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.

Theoretical predictions of internal bone remodeling around an elliptical hole are studied. The internal remodeling theory due to Cowin and Hegedus is employed. The bone is modeled as an initially homogeneous adaptive elastic plate with an elliptical hole under a superposed steady compressive load. It is shown that there will exist a final inhomogeneous remodeling distribution around the hole that will disappear away from the hole. The remodeling is such that the compressive stress concentration causes the bone structure to evolve to one of greater density and stiffer elastic coefficients. The speed of remodeling around the hole and its variation with respect to distance is investigated and discussed. It is shown that the rate of bone reinforcement in the area of compressive stress concentration is much higher than the rate of bone resorption in the area of existing tensile stress. Special cases of a circular hole and vertical and horizontal slots are studied and discussed.