1. Control 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 DC Drive Systems
Fig. 1 Stabilization of chaos in voltage controlled DC drive system using time-delayed feedback control.
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 DC Drive Systems
Fig. 2 Simulated trajectories (Left: original chaotic motion; Middle: controlled period-1 motion; Right: controlled period-2 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.

4. Stabilization of Chaos in DC Drive Systems
Fig. 3 Experimental trajectories (Left: original chaotic motion; Middle: controlled period-1 motion; Right: controlled period-2 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.

5. Stabilization of Chaos in PM Brushless AC Drive Systems
Fig. 4 Simulated responses (Upper left: nonlinear feedback control; Upper right: backstepping control; Lower left: dynamic surface control; Lower right: sliding mode control).
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. Stimulation of Chaos in DC Drive Systems
Fig. 5 Stimulation of chaos in DC drive system using time-delay feedback control (Left: block diagram; Right: 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.

7. Stimulation of Chaos in DC Drive Systems
Fig. 6 Experimental results of stimulation of chaos in DC drive system using time-delay feedback control (Left: constant speed operation; Right: chaotic speed operation).
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. Stimulation of Chaos in DC Drive Systems
Fig. 7 Stimulation of chaos in DC drive system using proportional time-delay control (Left: block diagram; Right: 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.

9. Stimulation of Chaos in DC Drive Systems
Fig. 8 Experimental waveforms in DC drive system using proportional time-delay control (Left: motor speed; Right: armature current).
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. Stimulation of Chaos in DC Drive Systems
Fig. 9 Stimulation of chaos in DC drive system using chaotic signal reference control (Left: block diagram; Right: 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.

11. Stimulation of Chaos in DC Drive Systems
Fig. 10 Experimental waveforms in DC drive system using chaotic signal reference control (Left: motor speed; Right: armature current).
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. Stimulation of Chaos in PM Brushless AC Drive Systems
Fig. 11 Stimulation of chaos in PM brushless AC drive system using time-delay feedback control (Left: block diagram; Right: measured 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.

13. Stimulation of Chaos in Doubly Salient PM Drive Systems
Fig. 12 Stimulation of chaos in doubly salient PM drive system by designing PM flux (Left: motor topology; Right: 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.

14. Stimulation of Chaos in Shaded Pole Induction Drive Systems
Fig. 13 Stimulation of chaos in shaded pole induction drive system by designing main winding voltage (Left: motor topology; Right: 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.