Multivariable Control of a Nonlinear Process Output Prioritisation by Error Redistribution

Abstract

All real systems experience input saturation. Since the first proportional controller

was implemented, systems have been susceptible to saturation. The introduction of

the proportional-integral (PI) controller complicates matters further, since it reduces

the steady state error to zero for zero-order setpoint tracking. This encompasses a

fair portion of the implemented control strategies in the world.

It is clear that saturation, by limiting the input state for the process, limits the possible

output region. This is true in an absolute as well as a relative sense, due to limited

rate of change of the physical actuator. Hence not only is the absolute output range

limited, but the nonlinear effects also limit the output value at the next instant.

In single variable digital systems the performance degradation can be crippling.

Performance and stability are easily lost in systems with either high gains or small

control ranges. In multivariable systems, the condition is aggravated by the

transference of the saturation effects across all interacting loops. lIot only is the loop

experiencing saturation affected, but also the loops with which it is interacting. This

results in a situation where these loops also lose their ability to track their setpoint.

Moreover, in high gain systems, stability is jeopardised.

This dissertation presents a general solution for the practical problem that given the

physical constraint of saturation, a multivariable system's control engineer would be

able to prioritise the process outputs, and be given a choice over which outputs are

maintained during periods of nonlinear operation.

A review of the work done in anti-windup bumpless transfer (AWBT), using Kothare

et a/.'s (1994) "Unified framework for analysis of anti-windup bump/ess transfer

techniques" as a reference, it will be shown how these techniques are employed to

ensure system stability and linear performance recovery. Anti-windup (AW)

Techniques that are designed specifically for multivariable systems will also be

reviewed. The performance of these techniques, while the requested operating pOints

are outside of the realisable operating region, will be of particular interest. AWBT

does not in general meet the objective of allowing the engineer to prioritise the

nonlinear mode's operation during these periods.

The novel concept of error redistribution (ER) is introduced to meet this objective.

Error redistribution is a multivariable technique which allows the redistribution of error

in the saturating loops to the non-saturating, or rather, the correcting loops, to

maintain the setpoint of prioritised outputs; thus exploiting all degrees of freedom to

reach the nonlinear mode objective. The formalisation of this concept, along with a

stability proof and design guidelines are presented. The guidelines include being able

to measure the suitability of using ER on a process. The nature of the technique

allows the designer a controlled use, applying it only to the loops where it will be

effective and with minimal disruption to the process.

Throughout this thesis, a simulated example of a multivariable thermal process

(MVTP) is used to illustrate the principles and results relevant to dealing with

saturation using AW and ER compensation. An application chapter includes the

results of applying ER to a laboratory version of the MVTP; a simulated distillation

column and a typical gold mine milling circuit. Comparisons are done for different

pairings of ER compensation and AW techniques, including the implementation of the

Hanus conditioning technique and artificial-nonlinearity (AN) described by Peng et al.

(1998).

The result of this thesis is that error redistribution has been proven to be a viable

technique for the optimisation of process outputs during nonlinear operation. The

general structure of the system can easily implemented on industrial control

platforms.