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Research Papers

An Innovative Method for Optimization Based, High Order Controller Autotuning

[+] Author and Article Information
Yaron Zimmerman

Technion—Israel Institute of Technology,
Faculty of Civil and Environmental Engineering,
Technion, Haifa 32000, Israel
e-mail: yaron.zimmerman@gmail.com

P.-O. Gutman

Technion—Israel Institute of Technology,
Faculty of Civil and Environmental Engineering,
Technion, Haifa 32000, Israel
e-mail: peo@technion.ac.il

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received September 18, 2012; final manuscript received September 13, 2013; published online December 9, 2013. Assoc. Editor: YangQuan Chen.

J. Dyn. Sys., Meas., Control 136(2), 021010 (Dec 09, 2013) (10 pages) Paper No: DS-12-1308; doi: 10.1115/1.4025798 History: Received September 18, 2012; Revised September 13, 2013

A new automatic method to tune the parameters of high order linear controllers is presented. The autotuning is achieved by minimizing, without constraints, a cost function that is related to the open loop shaping problem. The effort demanded from the designer is similar to that required to tune a low order controller, such as proportional integral (PI) or proportional integral differential (PID). The capabilities of the new method are demonstrated on two examples.

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References

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Figures

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Fig. 1

Nichols chart of the nominal open loop of plant (11 a) and G = 1

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Fig. 2

Nichols chart of the nominal open loop of plant (11 b) and G = 1

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Fig. 3

The cost, computed in Eq. (9), as function of controller gain, when the controlled plant is given in (11 a)

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Fig. 4

The cost, computed in Eq. (9), as function of controller gain, when the controlled plant is given in Eq. (11 b)

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Fig. 5

Horowitz–Sidi bounds and nominal plant for Example 1 in a Nichols chart. The Horowitz–Sidi bound labeled “0.07” is the cross-over frequency bound, and the other bounds are the sensitivity bounds for the chosen frequencies.

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Fig. 6

Horowitz–Sidi bounds and the open loops, G1(s)P(s), and Gf(s)P(s), respectively, for Example 1 in a Nichols chart. The “ + ” sign indicates the values at 0.7 rad/s.

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Fig. 7

Bode plot of the measured plant in example 2

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Fig. 8

The plant frequency function for Example 2 and the Horowitz–Sidi bounds for specifications (2), (5), and (6), in a Nichols chart

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Fig. 9

Horowitz–Sidi bounds for specifications (2) and (5), and the open loops, G1(s)P(s), and Gf(s)P(s), respectively, for Example 2 in a Nichols chart. The “+” sign indicates the values at 12 Hz.

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Fig. 10

Horowitz–Sidi bounds for specifications (2) and (5), and the open loops, Gf(s)P(s), and Ge(s)P(s), respectively, for Example 2 in a Nichols chart. The “+” sign indicates the values at 12 Hz.

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Fig. 11

Horowitz–Sidi bounds for specifications (2) and (5), and the open loops, Gy(s)P(s) (dashes), and Ge(s)P(s) (dashed-dotted), respectively, for Example 2 in a Nichols chart. The “+” sign indicates the values at 12 rad/s.

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Fig. 12

Horowitz–Sidi bounds for specifications (2) and (5), and the open loops, Gy(s)P(s), and Gye(s)P(s), respectively, for Example 2 in a Nichols chart. The “+” sign indicate the values at 12 Hz.

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