Time-optimal control of discrete-time systems with known waveform disturbances

In this thesis, a discrete-time observer based disturbance accommodation controller is designed that is capable of minimizing the effect of disturbances with known waveform in both the system state and measurement as fast as possible while also driving the state to zero. This control is achieved by designing a single control input to accommodate disturbances in both the system state and measurement. For controller design, the state and measurement equations are augmented, and a least squares minimization technique is used to find a control input that drives the system state and measurement to zero, guaranteeing deadbeat response. During the design it is assumed that all system and disturbance state variables are available for feedback. When this is not, an observer is needed. When using a deadbeat controller, the only option for the observer is to also be deadbeat. Two types of deadbeat observers are used in this work: full-order and reduced-order. The full-order observer generates estimates for both the system and disturbance state variables (measureable or not) and driving the estimation error to zero. For a faster time response, a reduced-order deadbeat observer was then designed. Reduced-order observers have a faster response because a reduced-order observer only constructs estimates for the un-measureable system and disturbance state variables. As an extension, a new model for the control input was introduced for the case when the feed-forward term in the measurement was not present. This involved using a so-called \u27pseudo-output\u27 that allows the controller to indirectly minimize the effect of the disturbance in the measurement. Simulations show that when this control scheme is used, the system state and measurement are driven to zero when no disturbance. When disturbances are present, their effects are minimized. In all cases control action is achieved in the appropriate number of time steps for the given system