Control design for recycled, multi unit processes

An integrated multi-unit chemical plant presents a challenging control design problem due to the existence of recycling streams. In this paper, we develop a framework for analyzing the effects of recycling dynamics on closed-loop performance from which a systematic design of a decentralized control system for a recycled, multi-unit plant is established. In the proposed approach, the recycled streams are treated as unmodelled dynamics of the “unit” model so that their effects on closed-loop stability and performance can be analyzed using the robust control theory. As a result, two measures are produced: (1) the ν-gap metric, which quantifies the strength of recycling effects, and (2) the maximum stability margin of “unit” controller, which represents the ability of the “unit” controller to compensate for such effects. A simple rule for the “unit” control design is then established using the combined two measures in order to guarantee the attainment of good overall closed-loop performances. As illustrated by several design examples, the controllability of a recycled, multi unit process under a decentralized “unit” controller can be determined without requiring any detailed design of the “unit” controller because the simple rule is calculated from the open-loop information only.     

Optimal finite wordlength linear quadratic regulation

The authors consider the design of an LQG regulator, implemented in fixed-point arithmetic, which is optimized with respect to its state wordlength and structure. The approach extends previous design methods so that arithmetic errors are directly included. The optimal finite controller gains are computed as a function of the arithmetic wordlength subject to an l₂-scaling constant on the controller states. The design method used permits the cost for the (near) optimal structure to be developed so that this can then be used as a basis for comparison to other less complex structures     

Discrete minimax linear quadratic regulation of continuous-time systems

In this paper, the statistical cyclostationary characteristics of a controlled continuous-time system which result as a consequence of implementing a digital controller are investigated. A minimax quadratic cost function which takes into account the periodic nature of the statistics is defined and optimized. The resulting linear state feedback law improves the intersample behavior of the controlled system when compared to discrete-time optimization. In particular, the minimax variance regulator which is proposed as a new design method for regulating the output variance offers a significant improvement over the classical minimum variance regulator.