Page 287 - Modern Control Systems

Section 4.8 Design Examples 261
Control Goal
Regulate the mean arterial pressure to any desired set-point and maintain the
prescribed set-point in the presence of unwanted disturbances.
Associated with the stated control goal, we identify the variable to be controlled:

Variable to Be Controlled
Mean arterial pressure (MAP).

Because it is our desire to develop a system that will be used in clinical appli-
cations, it is essential to establish realistic design specifications. In general terms
the control system should have minimal complexity while satisfying the control
specifications. Minimal complexity translates into increased system reliability and
decreased cost.
The closed-loop system should respond rapidly and smoothly to changes in the
MAP set-point (made by the anesthetist) without excessive overshoot. The closed-
loop system should minimize the effects of unwanted disturbances. There are two
important categories of disturbances: surgical disturbances, such as skin incisions
and measurement errors, such as calibration errors and random stochastic noise. For
example, a skin incision can increase the MAP rapidly by 10 mmHg [26]. Finally,
since we want to apply the same control system to many different patients and we
cannot (for practical reasons) have a separate model for each patient, we must have
a closed-loop system that is insensitive to changes in the process parameters (that is,
it meets the specifications for many different people).
Based on clinical experience [24], we can explicitly state the control specifica-
tions as follows:
Control Design Specifications
DS1 Settling time less than 20 minutes for a 10% step change from the MAP set-point.
DS2 Percent overshoot less than 15% for a 10% step change from the MAP set-point.
DS3 Zero steady-state tracking error to a step change from the MAP set-point.
DS4 Zero steady-state error to a step surgical disturbance input (of magnitude
\d(t)\ ^ 50) with a maximum response less than ±5% of the MAP set-point.
DS5 Minimum sensitivity to process parameter changes.
We cover the notion of percent overshoot (DS1) and settling time (DS2) more thor-
oughly in Chapter 5. They fall more naturally in the category of system perfor-
mance. The remaining three design specifications, DS3-DS5, covering steady-state
tracking errors (DS3), disturbance rejection (DS4), and system sensitivity to para-
meter changes (DS5) are the main topics of this chapter. The last specification, DS5,
is somewhat vague; however, this is a characteristic of many real-world specifica-
tions. In the system configuration, Figure 4.24, we identify the major system ele-
ments as the controller, anesthesia pump/vaporizer, sensor, and patient.
The system input R(s) is the desired mean arterial pressure change, and the out-
put Y(s) is the actual pressure change. The difference between the desired and the
measured blood pressure change forms a signal used by the controller to determine
value settings to the pump/vaporizer that delivers anesthesia vapor to the patient.
The model of the pump/vaporizer depends directly on the mechanical design.
We will assume a simple pump/vaporizer, where the rate of change of the output