Controller synthesis for negative imaginary systems using nonlinear optimisation and H₂ performance measure

ABSTRACT

Negative imaginary (NI) systems theory has attracted considerable attention in the area of robust control of highly resonant flexible structures systems and nano-positioning systems, where the NI property is naturally satisfied. In this paper, we present a control synthesis methodology for NI systems based on nonlinear optimisation techniques. In the presented method, a parametrised library of strictly negative imaginary (SNI) controllers is created and used in a standard numerical nonlinear optimisation setup. The SNI controller library contains generic controllers that are widely used in the control highly resonant flexible structures such as positive position feedback (PPF) and integral resonant control (IRC). Sequential quadratic programming (SQP) techniques are used in the numerical optimisation problem. The synthesised controller satisfies the SNI property as well as optimising $H_2$ performance. As an application of these results, an example of controlling a Euler–Bernoulli beam with piezoelectric actuator and sensor is presented.

Keywords:

• Negative imaginary systems
• flexible structures systems
• linear systems
• optimisation

Disclosure statement

No potential conflict of interest was reported by the author.