Sigurd Skogestad

Robust control of ill-conditioned plants: high-purity distillation

Using a high-purity distillation column as an example, the physical reason for the poor conditioning and its implications on control system design and performance are explained. It is shown that an acceptable performance/robustness tradeoff cannot be obtained by simple loop-shaping techniques (using singular values) and that a good understanding of the model uncertainty is essential for robust control system design. Physically motivated uncertainty descriptions (actuator uncertainties) are translated into the H/sup infinity //structured singular value framework, which is demonstrated to be a powerful tool to analyze and understand the complex phenomena. >

Control structure design for complete chemical plants

Control structure design deals with the structural decisions of the control system, including what to control and how to pair the variables to form control loops. Although these are very important issues, these decisions are in most cases made in an ad hoc fashion, based on experience and engineering insight, without considering the details of each problem. In the paper, a systematic procedure for control structure design for complete chemical plants (plantwide control) is presented. It starts with carefully defining the operational and economic objectives, and the degrees of freedom available to fulfill them. Other issues, discussed in the paper, include inventory and production rate control, decentralized versus multivariable control, loss in performance by bottom-up design, and a definition of a the ‘‘complexity number’’ for the control system. # 2003 Elsevier Ltd. All rights reserved.

DYNAMICS AND CONTROL OF DISTILLATION COLUMNS A tutorial introduction

The paper summarizes some of the important aspects of the steady-state operation, dynamics and control of continuous distillation columns. The treatment is mainly limited to two-product distillation columns separating relatively ideal binary mixtures.

Simple frequency-dependent tools for control system analysis, structure selection and design: thr

Abstract The paper presents results on frequency-dependent tools for analysis, structure selection and design of control systems. This includes relationships between the relative gain array (RGA) and right half plane zeros, and the use of the RGA as a sensitivity measure with respect to individual element uncertainty and diagonal input uncertainty. It is also shown how frequency-dependent plots of the closely related performance relative gains (PRGA) and a new proposed disturbance measure, the closed-loop disturbance gains (CLDG), can be used to evaluate the achievable performance (controllability) of a plant under decentralized control. These controller-independent measures give constraints on the design of the individual loops, which when satisfied guarantee that the overall system satisfies performance objectives with respect to setpoint tracking and disturbance rejection.

Robust performance of decentralized control systems by independent designs

Decentralized control systems have fewer tuning parameters, are easier to understand and tune, and are more easily made failure tolerant than general multivariable control systems. In this paper the decentralized control problem is formulated as a series of independent designs. Simple bounds on these individual designs are derived, which when satisfied, guarantee robust performance of the overall system. The results provide a generalization of the ¿-Interaction Measure introduced by Grosdidier and Morari (1986).

Sequential design of decentralized controllers

Abstract A procedure for sequential design of decentralized controllers for linear systems is presented. It is shown how to include a simple estimate of the effect of closing subsequent loops into the design problem for the loop which is to be closed. In the examples the robust performance in terms of the structured singular value is used as the measure of control performance, but the procedure may be applied also for other performance measures.

Limitations of dynamic matrix control

Abstract Dynamic matrix control (DMC) is based on two assumptions which limit the feedback performance of the algorithm. The first assumption is that a stable step response model can be used to represent the plant. The second assumption is that the difference between the measured and the predicted output can be modeled as a step disturbance acting on the output. These assumptions lead to the following limitations: 1 Good performance may require an excessive number of step response coefficients. 2 Poor performance may be observed for disturbances affecting the plant inputs. 3 Poor robust performance may be observed for multivariable plants with strong interactions. Limitations 1 and 2 apply when the plants open-loop time constant is much larger than the desired closed-loop time constant. Limitation 3 is caused by gain uncertianty on the inputs. In this paper we separate the DMC algorithm into a predictor and an optimizer. This enables us to highlight the DMC limitations and to suggest how they can be avoided. We demonstrate that a new model predictive control (MPC) algorithm, which includes an observer, does not suffer from the listed limitations.

Azeotropic phase equilibrium diagrams: a survey

Abstract An analysis of the structural properties of vapor–liquid equilibrium (VLE) diagrams provides a fundamental understanding of the thermodynamic behavior of azeotropic mixtures upon distillation. In addition to a review of well-known fundamental work on the analysis of VLE diagrams, this survey comprises less-known published results, especially from the Russian literature. Some new results are also presented for the first time.

LV-Control of a high-purity distillation column

Abstract A realistic study of the LV-control of a high-purity distillation column is presented. Linear controllers designed based on a linearized model of the plant are found to yield acceptable performance also when there is model—plant mismatch. The mismatch can be caused by uncertainty on the manipulated inputs, nonlinearity and variations in reboiler and condenser holdup. The presence of input uncertainty makes the use of a steady-state decoupler unacceptable. The effect of nonlinearity is strongly reduced by using the logarithm of the compositions. A simple diagonal PI-controller is not sensitive to model—plant mismatch, but yields a response with a sluggish return to steady-state.

Control of symmetrically interconnected plants

Abstract This paper is concerned with control of plants composed of n similar interacting subsystems. Such plants are common in practice and include paper machines, distribution networks, coating processes, and plants consisting of units operating in parallel. The transfer function matrices for these systems are block symmetric circulant. For H∞- and H2-optimal control, controller synthesis is simplified by considering n 2 + 1 independent problems of dimension n times smaller than the original problem. For the case of H∞-optimal control this also yields ‘super-optimality’, where the H∞ criterion is optimized in n directions, and not only in the worst direction. If the offdiagonal blocks (‘interactions’) are identical the matrix is termed block parallel, and controller synthesis involves only two independent subproblems of the same dimension as the subsystems. This leads to a dramatic reduction in dimension for systems composed of many subsystems.