2.7. PROPORTIONAL-INTEGRAL-DERIVATIVE CONTROL 53
This computation showingRank< 2 implies the system is not fully controllable,
but this does not, by itself, indicate which of the two eigenvalues is uncontrol-
lable.
2.7 Proportional-integral-derivativecontrol...............
Most industrial systems are controlled by classical proportional-integral-deriva-
tive (PID) controllers (including P, PD, and PI). This is done despite the system
being nonlinear and despite the fact that the simplicity of the concept often
limits the performance. The reason why PID controllers have gained such pop-
ularity is that detailed knowledge about the system is not required, but the
controller can be tuned by means of simple rules of thumb or by PID ìauto-
tuners.î
In this section, we demonstrate with several examples the design of con-
trollers using the standard approach. These same examples will be developed
using a fuzzy, neural, or neural-fuzzy approach in later chapters. The automo-
bile cruise control and temperature control problems are examples ofregulation
problems, where the fundamental desired behavior is to keep the output of the
system at a constant level, regardless of disturbances acting on the system.
The servomotor dynamics control problem is a component of aservoproblem,
where the fundamental desired behavior is to make the output follow a reference
trajectory.
2.7.1 Example:automobilecruisecontrolsystem
In this example, we develop a simple model of an automobile cruise control
system. The control objective is to maintain a speed preset by the driver. If we
Figure 2.18. Mass and damper systemneglect the inertia of the wheels, and assume that friction (which is proportional
to the carís speed) is what is opposing the motion of the car, then the plant
description is reduced to the simple mass and damper system shown in Figure