An Analytical Approach to Integral Resonant Control of Second-Order Systems

Systems with colocated sensor-actuator pairs exhibit the interesting property of pole-zero interlacing. Integral resonance control (IRC) exploits this property by changing the pole-zero interlacing to zero-pole interlacing. The unique phase response of this class of systems enables a simple integral feedback controller to add substantial damping. Over the past few years, IRC has proven to be extremely versatile and has been applied to a wide variety of systems whose dominating dynamics of interest can be accurately modeled by second-order transfer functions. To date, a manual approach has been employed to determine the parameters of the IRC scheme, namely the feed-through term and the integral gain. In this paper, the relationship between the feed-through term, integral gain, and achievable damping is derived analytically for undamped/lightly damped second-order systems. The relationship between damping controller and an outer servo loop is also derived. These results add to the current understanding of colocated systems and automate the design of IRC controllers with a specified damping and tracking bandwidth. The presented results are applied to design and implement a damping and tracking controller for a piezoelectric nanopositioning stage.