This paper investigates the numerical issue of a discrete-time induction-motor emulator implementation. The stability analysis of the finite-word-length implementation shows a coupling between required word length and the sample rate. We propose specific guidelines to analyze this coupling and to estimate the required data word length for both signals and coefficients of the model. To respect algorithm requirements, an FPGA-based implementation was used for architecture development. The direct torque control is implemented to verify in real time the AC-motor emulator prototype. 1. Introduction Control algorithms of electrical drives are usually tested by the attachment of electrical motors. Experimental testing requires direct measuring by employing measurement instrumentation and sensors that would be complex, impractical, noise sensitive, and expensive. Traditionally these tests are performed on motor and inverter models under software simulation environments which are, in most cases, non-real-time and unable to exactly replicate real operational conditions. In order to provide a real-time verification of the implemented control algorithm and increase the realism of simulation, the control algorithm is tested while connected to a real-time emulator for the plant (induction motor and inverter) [1]. Due to their high capacities of executing in real-time complex algorithm, FPGA technology is a good candidate for this kind of RT emulator [2]. For reasons of cost, simplicity, speeds and memory space, the real-time emulator of the induction motor is performed with the Euler’s shift discretization method and quantized with fixed point format [3]. The robustness of the discretized algorithm is a critical issue in fixed-point format implementation. It is well known that, stable, closed-loop system may become unstable when the algorithm is implemented using a fixed-point processor due to finite-word-length effects. The fractional part precisions in fixed point are chosen to guarantee a minimum signal-to-noise ratio for finite-word-length quantization effects. The integer part is computed using norms [4]. In an FPGA implementation, it is possible to use separate fixed-point format for each coefficient and signal in the algorithm. Hence, the use of FPGA allows maintaining a higher computational precision at critical points. In this paper, authors propose a real-time induction motor emulator designed in fixed point format for an FPGA implementation. The starting point is a continuous-time model. Discrete-time models are derived using the traditional shift form
References
[1]
S. Lentijo, A. Monti, E. Santi, C. Welch, and R. Dougal, “A new testing tool for power electronic digital control,” in Proceedings of the IEEE 34th Annual Power Electronics Specialists Conference, vol. 1, pp. 81–87, Acapulco, Mexico, June 2003.
[2]
T. Grandpierre, C. Lavarenne, and Y. Sorel, “Optimized rapid prototyping for real-time embedded heterogeneous multiprocessors,” in Proceedings of the 1999 7th International Conference on Hardware/Software Codesign (CODES '99), pp. 74–78, Rome, Italy, May 1999.
[3]
J. Wu, S. Chen, G. Li, and J. Chu, “Optimal finite-precision state-estimate feedback controller realizations of discrete-time systems,” IEEE Transactions on Automatic Control, vol. 45, no. 8, pp. 1550–1554, 2000.
[4]
D. Menard and O. Sentieys, “Automatic evaluation of the accuracy of fixed-point algorithms,” in Proceedings of the IEEE/ACM Conference on Design, Automation and Test in Europe (DATE '02), Paris, France, March 2002.
[5]
H.-M. Cheng and G. T.-C. Chiu, “Coupling between sample rate and required wordlength for finite precision controller implementation with delta transform,” in Proceedings of the American Control Conference (ACC '07), pp. 3588–3593, New York, NY, USA, July 2007.
[6]
R. S. H. Istepanian, G. Li, J. Wu, and J. Chu, “Analysis of sensitivity measures of finite-precision digital controller structures with closed-loop stability bounds,” IEEE Proceedings of control Theory Application, vol. 145, no. 5, pp. 472–478, 1998.
[7]
I. Takahachi and T. Nogushi, “A new quick response and high efficiency control strategy of an induction motor,” IEEE Transactions on Industry Applications, vol. IA-22, no. 5, pp. 820–827, 1986.
[8]
O. Vainio, S. J. Ovaska, and J. J. Pasanen, “A digital signal processing approach to real-time AC motor modeling,” IEEE Transactions on Industrial Electronics, vol. 39, no. 1, pp. 36–45, 1992.
[9]
L. Charaabi, E. Monmasson, and I. Slama-Belkhodja, “FPGA-based real-time emulation of induction motor using fixed point representation,” in Proceedings of the 34th Annual Conference of the IEEE Industrial Electronics Society (IECON '08), pp. 2393–2398, November 2008.
[10]
Z. Fang, J. E. Carletta, and R. J. Veillette, “A methodology for FPGA-based control implementation,” IEEE Transactions on Control Systems Technology, vol. 13, no. 6, pp. 977–987, 2005.
[11]
M. H. Hayes, Schaum's Outline of Theory and Problems of Digital Signal Processing, McGraw-Hill, New York, NY, USA, 1998.
[12]
T. Grandpierre, C. Lavarenne, and Y. Sorel, “Optimized rapid prototyping for real-time embedded heterogeneous multiprocessors,” in Proceedings of the 1999 7th International Conference on Hardware/Software Codesign (CODES'99), pp. 74–78, May 1999.
[13]
E. Monmasson and M. N. Cirstea, “FPGA design methodology for industrial control systems-a review,” IEEE Transactions on Industrial Electronics, vol. 54, no. 4, pp. 1824–1842, 2007.