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## On the synthesis of fixed order stabilizing controllers

In this dissertation, we consider two problems concerning the synthesis of fixed order

controllers for Single Input, Single Output systems. The first problem deals with the

synthesis of absolutely stabilizing fixed order controllers for Lure-Postnikov systems. The

second problem deals with the synthesis of fixed order stabilizing controllers directly from

the empirical frequency response data and from some coarse information of the plant.

Lure-Postnikov systems are frequently encountered in mechanical engineering applications.

Analytical tools for synthesizing stabilizing fixed structure controllers, such as the

PID controllers examining the absolute stability of Lure-Postnikov systems, have recently

been studied in the literature. However, tools for synthesizing controllers of arbitrary order

have not been studied yet. We propose a systematic method for synthesizing absolutely

stabilizing controllers of arbitrary order for the Lure-Postnikov systems. Our approach is

based on recent results in the literature on approximation of the set of stabilizing controller

parameters that render a family of real and complex polynomials Hurwitz. We provide an

example of a robotic system to illustrate the procedure developed.

Exact analytical models of plants may not be readily available for controller design.

The current approach is to synthesize controllers through the identification of the analytical

model of the plant from empirical frequency response data. In this dissertation, we

depart from this conventional approach. We seek to synthesize controllers directly (i.e.

without resort to identification) from the empirical frequency response data of the plant and coarse information about it. The coarse information required is the number of nonminimum

phase zeros of the plant(or the number of poles of the plant with positive real

parts) and the frequency range beyond which the phase response of the LTI plant does not

change appreciably and the amplitude response goes to zero. We also assume that the LTI

plant does not have purely imaginary zeros or poles. The method of synthesizing stabilizing

controllers involves the use of generalized Hermite-Biehler theorem for counting the

roots of rational functions and the use of recently developed Sum-of-Squares techniques

for checking the nonnegativity of a polynomial in an interval through the Markov-Lucaks

theorem. The method does not require an explicit analytical model of the plant that must

be stabilized or the order of the plant, rather, it only requires the empirical frequency response

data of the plant. The method also allows for measurement errors in the frequency

response of the plant. We illustrate the developed procedure with an example. Finally, we

extended the technique to the synthesis of controllers of arbitrary order that also guarantee

performance specifications such as the phase margin and gain margin.

Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/4665 |

Date | 25 April 2007 |

Creators | Kang, Sin Cheon |

Contributors | Darbha, Swaroop |

Publisher | Texas A&M University |

Source Sets | Texas A and M University |

Language | en_US |

Detected Language | English |

Type | Book, Thesis, Electronic Dissertation, text |

Format | 677340 bytes, electronic, application/pdf, born digital |

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