TIME DELAY CONTROL AND ITS APPLICATIONS

The main motivation and the topic of this dissertation is time delay control, i.e., to explore the merit of time delay and to use it, intentionally and reasonably, to improve control performances.

The framework of time delay control, consisting of time delay filter, time delay observer and time delay learning control, is constructed at first. Control system performance can be improved by using delay elements from different ways. Time delay filter, as a filter with only zeros, can attenuate damped sinusoidal signals. Time delay observer, a closed-loop control method, adopting a sufficiently short time delay to observe system uncertainties and disturbances, is a robust control method with good performance. Time delay learning control, also a closed-loop control method, uses time delay to track a periodic command signal or to reject a periodic disturbance.

Various tools such as zero-pole placement, impulse responses, sensitivity curves and vector diagrams are studied in details to design and to analyze time delay filter. The damped frequency magnitude of time delay filter is introduced to reveal the nature of capability to reduce residual vibrations of oscillatory modes. Damped polar coordinates and, in addition, the damped vector diagram are presented to design and analyze time delay filters. In order to enhance the robustness of time delay filter, the zero derivative method and extra-insensitive method are studied. Feasible magnitude method is presented in view of the frequency magnitude, to avoid the solution of nonlinear constraint equations. Time delay filter, as a forward control technique, is difficult to be applied to the industrial process that has severe disturbances. A possible solution is presented here. In order to use the solution, multi-point digital filter method to reduce the process to a first-order process with dead time is proposed. A stable PID controller is designed using the Nyquist criterion to reject disturbances, and then time delay filter is used to acquire desired dynamic performance. Furthermore, the deadbeat control scheme for first-order processes with dead time is implemented using time delay filter.

The basic algorithm of time delay observer and the structure constraint are analyzed. It is proved that the system in canonical form satisfies the structure constraint. Time delay observer can be applied to LTI-SISO systems with uncertainties in the state matrix A to obtain good performances in both dynamic response and disturbance-rejection. Time delay filter is a good robust control method. However, the good performance is gained at the cost of losing the smoothness of the control signal.

Time delay learning control (often called repetitive control), which is based on the internal model principle, can track periodic signals without error. The algorithm and stability analysis are presented and then the time delay learning control is designed using frequency response. According to the requirement of the stability, time delay learning unit is modified as inserting a low-pass filter. Since the information before one period as well as the current information are adopted, time delay control gains better performances than the common controller. In addition, time delay control can reject periodic disturbances.

Many simulations on the spring-mass system, damped spring-mass system, crane, and system with uncertainties show that using time delay, intentionally and reasonably, can improve control performances, such as robustness, disturbance-rejection, dynamic performance and the steady-state error, or simplify the controller design. Time delay control has promising perspective.

KEY WORDS:  Time delay; Time delay control (TDC); Time delay filter (TDF); Time delay observer(TDO); Time delay learning control(TDL); Input shaping; Repetitive control

Note: Recent research has shown that the use of a time delay observer is not necessary. It can be replaced by an Uncertainty and Distubance Observer (UDO), which does not introduce a delay. It brings similar performance as the time delay observer but without the disadvatages of TDO. See the paper below for more details.

Q.-C. Zhong and D. Rees. Control of uncertain LTI systems based on an uncertainty and disturbance estimator. ASME J. Dyn. Syst., Meas., Control,  Accepted for publication, Mar. 2004.