Loop Shaping in the 21st Century - American Automatic...
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Abstract—We propose to reprise our highly successful workshop on loop shaping from the 2011 ACC. Loop shaping remains popular for designing SISO controllers, and several tools developed over the last fifteen years or so make it even more useful. Theses tools include new compensator structures (e.g., lead and lag compensators with complex poles and zeros, the complex proportional integral lead compensator, and phase-adjustable resonant filter), new visualization methods such as the Robust Bode (RBode) plot for designing for robust performance, and new techniques for phase stabilization. This one-day workshop will teach the features of these tools and how to use them effectively. We envision this workshop will be particularly valuable to the large portion of the industrial controls community in the Greater Boston area and beyond that uses loop shaping and to educators. I. THE NEED FOR THIS WORKSHOP Loop shaping remains a popular method for controller design for SISO systems because it is powerful and intuitive. In spite of its long history, a number of developments over the last fifteen years or so have led to new tools for making loop shaping even more useful (e.g. [1], [2], [3], [4], [5], [6], [7], [8], [9], [10]). This one-day workshop will teach the features of these tools and how to use them effectively. This workshop will be particularly valuable to the large portion of the industrial controls community that uses loop shaping. Educators should find this valuable because the material on compensator structures is suitable for advanced undergraduates. There are a large number of companies in the Greater Boston Area and in southern New England that work in precision motion control, in robotics control, or aerospace. There are also many nearby colleges and universities that teach controls. Thus, we think that attendance will be at least good as it was for our workshop given at the 2011 ACC in San Francisco, which had nearly 30 attendees. II. TOPICS The advances in loop shaping of the past 15 years fall primarily two areas. The first area is using complex zeros and complex poles for decoupling the phase contribution of a compensator from its shape at a particular frequency. (See Fig. 1.) Among other advantages, these new compensator structures more readily provide the capability of designing phase stabilized systems. The second area is new visualization tools. The visualization tools are enhancements of the Bode plot that depict closed-loop specifications on the open-loop Bode T. Atsumi is with the Department of Mechanical Engineering, Chiba Institute of Technology, 2-17-1 Tsudanuma, Narashino, Chiba 275--0016 Japan, [email protected] W. Messner is with the Department of Mechanical Engineering, Tufts University, Medford, MA 02155 USA, [email protected] plot. (See Fig. 2.) These tools provide the capability for designing low order controllers for robust performance from frequency response data alone. That is, realizable transfer functions are not need for the plant model, nor for the performance weighting function, nor for the uncertainty weighting function. Figure 1. Comparison of lead compensators with complex poles and zeros Figure 2. Example of an RCBode plot showing the frequency response of the controller avoiding forbidden regions. The closed-loop system exhibits robust performance if and only if there are no intersections. Our workshop with cover topics in Advanced Compensator Structures and in Advanced Techniques as follows. −20 −10 0 10 20 Magnitude (dB) 10 −1 10 0 10 1 10 2 10 3 0 30 60 90 Phase (deg) Bode Diagram Frequency (rad/sec) 1st order 2nd order ζ = 0.5 2nd order ζ = 1.0 2nd order ζ = 1.8 10 2 10 3 10 4 −60 −50 −40 −30 Frequency [Hz] Gain [dB] 10 2 10 3 10 4 −180 −90 0 90 180 Frequency [Hz] Phase [deg.] Loop Shaping in the 21 st Century A proposal for a 1-day pre-conference workshop at the 2016 American Controls Conference Takenori Atsumi and William C. Messner CONFIDENTIAL. Limited circulation. For review only. Preprint submitted to 2016 American Control Conference. Received September 27, 2015.
Transcript of Loop Shaping in the 21st Century - American Automatic...
Abstract—We propose to reprise our highly successful workshop on loop shaping from the 2011 ACC. Loop shaping remains popular for designing SISO controllers, and several tools developed over the last fifteen years or so make it even more useful. Theses tools include new compensator structures (e.g., lead and lag compensators with complex poles and zeros, the complex proportional integral lead compensator, and phase-adjustable resonant filter), new visualization methods such as the Robust Bode (RBode) plot for designing for robust performance, and new techniques for phase stabilization. This one-day workshop will teach the features of these tools and how to use them effectively. We envision this workshop will be particularly valuable to the large portion of the industrial controls community in the Greater Boston area and beyond that uses loop shaping and to educators.
I. THE NEED FOR THIS WORKSHOP
Loop shaping remains a popular method for controller design for SISO systems because it is powerful and intuitive. In spite of its long history, a number of developments over the last fifteen years or so have led to new tools for making loop shaping even more useful (e.g. [1], [2], [3], [4], [5], [6], [7], [8], [9], [10]). This one-day workshop will teach the features of these tools and how to use them effectively.
This workshop will be particularly valuable to the large portion of the industrial controls community that uses loop shaping. Educators should find this valuable because the material on compensator structures is suitable for advanced undergraduates. There are a large number of companies in the Greater Boston Area and in southern New England that work in precision motion control, in robotics control, or aerospace. There are also many nearby colleges and universities that teach controls. Thus, we think that attendance will be at least good as it was for our workshop given at the 2011 ACC in San Francisco, which had nearly 30 attendees.
II. TOPICS
The advances in loop shaping of the past 15 years fall primarily two areas. The first area is using complex zeros and complex poles for decoupling the phase contribution of a compensator from its shape at a particular frequency. (See Fig. 1.) Among other advantages, these new compensator structures more readily provide the capability of designing phase stabilized systems.
The second area is new visualization tools. The visualization tools are enhancements of the Bode plot that depict closed-loop specifications on the open-loop Bode
T. Atsumi is with the Department of Mechanical Engineering, Chiba
Institute of Technology, 2-17-1 Tsudanuma, Narashino, Chiba 275--0016 Japan, [email protected]
W. Messner is with the Department of Mechanical Engineering, Tufts University, Medford, MA 02155 USA, [email protected]
plot. (See Fig. 2.) These tools provide the capability for designing low order controllers for robust performance from frequency response data alone. That is, realizable transfer functions are not need for the plant model, nor for the performance weighting function, nor for the uncertainty weighting function.
Figure 1. Comparison of lead compensators with complex poles and zeros
Figure 2. Example of an RCBode plot showing the frequency response of the controller avoiding forbidden regions. The closed-loop system exhibits robust performance if and only if there are no intersections.
Our workshop with cover topics in Advanced Compensator Structures and in Advanced Techniques as follows.
−20
−10
0
10
20
Mag
nitu
de (d
B)
10−1 100 101 102 1030
30
60
90
Phas
e (d
eg)
Bode Diagram
Frequency (rad/sec)
1st order2nd order ζ = 0.52nd order ζ = 1.02nd order ζ = 1.8
102 103 104−60
−50
−40
−30
Frequency [Hz]
Gai
n [d
B]
102 103 104−180
−90
0
90
180
Frequency [Hz]
Phas
e [d
eg.]
Loop Shaping in the 21st Century A proposal for a 1-day pre-conference workshop at the 2016 American Controls Conference
Takenori Atsumi and William C. Messner
CONFIDENTIAL. Limited circulation. For review only.
Preprint submitted to 2016 American Control Conference.Received September 27, 2015.
1. Advanced Compensator Structures (e.g. Fig. 1) a. Lead and lag compensators with complex poles and
zeros [4] b. Phase adjustable resonance and notch filters [6] c. Complex proportional integral lead compensators [6] d. Placement of complex poles and zeros for specific
angle contributions at points in the complex plane [8] 2. Advanced Techniques
a. Phase stabilization. i. resonance stabilization [2] ii. narrow band high gain [5]
b. Controller Design with the RBode Plot (e.g. Fig. 2) i. unstructured uncertainty [9] ii. structured uncertaintly [10]
III. STRUCTURE This 1-day workshop will consist of a series of modules
of approximately 30-45 minutes. Each module will have 10-20 minutes of instruction followed by the participants using their laptops to perform loopshaping exercises using MATLAB™. We will distribute MATLAB™ code for the various compensator structures and visualization techniques for participants to use at the workshop. They may and then take the software with them. afterwards. We will provide copies of appropriate references.
We plan to use the head-positioning control system in hard disk drives as an example problem (Figure 3).
Figure 3. A disk drive with various components labeled.
REFERENCES [1] W. Messner, “Some Advances in Loop Shaping Controller Design
with Applications to Disk Drives,” The IEEE Transactions on Magnetics, v. 37, n. 2, p. 651–656, 2001.
[2] M. Kobayashi, S. Nakagawa, and S. Nakamura, “A phase-stabilized ervo controller for dual-stage actuators in hard disk drives”, IEEE Transactions on Magnetics, v. 39, n. 2, p. 844 - 850, Mar 2003.
[3] L. Xia and W. Messner, “Loop shaping for robust performance using the RBode plot,” in Proceedings of the 2005 American Controls Conference, 2005, p. 2869–2874.
[4] W. Messner, M. Bedillion, L. Xia, and D. Karns, “Lead and Lag Compensators with Complex Poles and Zeros,” IEEE Control Systems Magazine, v. 27, n. 1, p. 44–54, 2007.
[5] T. Atsumi, T. Okuyama, and M. Kobayashi, “Track-Following Control Using Resonant Filter in Hard Disk Drives”, IEEE/ASME
Transactionson Mechatronics, v. 12, n. 4, p. 472 - 479, 2007. [6] W. Messner, “Classical Control Revisited: Variations on a Theme,” in
Proceedings of the 10th IEEE International Workshop on Advanced Motion Control, 2008, p. 15 - 20.
[7] L. Xia and W. Messner, “An Improved Version of the RBode Plot,” in Proceedings of the 2008 American Controls Conference, 2008, p. 4940–4945.
[8] W. Messner, “Formulas for Asymmetric Lead and Lag Compensators,” in Proceedings of the 2009 American Control Conference, 2009, p. 3769–3774.
[9] T. Atsumi, W. Messner, “Optimization of head-positioning control in hard disk drive using the RBode plot,” IEEE Transactions on Industrial Electronics, v. 59, n. 1, p. 521-529, Jan 2012. DOI : 10.1109/TIE.2011.2143377.
[10] T. Atsumi, and W. Messner, “Modified Bode Plots for Robust Performance in SISO Systems with Structured and Unstructured Uncertainties,” IEEE Transactions on Control Systems Technology, v. 20, n. 2, pt. 1, p. 356-368, Mar 2012.
CONFIDENTIAL. Limited circulation. For review only.
Preprint submitted to 2016 American Control Conference.Received September 27, 2015.
