Robust control of saturating, non-monotone hysteretic systems with nonlinear frequency-dependent power losses

The focus of this thesis is to investigate the modelling of magnetic and smart actuators and to develop a controller strategy that can exploit the full range of actuator capabilities. In recent years, magnetic and smart actuators have received much attention due to emerging actuator technologies and a growing number of industrial applications. Many modern applications require actuators that are capable of producing outputs that can precisely control in high frequencies, such as in noise cancellation systems. Magnetic and smart actuators are able to generate outputs with nanometer level resolution and are useful in many precision positioning applications. However, they exhibit a variety of complex rate-independent phenomena (such as hysteresis and saturation) and rate-dependent phenomena (such as frequency dependent power losses) that impede effective use of them for precision and high frequency applications.

To exploit the full range of operation of these actuators, control strategies must be developed by considering the physical phenomena exhibited by these actuators. However, control schemes studied in literature fall short of controlling linear magnetic and smart actuators in a broad frequency range and in a complete actuator displacement range. A model for smart and magnetic actuators with a composition of hysteresis operator and a square function as a subsystem have been reported in the literature and used for control system design at low frequencies. Magnetic and smart actuators exhibit saturation, whereas, hysteresis is not considered to be saturating in current literature on controller design. Closer examination of the system input--output graph near DC frequencies reveals rich hysteresis phenomena, whereby minor loops close on themselves. Any control of smart and magnetic actuators must take into account such phenomena. Additionally, difficulties modelling these actuators for a broad frequency range limit application of any model-based controllers. This thesis discusses how to model and control magnetic and smart actuators to exploit the full range of actuator capabilities.