was the design of dedicated versions of fuzzyTECH that allow the implementation of fuzzy logic systems on standard TI-DSPs. The primary objective was to reach an acceptable computing performance level for fuzzy logic on DSPs, a quality previously unknown to software implementations of fuzzy logic. Using the fuzzyTECH assembly kernel for 16 bit resolution, 2.98 million fuzzy rules per second can be computed on the TMS230C52 (25ns instruction cycle DSP), including fuzzification and defuzzification. For comparison: the most recent dedicated fuzzy processor of VLSI (VY86C500/20) only computes 0.87 million fuzzy rules per second (not including fuzzification and defuzzification) with just 12 bit resolution (VLSI data sheet). While the referenced DSP only costs a few dollars in large quantities, the fuzzy processor is quoted at $75 each. This comparison shows that in most applications, the use of dedicated fuzzy processors is not necessary.
7. Result Discussion The application project discussed in this paper shows that even in areas where traditional control engineering already offers comprehensive solutions, fuzzy logic can deliver substantial benefits. The authors were astounded by the dramatically shorter design time for the fuzzy approach which delivered similar performance and higher robustness than the traditional approach. While the traditional approach required three (3) people months by a known expert in the area, the enhanced fuzzy flux controller only took seven (7) people days to implement. The fuzzyTECH assembly kernel for DSPs developed by Texas Instruments and Inform Software Corp. allows for the integration of fuzzy logic systems together with conventional algorithms on the same chip, even when control loop times of a fraction of a millisecond are required. Texas Instruments and Inform Software Corp. now work on further enhancements of the fuzzy flux controller. The companies are currently striving for even better dynamic performance by adding a fuzzy air-gap flux observer to the system.
Figure 6: Set Speed Response Comparison of the two Fuzzy Flux Control Approaches with the Field Oriented Control Approach (large)
8. Literature [1] v. Altrock, C.: "Fuzzy Logic and NeuroFuzzy Applications Explained"; Prentice Hall; ISBN 0-13-368465-2; 1995. [2] S. Beierke, R. Konigbauer, B. Krause, and C. v. Altrock: "Fuzzy Logic Enhanced Control of AC Motor Using DSP"; Embedded Systems Conference California; 1995. [3] D. Naunin, S. Beierke, and P. Heidrich: "Transputer Control of Asynchronous Servo Drives"; EPE Florence; 1991. [4] "fuzzyTECH User's Manual"; INFORM Software Corp., 2001 Midwest Rd., Oak Brook, IL60521, U.S.A.; 1995. [5] "TMS320C3X User's Guide; Texas Instruments; 1994.
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