| The problem of nonlinear identification and energy conservative control of balance in a monopod is addressed in this thesis. A monopod is emulated using a concave balancing mechanism, referred to as the body, mounted on an inverted pendulum, referred to as the leg, via a hip joint. The body curvature, represented by &phis;, can be altered and is elected as the design parameter of interest as it is observed that at an optimal body span angle, &phis; opt, certain interesting phenomena transpire: The linearized system is transformed from non-minimum to minimum phase, the conditions for feedback linearization of the nonlinear model satisfied, and minimal mechanical power required for stability of the simulated model is observed.; A nonlinear gray-box system identification routine is developed in and implemented, within MATLAB, to estimate certain non-measurable parameters that arise within the original system dynamics. To estimate the optimal angle &phis; opt, another non-measurable parameter, the identification routine is further employed for various values of &phis;. A locus of the transfer function zeros is then used to interpolate the value of &phis; at which the system achieves minimum phase behaviour. At this configuration, the magnitude of the transfer function zeros become much larger in comparison with that of the largest pole and therefore has a negligible contribution to the phase characteristics of the system.; After the experimental identification of &phis;opt, a Linear Quadratic Regulator with integral action is design and implemented to achieve the control objectives, with the design parameters set as close as physically realizable to the optimal setting. A nonlinear controller based on Feedback Linearization is also designed and implemented to take advantage of one benefit of this proposed design. The performance of the nonlinear controller is also compared against that of the LQ Regulator.; Analysis and documentation of the power savings from the proposed design, in relation to existing prototypes, is a subject of further works. Furthermore, the performance of the developed controllers can be further improved via careful tuning to meet more stringent control objectives. |
