Negative imaginary systems theory in the robust control of highly resonant flexible structures

This paper covers recent developments in the theory of negative imaginary systems and their application to the control of highly resonant flexible structures. The theory of negative imaginary systems arose out of a desire to unify a number of classical methods for the control of lightly damped structures with collocated force actuators and position sensors including positive position feedback and integral force feedback. The key result is a stability result which shows why these methods are guaranteed to yield robust closed loop stability in the face of unmodelled spillover dynamics. Related results to be presented connect the theory of negative imaginary systems to positive real systems theory and a negative imaginary lemma has been established which is analogous to the positive real lemma. The paper also presents recent controller synthesis results based on the theory of negative imaginary systems.