TIME OPTIMAL DIGITAL CONTROL OF MULTI-UNIT PAPER WEB DYNAMICS

This thesis describes an attempt to apply the classical and modern control theories for a multi-unit paper web tension control problem. Particular attention is given to the problem of developing and applying the time-optimal control theory in the discrete-time domain for a paper web dynamic system.; A digital control algorithm utilizing time-optimal control theory, and a compact form deadbeat controller with a generalized compact form deadbeat reduced order observer for controlling the paper web dynamics has been developed.; In the continuous time domain, the multivariable control technique, either the pole assignment method or the optimal linear regulator method, incorporated with a reduced order observer for controlling the paper web dynamics has been obtained. Several simulations of the multivariable control of the papter web dynamics show that it is not only able to design optimally a control system, but that it also can employ an observer to replace the tension transducers which sometimes might cause undesirable behavior due to unexpected oscillation. This is a significant improvement over that which is controlled by the classical control method.; In the discrete time domain, the time-optimal control theory has been studied extensively. There are two ways of approaching the time optimal deadbeat regulator problem, one based on system controllability, and the other on eigenvalue assignment. The compact form deadbeat controller is based on the eigenvalue assignment method and has an explicit expression for the feedback gain constant. A compact form deadbeat reduced order observer based on the partition of state transition matrix can be constructed directly by the dual approach of deadbeat controller. But the application of this kind of observer is limited to some special cases, while the paper web tension control system does not belong to this category.; Finally, a generalized, compact form deadbeat reduced order observer has been developed. The combination of the compact form deadbeat controller and generalized reduced order observer for controlling the paper web dynamics has been simulated. The augmented system can be controlled to the desired state within (nu)(,c) + (nu)(,0)-1 steps, while (nu)(,c) is the controllability index and (nu)(,0) is the observability index.; The design procedure and techniques presented in this work are general and can be implemented for a wide variety of control systems.