Flexible system dynamics plays a vital role in the performance of several motion and vibration control applications such as space structures, rotorcraft blades, hard-disk drives, flexure mechanisms, and motion systems with transmission compliance. These applications often require the use of feedback and feedforward controls in an attempt to achieve desirable dynamic performance, which generally includes high speed, low settling time, strong disturbance rejection, low sensitivity to modeling uncertainties, and stability robustness.

However, the presence of undamped poles and ill-behaved zero dynamics in the transfer function, defined by the actuated load input and sensed displacement output of a flexible system, lead to significant tradeoffs amongst these competing dynamic performance requirements. Ill-behave zero dynamics is driven by the location of zeros. Zeros on the left side of the s-plane are referred to as non-minimum phase (NMP) zeros and have been shown to impact dynamic performance with feedback as well as feedforward controllers. Also, the placement of zeros on the imaginary axis of the z plane (MMP zeros) with respect to system poles also impacts the dynamic performance. It is therefore imperative that flexible systems should be designed such that their transfer functions do not exhibit such zeros.

The focus of this research is to comprehensively investigate the occurrence and location of zeros and use this knowledge to eliminate ill-behaved zero dynamics via robust design of the physical system (including the flexible system/structure and the location of sensors and actuators). Specifically, we seek to derive the necessary and sufficient conditions (in terms of the system physical parameters) under which under NMP zeros can be eliminated in the transfer functions of flexible systems, with and without damping.

These necessary and sufficient conditions can aid the robust physical design of flexible systems i.e. as long as these conditions are satisfied, the elimination of NMP zeros is guaranteed even when the parameters associated with the flexible systems undergo variations. Finally, we translate these mathematical conditions into design methodologies that involve informed choices of actuator-sensor placements and mass-stiffness distribution for specific flexible systems to demonstrate the elimination of NMP zeros and therefore lead to better dynamic performance.