Adaptive Output Feedback Control Applied to the Rigid Body Equations of Motion

Abstract

A varied method for producing adaptive control is developed in this paper. It involves developing a simplified version of the current Nonlinear Direct Model Reference Adaptive Control (NDMRAC) method. This simplified model of NDMRAC is called Adaptive Output Feedback (AOF) Control. Both types of controllers have varying applications, but in this paper the AOF controller was applied to control the rigid body equations of motion. It was realized that the AOF controller could have an advantage over the NDMRAC controller in the sense of ease of implementation, and also in being better in computational expense. The adaptive method was found to perform better than the standard Full State Feed Back (FSFB) method in this application in the aspect of system response and settling time. The adaptive method was particularly better in the cases when the system being controlled was instantaneously changed during simulation. The adaptive method compensated for the system change with little too no change in trajectory or settling time whereas the FSFB method deviated in both. Control systems of some form can be found in most autonomous systems. The type of control that is used in a system varies primarily on the need for robustness or ease of implementation for the given application. For example, it can be safely concluded that your home thermostat does not need the same type of control as the auto pilot for a fighter jet. This is the reason why there are different types of controllers and many sub-variations of each type of controller. Each one although not necessarily as wide in applicability as the example given, still gives the engineer options in picking a controller that is best suited for the task at hand. With that in mind, this paper takes a look at a type of adaptive control in application to the rigid body equations of motion. The developed controller and the one it is drawn from may or may not be more suited for this particular application, but still add a new potential selection for the engineer in another application. Adaptive control methods are getting more attention since they attempt to deal with new complex control scenarios in an efficient way. Each type of adaptive controller is different in its own way, but fundamentally each one tries to compensate for a system which is dynamically changing, unknown, or even random (in stochastic applications), in an adaptive way. Within adaptive control there exist various subdivisions of the theory. The main classifications of adaptive control fall under direct adaptive control, indirect adaptive control, and robust adaptive control. The indirect adaptive method relies on approximating the plant online, which the controller then adapts too. This system can become very computationally expensive when the order of the plant gets too big in larger systems. Direct adaptive control (DAC) is different in that it requires little to no knowledge of how the plant changes with time, but instead relies on trying to adaptively track the output of a user defined reference model. Indirect adaptive control although more computationally expensive is still a major source of research and types of it can be found in application. It relies on, as mentioned before, on the online identification of the plant. The plant originally was assumed to change slowly with time, but was extended by Tsakalis and Ioannou 1 for faster changing plants, which extends its application range. Ruznik, Guez, Bar-Kana, and Steinberg