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2 MULTIVARIABLE FEEDBACK CONTROL
control systems, often based on a hierarchy of cascaded control loops, using only on-line
tuning (involving steps 1, 4, 5, 6, 7, 13 and 14). However, even in such cases a suitable
control structure may not be known at the outset, and there is a need for systematic tools
and insights to assist the designer with steps 4, 5 and 6. A special feature of this book is the
provision of tools for input–output controllability analysis (step 3) and for control structure
design (steps 4, 5, 6 and 7).
Input–output controllability is the ability to achieve acceptable control performance. It is
affected by the locations of the sensors and actuators, but otherwise it cannot be changed by
the control engineer. Simply stated, “even the best control system cannot make a Ferrari out
of a Volkswagen”. Therefore, the process of control system design should in some cases also
include a step 0, involving the design of the process equipment itself. The idea of looking at
process equipment design and control system design as an integrated whole is not new, as is
clear from the following quote taken from a paper by Ziegler and Nichols (1943):
In the application of automatic controllers, it is important to realize that
controller and process form a unit; credit or discredit for results obtained are
attributable to one as much as the other. A poor controller is often able to
perform acceptably on a process which is easily controlled. The £nest controller
made, when applied to a miserably designed process, may not deliver the desired
performance. True, on badly designed processes, advanced controllers are able
to eke out better results than older models, but on these processes, there is a
de£nite end point which can be approached by instrumentation and it falls short
of perfection.
Ziegler and Nichols then proceed to observe that there is a factor in equipment design that is
neglected, and state that
the missing characteristic can be called the “controllability”, the ability of the
process to achieve and maintain the desired equilibrium value.
To derive simple tools with which to quantify the inherent input–output controllability of a
plant is the goal of Chapters 5 and 6.
1.2 The control problem
The objective of a control system is to make the output y behave in a desired way by
manipulating the plant input u. The regulator problem is to manipulate u to counteract the
effect of a disturbance d. The servo problem is to manipulate u to keep the output close to
a given reference input r. Thus, in both cases we want the control error e = y − r to be
small. The algorithm for adjusting u based on the available information is the controller K.
To arrive at a good design for K we need a priori information about the expected disturbances
and reference inputs, and of the plant model (G) and disturbance model (G
d
). In this book,
we make use of linear models of the form
y = Gu + G
d
d (1.1)
A major source of dif£culty is that the models (G, G
d
) may be inaccurate or may change
with time. In particular, inaccuracy in G may cause problems because the plant will be part