The system to be controlled, along with its sensors and actuators, is modeled
as the plant .
P
Vague goals for the behavior of the closed-loop system are formulated as a set
of design speci cations (chapters 8{10).
If the plant is LTI and the speci cations are closed-loop convex, the resulting
feasibility problem can be solved (chapters 13{15).
If the speci cations are achievable, the designer will check that the design is
satisfactory, perhaps by extensive simulation with a detailed (probably non-
linear) model of the system.
System
Plant
Feas. yes
yes
Prob.
OK?
no
no
Goals
Specs.
A partial owchart of the control engineer's tasks.
Figure
16.1
One design will involve many iterations of the steps shown in gure 16.1. We
now discuss some possible design iterations.
Modifying the Specifications
The speci cations are weakened if they are infeasible, and possibly tightened if they
are feasible, as shown in gure 16.2. This iteration may take the form of a search
over Pareto optimal designs (chapter 3).
System
Plant
Feas. yes
yes
Prob.
OK?
no
no
Goals
Specs.
Based on the outcome of the feasibility problem, the designer
Figure
16.2
may decide to modify ( , tighten or weaken) some of the specications.
e.g.
16.2 CONTROL ENGINEERING REVISITED
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Modifying the Control Configuration
Based on the outcome of the feasibility problem, the designer may modify the
choice and placement of the sensors and actuators, as shown in gure 16.3. If the
speci cations are feasible, the designer might remove actuators and sensors to see
if the speci cations are still feasible if the speci cations are infeasible, the designer
may add or relocate actuators and sensors until the speci cations become achievable.
The value of knowing that a given set of design speci cations cannot be achieved
with a given con guration should be clear.
System
Plant
Feas. yes
yes
Prob.
OK?
no
no
Goals
Specs.
Based on the outcome of the feasibility problem, the designer
Figure
16.3
may decide to add or remove sensors or actuators.
These iterations can take a form that is analogous to the iteration described
above, in which the speci cations are modi ed. We consider a xed set of speci -
cations, and a family (which is usually nite) of candidate control con gurations.
Figure 16.4 shows fourteen possible control con gurations, each of which consists of
some selection among the two potential actuators 1 and 2 and the three sensors
A
A
1, 2, and 3. (These are the con gurations that use at least one sensor, and one,
S
S
S
but not both, actuators. 1 and 2 might represent two candidate motors for a
A
A
system that can only accommodate one.) These control con gurations are partially
ordered by inclusion for example, 1 1 consists of deleting the sensor 3 from the
A
S
S
con guration 1 1 3.
A
S
S
These di erent control con gurations correspond to di erent plants, and there-
fore di erent feasibility problems, some of which may be feasible, and others in-
feasible. One possible outcome is shown in gure 16.5: nine of the con gurations
result in the speci cations being feasible, and ve of the con gurations result in
the speci cations being infeasible. In the iteration described above, the designer
could choose among the achievable speci cations here, the designer can choose
among the control con gurations that result in the design speci cation being feasi-
ble. Continuing the analogy, we might say that 1 1 2 is a Pareto optimal control
A
S
S
con guration, on the boundary between feasibility and infeasibility.
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