1. Application of Chaos in Electric Drive Systems
K. T. Chau
Department of Electrical and Electronic Engineering, The University of Hong Kong, Hong Kong, China
Zheng Wang
School of Electrical Engineering,
Southeast University, Nanjing, China
Chaos in Electric Drive Systems: Analysis, Control and Application, First Edition. K.T. Chau and Zheng Wang.
© 2011 John Wiley & Sons (Asia) Pte Ltd. Published 2011 by John Wiley & Sons (Asia) Pte Ltd.

2. Stabilization of Chaos in Automotive Wiper Systems
Fig. 1 Automotive wiper system (Left: structure; Right: equivalent circuit).
Chaos in Electric Drive Systems: Analysis, Control and Application, First Edition. K.T. Chau and Zheng Wang.
© 2011 John Wiley & Sons (Asia) Pte Ltd. Published 2011 by John Wiley & Sons (Asia) Pte Ltd.

3. Stabilization of Chaos in Automotive Wiper Systems
Fig. 2 Bifurcation diagram.
Chaos in Electric Drive Systems: Analysis, Control and Application, First Edition. K.T. Chau and Zheng Wang.
© 2011 John Wiley & Sons (Asia) Pte Ltd. Published 2011 by John Wiley & Sons (Asia) Pte Ltd.

4. Stabilization of Chaos in Automotive Wiper Systems
Fig. 3 Extended time delayed auto-synchronization (Upper: block diagram; Lower: bifurcation diagram).
Chaos in Electric Drive Systems: Analysis, Control and Application, First Edition. K.T. Chau and Zheng Wang.
© 2011 John Wiley & Sons (Asia) Pte Ltd. Published 2011 by John Wiley & Sons (Asia) Pte Ltd.

5. Stabilization of Chaos in Automotive Wiper Systems
Fig. 4 Simulated performance of ETDAS (Left: stabilization of chaotic motion; Right: suppression of periodic motion).
Chaos in Electric Drive Systems: Analysis, Control and Application, First Edition. K.T. Chau and Zheng Wang.
© 2011 John Wiley & Sons (Asia) Pte Ltd. Published 2011 by John Wiley & Sons (Asia) Pte Ltd.

6. Stabilization of Chaos in Automotive Wiper Systems
Fig. 5 Experimental waveforms (Left: without control; Right: with ETDAS).
Chaos in Electric Drive Systems: Analysis, Control and Application, First Edition. K.T. Chau and Zheng Wang.
© 2011 John Wiley & Sons (Asia) Pte Ltd. Published 2011 by John Wiley & Sons (Asia) Pte Ltd.

7. Stabilization of Chaos in Centrifugal Governor Systems
Fig. 6 Stabilization of chaos in centrifugal governor system with ETDAS (Left: structure; Right: waveform).
Chaos in Electric Drive Systems: Analysis, Control and Application, First Edition. K.T. Chau and Zheng Wang.
© 2011 John Wiley & Sons (Asia) Pte Ltd. Published 2011 by John Wiley & Sons (Asia) Pte Ltd.

8. Stabilization of Chaos in Rate Gyro Systems
Fig. 7 Stabilization of chaos in rate gyro systems with ETDAS (Left: structure; Right upper: trajectory without control; Right lower: trajectory with ETDAS).
Chaos in Electric Drive Systems: Analysis, Control and Application, First Edition. K.T. Chau and Zheng Wang.
© 2011 John Wiley & Sons (Asia) Pte Ltd. Published 2011 by John Wiley & Sons (Asia) Pte Ltd.

9. Chaotic Modulation for EMC Improvement in Electric Drive Systems
Fig. 8 Conducted EMI in induction drive system.
Chaos in Electric Drive Systems: Analysis, Control and Application, First Edition. K.T. Chau and Zheng Wang.
© 2011 John Wiley & Sons (Asia) Pte Ltd. Published 2011 by John Wiley & Sons (Asia) Pte Ltd.

10. Chaotic Modulation for EMC Improvement in Electric Drive Systems
Fig. 9 Principle of chaotic space vector PWM (Left: switching logic; Right: flowchart).
Chaos in Electric Drive Systems: Analysis, Control and Application, First Edition. K.T. Chau and Zheng Wang.
© 2011 John Wiley & Sons (Asia) Pte Ltd. Published 2011 by John Wiley & Sons (Asia) Pte Ltd.

11. Chaotic Modulation for EMC Improvement in Electric Drive Systems
Fig. 10 Comparison of measured power spectra (Upper left: fixed switching frequency SVPWM; Upper right: random switching frequency SVPWM; Lower left: chaotically amplitude-modulated switching frequency (CAFM) SVPWM; Lower right: chaotically frequency-modulated switching frequency (CFFM) SVPWM).
Chaos in Electric Drive Systems: Analysis, Control and Application, First Edition. K.T. Chau and Zheng Wang.
© 2011 John Wiley & Sons (Asia) Pte Ltd. Published 2011 by John Wiley & Sons (Asia) Pte Ltd.

12. Chaotic Modulation for EMC Improvement in Electric Drive Systems
Fig. 11 Vector control of chaotic SVPWM inverter fed induction drive system.
Chaos in Electric Drive Systems: Analysis, Control and Application, First Edition. K.T. Chau and Zheng Wang.
© 2011 John Wiley & Sons (Asia) Pte Ltd. Published 2011 by John Wiley & Sons (Asia) Pte Ltd.

13. Chaotic Modulation for EMC Improvement in Electric Drive Systems
Fig. 12 Measured stator currents of vector controlled induction drive system (Upper: CAFM-SVPWM; Lower: CFFM-SVPWM).
Chaos in Electric Drive Systems: Analysis, Control and Application, First Edition. K.T. Chau and Zheng Wang.
© 2011 John Wiley & Sons (Asia) Pte Ltd. Published 2011 by John Wiley & Sons (Asia) Pte Ltd.

14. Chaotic Compaction
Fig. 13 Chaotic compactors (Left: Mechanically; Right: Electrically).
Chaos in Electric Drive Systems: Analysis, Control and Application, First Edition. K.T. Chau and Zheng Wang.
© 2011 John Wiley & Sons (Asia) Pte Ltd. Published 2011 by John Wiley & Sons (Asia) Pte Ltd.

15. Chaotic Compaction
Fig. 14 Experimental setup of electrically chaotic compactor (Left: configuration; Right: block diagram).
Chaos in Electric Drive Systems: Analysis, Control and Application, First Edition. K.T. Chau and Zheng Wang.
© 2011 John Wiley & Sons (Asia) Pte Ltd. Published 2011 by John Wiley & Sons (Asia) Pte Ltd.

16. Chaotic Compaction
Fig. 15 Measured speed waveforms under different control strategies (Upper left: constant feed-in voltage (CFV); Upper right: sinusoidal speed reference (SSR); Lower left: proportional time delay feedback (PTF); Lower right: chaotic speed reference (CSR)).
Chaos in Electric Drive Systems: Analysis, Control and Application, First Edition. K.T. Chau and Zheng Wang.
© 2011 John Wiley & Sons (Asia) Pte Ltd. Published 2011 by John Wiley & Sons (Asia) Pte Ltd.

17. Chaotic Compaction Height before compaction (mm)
Height after compaction (mm)
Fall height (mm)
CFV 95
71.6
23.4
SSR
70.5
24.5
PTD
69.9
25.1
CSR
69.8
25.2
Periodic compaction
Chaotic compaction
The compaction of each control is carried out for five times, and the average fall height of the solid particles under compaction is physically measured. For all compaction processes, the energy consumption is kept the same.
Chaos in Electric Drive Systems: Analysis, Control and Application, First Edition. K.T. Chau and Zheng Wang.
© 2011 John Wiley & Sons (Asia) Pte Ltd. Published 2011 by John Wiley & Sons (Asia) Pte Ltd.

18. Chaotic Mixing
Fig. 16 Electrically chaotic mixer (Left: structure; Right: control diagram).
Chaos in Electric Drive Systems: Analysis, Control and Application, First Edition. K.T. Chau and Zheng Wang.
© 2011 John Wiley & Sons (Asia) Pte Ltd. Published 2011 by John Wiley & Sons (Asia) Pte Ltd.

19. Chaotic Mixing 5s 10s 20s 360s Fig. 17 Constant speed mixing.
Chaos in Electric Drive Systems: Analysis, Control and Application, First Edition. K.T. Chau and Zheng Wang.
© 2011 John Wiley & Sons (Asia) Pte Ltd. Published 2011 by John Wiley & Sons (Asia) Pte Ltd.

20. Chaotic Mixing 5s 10s 20s 30s Fig. 18 Chaotic speed mixing.
Chaos in Electric Drive Systems: Analysis, Control and Application, First Edition. K.T. Chau and Zheng Wang.
© 2011 John Wiley & Sons (Asia) Pte Ltd. Published 2011 by John Wiley & Sons (Asia) Pte Ltd.

21. Chaotic Mixing Mixing Method Time (s) Constant-speed 360
Rectangularly bidirectional 33
Sinusoidally bidirectional
Chaotic 30
The mixing of each control is carried out until homogeneity is achieved. For all mixing processes, the average input power is kept the same.
Chaos in Electric Drive Systems: Analysis, Control and Application, First Edition. K.T. Chau and Zheng Wang.
© 2011 John Wiley & Sons (Asia) Pte Ltd. Published 2011 by John Wiley & Sons (Asia) Pte Ltd.