Analysis of a Time Delay Controller Based on Convolutions - with Application to a Cruise Control System

Time Delay Control has been proposed as an effective control method for a class of systems with unknown dynamics and unpredictable disturbances. The control algorithm uses recent past data to estimate the uncertain dynamics and disturbances in the system. This Thesis presents a method based on convolutions to attenuate the noise amplification in the calculation of the estimated functions. This method suggests a delay time to be much larger than the sampling period. Through the accuracy analysis, an extrapolation scheme is found to be useful to improve the performance while keeping the delay time at an appropriate level. Stability analysis shows that a trade-off exists between robustness and performance. For a special class of systems with slow changing dynamics during the delay time, the convolution method with an extrapolation scheme is shown to provide a very satisfactory performance. An application of Time Delay Control to an intelligent automotive cruise control system is presented to show the performance of Time Delay Controller on actual systems. In this system, a vehicle is equipped with a ranging sensor which measures the distance between a preceding car and itself. The relative distance between the two vehicles is the control output [the state] of the system and the dynamics of the leading car are treated as a disturbance. The performance of the Time Delay Control Method in this intelligent longitudinal cruise control system was evaluated using a one-fifth scale car model. Through simulations and experiments, the Time Delay Control technique is shown to be well suited for intelligent cruise controls because of its rapid estimation of system dynamics changes and ease of implementation. If noise is a significant problem, the method based on convolutions and extrapolations can be used to attenuate the noise while keeping a good performance. This implementation and the above analysis show that the flexibility and feasibility of Time Delay Controller are largely increased by the method based on convolutions.