1. Date of download: 10/8/2017
Copyright © ASME. All rights reserved.
From: Stochastic Approximation Approach to Design of Linear Controllers for Tracking Systems With Asymmetric Saturation
J. Dyn. Sys., Meas., Control. 2015;137(12): doi: /
Figure Legend:
Stochastic linearization of asymmetric nonlinearity

2. Date of download: 10/8/2017
Copyright © ASME. All rights reserved.
From: Stochastic Approximation Approach to Design of Linear Controllers for Tracking Systems With Asymmetric Saturation
J. Dyn. Sys., Meas., Control. 2015;137(12): doi: /
Figure Legend:
Control-theoretic representations of stochastically linearized asymmetric nonlinearity. (a) Coupled representation and (b) decoupled representation.

3. Date of download: 10/8/2017
Copyright © ASME. All rights reserved.
From: Stochastic Approximation Approach to Design of Linear Controllers for Tracking Systems With Asymmetric Saturation
J. Dyn. Sys., Meas., Control. 2015;137(12): doi: /
Figure Legend:
Equivalent gain, N, and decoupled bias, md, as a function of measure of asymmetry, A. (a) N(A) and (b) md(A).

4. Date of download: 10/8/2017
Copyright © ASME. All rights reserved.
From: Stochastic Approximation Approach to Design of Linear Controllers for Tracking Systems With Asymmetric Saturation
J. Dyn. Sys., Meas., Control. 2015;137(12): doi: /
Figure Legend:
Coupled bias, |mc|, as a function of |A|

5. Date of download: 10/8/2017
Copyright © ASME. All rights reserved.
From: Stochastic Approximation Approach to Design of Linear Controllers for Tracking Systems With Asymmetric Saturation
J. Dyn. Sys., Meas., Control. 2015;137(12): doi: /
Figure Legend:
Nonlinear system

6. Date of download: 10/8/2017
Copyright © ASME. All rights reserved.
From: Stochastic Approximation Approach to Design of Linear Controllers for Tracking Systems With Asymmetric Saturation
J. Dyn. Sys., Meas., Control. 2015;137(12): doi: /
Figure Legend:
Stochastically linearized system in the coupled representation

7. Date of download: 10/8/2017
Copyright © ASME. All rights reserved.
From: Stochastic Approximation Approach to Design of Linear Controllers for Tracking Systems With Asymmetric Saturation
J. Dyn. Sys., Meas., Control. 2015;137(12): doi: /
Figure Legend:
Measure of asymmetry, A, as a function of μu and σu. (a) A(μu) and (b) A(σu).

8. Date of download: 10/8/2017
Copyright © ASME. All rights reserved.
From: Stochastic Approximation Approach to Design of Linear Controllers for Tracking Systems With Asymmetric Saturation
J. Dyn. Sys., Meas., Control. 2015;137(12): doi: /
Figure Legend:
Stochastically linearized system in the decoupled representation

9. Date of download: 10/8/2017
Copyright © ASME. All rights reserved.
From: Stochastic Approximation Approach to Design of Linear Controllers for Tracking Systems With Asymmetric Saturation
J. Dyn. Sys., Meas., Control. 2015;137(12): doi: /
Figure Legend:
Equivalent gain, N, and decoupled bias, md, as a function of A. (a) N(A) and (b)md(A).

10. Date of download: 10/8/2017
Copyright © ASME. All rights reserved.
From: Stochastic Approximation Approach to Design of Linear Controllers for Tracking Systems With Asymmetric Saturation
J. Dyn. Sys., Meas., Control. 2015;137(12): doi: /
Figure Legend:
AS-root locus of Example 1 with β=0.92

11. Date of download: 10/8/2017
Copyright © ASME. All rights reserved.
From: Stochastic Approximation Approach to Design of Linear Controllers for Tracking Systems With Asymmetric Saturation
J. Dyn. Sys., Meas., Control. 2015;137(12): doi: /
Figure Legend:
TE loci of system (27)

12. Date of download: 10/8/2017
Copyright © ASME. All rights reserved.
From: Stochastic Approximation Approach to Design of Linear Controllers for Tracking Systems With Asymmetric Saturation
J. Dyn. Sys., Meas., Control. 2015;137(12): doi: /
Figure Legend:
Tracking error distortion, δ, as a function of measure of asymmetry, A

13. Date of download: 10/8/2017
Copyright © ASME. All rights reserved.
From: Stochastic Approximation Approach to Design of Linear Controllers for Tracking Systems With Asymmetric Saturation
J. Dyn. Sys., Meas., Control. 2015;137(12): doi: /
Figure Legend:
Sketch of the TE locus for system (27) with μr=1, α=−0.5, and β=1.5

14. Date of download: 10/8/2017
Copyright © ASME. All rights reserved.
From: Stochastic Approximation Approach to Design of Linear Controllers for Tracking Systems With Asymmetric Saturation
J. Dyn. Sys., Meas., Control. 2015;137(12): doi: /
Figure Legend:
The TE locus for Example 1

15. Date of download: 10/8/2017
Copyright © ASME. All rights reserved.
From: Stochastic Approximation Approach to Design of Linear Controllers for Tracking Systems With Asymmetric Saturation
J. Dyn. Sys., Meas., Control. 2015;137(12): doi: /
Figure Legend:
Measure of asymmetry, A, as a function of controller gain, K

16. Date of download: 10/8/2017
Copyright © ASME. All rights reserved.
From: Stochastic Approximation Approach to Design of Linear Controllers for Tracking Systems With Asymmetric Saturation
J. Dyn. Sys., Meas., Control. 2015;137(12): doi: /
Figure Legend:
AS-root locus of Example 1 with β=1.3

17. Date of download: 10/8/2017
Copyright © ASME. All rights reserved.
From: Stochastic Approximation Approach to Design of Linear Controllers for Tracking Systems With Asymmetric Saturation
J. Dyn. Sys., Meas., Control. 2015;137(12): doi: /
Figure Legend:
Equivalent gain, Keff, and tracking error distortion, δ, as a function of measure of asymmetry, A. (a) Keff(A) and (b) δ(A).

18. Date of download: 10/8/2017
Copyright © ASME. All rights reserved.
From: Stochastic Approximation Approach to Design of Linear Controllers for Tracking Systems With Asymmetric Saturation
J. Dyn. Sys., Meas., Control. 2015;137(12): doi: /
Figure Legend:
Measure of asymmetry, A, as a function of average value of the reference, μr

19. Date of download: 10/8/2017
Copyright © ASME. All rights reserved.
From: Stochastic Approximation Approach to Design of Linear Controllers for Tracking Systems With Asymmetric Saturation
J. Dyn. Sys., Meas., Control. 2015;137(12): doi: /
Figure Legend:
The TE locus for Example 1 with β=0.92 and β=1.3

20. Date of download: 10/8/2017
Copyright © ASME. All rights reserved.
From: Stochastic Approximation Approach to Design of Linear Controllers for Tracking Systems With Asymmetric Saturation
J. Dyn. Sys., Meas., Control. 2015;137(12): doi: /
Figure Legend:
Responses of the system of Example 1 with β=0.92 and β=1.3. (a) β=0.92 and (b) β=1.3.

21. Date of download: 10/8/2017
Copyright © ASME. All rights reserved.
From: Stochastic Approximation Approach to Design of Linear Controllers for Tracking Systems With Asymmetric Saturation
J. Dyn. Sys., Meas., Control. 2015;137(12): doi: /
Figure Legend:
Performance loci of Example 2. (a) AS-root locus and (b) TE locus.

22. Date of download: 10/8/2017
Copyright © ASME. All rights reserved.
From: Stochastic Approximation Approach to Design of Linear Controllers for Tracking Systems With Asymmetric Saturation
J. Dyn. Sys., Meas., Control. 2015;137(12): doi: /
Figure Legend:
Responses of the system of Example 2 with K = 1.3 and K = 22. (a) K = 1.3 and (b) K = 22.

23. Date of download: 10/8/2017
Copyright © ASME. All rights reserved.
From: Stochastic Approximation Approach to Design of Linear Controllers for Tracking Systems With Asymmetric Saturation
J. Dyn. Sys., Meas., Control. 2015;137(12): doi: /
Figure Legend:
Responses of the system of Example 3 without the precompensator. (a) System output and (b) controller output and plant input.

24. Date of download: 10/8/2017
Copyright © ASME. All rights reserved.
From: Stochastic Approximation Approach to Design of Linear Controllers for Tracking Systems With Asymmetric Saturation
J. Dyn. Sys., Meas., Control. 2015;137(12): doi: /
Figure Legend:
The step tracking nonlinear system

25. Date of download: 10/8/2017
Copyright © ASME. All rights reserved.
From: Stochastic Approximation Approach to Design of Linear Controllers for Tracking Systems With Asymmetric Saturation
J. Dyn. Sys., Meas., Control. 2015;137(12): doi: /
Figure Legend:
AS-root locus of Example 3

26. Date of download: 10/8/2017
Copyright © ASME. All rights reserved.
From: Stochastic Approximation Approach to Design of Linear Controllers for Tracking Systems With Asymmetric Saturation
J. Dyn. Sys., Meas., Control. 2015;137(12): doi: /
Figure Legend:
Responses of the system of Example 3. (a) Random reference tracking and (b) step tracking with precompensator.

27. Date of download: 10/8/2017
Copyright © ASME. All rights reserved.
From: Stochastic Approximation Approach to Design of Linear Controllers for Tracking Systems With Asymmetric Saturation
J. Dyn. Sys., Meas., Control. 2015;137(12): doi: /
Figure Legend:
Performance loci of Example 4. (a) AS-root locus and (b) TE locus.

28. Date of download: 10/8/2017
Copyright © ASME. All rights reserved.
From: Stochastic Approximation Approach to Design of Linear Controllers for Tracking Systems With Asymmetric Saturation
J. Dyn. Sys., Meas., Control. 2015;137(12): doi: /
Figure Legend:
Responses of the system of Example 4. (a) Random reference tracking and (b) step tracking with precompensator.