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Multi-objective Control using the Principle of Inequalities

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Book cover Control Systems Design

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Abstract

This chapter is concerned with three different multi-objective control schemes. These are, respectively, PID control, critical control and eigenstructure assignment. In each case the design problem is formulated in accordance with the principle of inequalities. This is a multi-objective design rule where each design specification is expressed as an inequality. In the PID control problem, a set of frequency-domain performance requirements, such as gain margin, phase margin, crossover frequency and steady-state error are used to construct inequalities. In the critical control problem, the issue of robustness of multivariable critical systems with external and internal uncertainties is addressed. The design inequalities are based on the output performance in the time domain and the robust performance in the frequency domain. The eigenstructure assignment problem considers robustness in multivariable control systems. The performance functions are individual eigenvalue sensitivity functions and the system robustness functions. Based on those performance functions above, the performance criteria for each multi-objective scheme are expressed by a set of inequalities. Some examples demonstrate the operation of the three multi-objective control schemes.

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Author information

Authors and Affiliations

  1. School of Electronics, University of Glamorgan, Pontypridd, CF37 1GY, UK

    G P Liu

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  1. G P Liu
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Editors and Affiliations

  1. 12 Cote Green Road, Marple Bridge, Stockport, SK6 5EH, UK

    Vladimir Zakian PhD

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© 2005 Springer-Verlag London Limited

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Liu, G.P. (2005). Multi-objective Control using the Principle of Inequalities. In: Zakian, V. (eds) Control Systems Design. Springer, London. https://doi.org/10.1007/1-84628-215-2_10

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  • DOI: https://doi.org/10.1007/1-84628-215-2_10

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-85233-913-5

  • Online ISBN: 978-1-84628-215-7

  • eBook Packages: EngineeringEngineering (R0)

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