Signal Processing for Control - Signal Processing Systems - page 263

3 Signal Processing in Control

An understanding of the role of signal processing in control begins with a refinement
of the abstract system model in Fig. 1 to that shown in Fig. 3 .
Although control theorists usually include the sensors and actuators as part of
the plant, it is important to understand their presence and their role. In almost all
modern control systems excepting the float valve, the sensors convert the physical
signal of interest into an electronic version and the actuator takes an electronic signal
as its input and converts it into a physical signal. Both sensing and actuation involve
specialized signal processing. A common issue for sensors is that there is very little
energy in the signal so amplification and other buffering is needed. Most actuation
requires much greater power levels than are used in signal processing so some form
of power amplification is needed. Generally, the power used in signal processing
for control is a small fraction of the power consumed by the closed-loop system.
For this reason, control designers rarely concern themselves with the power needed
by the controller.
Most modern control systems are implemented digitally. The part of a digital
control system between the sensor output and the actuator input is precisely a digital
signal processor (DSP). The fact that it is a control system impacts the DSP in
at least three ways. First, it is essential that a control signal be produced on time
every time. This is a hard real-time constraint. Second, the fact that the control
signal eventually is input into an actuator also imposes some constraints. Actuators
saturate. That is, there are limits to their output values that physically cannot be
exceeded. For example, the rudder on a ship and the control surfaces on a wing can
only turn so many degrees. A pump has a maximum amount it can move. A motor
has a limit on the torque it can produce. Control systems must either be designed to
avoid saturating the actuator or to avoid the performance degradation that can result
from saturation. A mathematical model of saturation is given in Fig. 4 .
Another nonlinearity that is difficult, if not impossible, to avoid is the so-called
dead zone illustrated in Fig. 4 . This arises, for example, in the control of movement
because very small motor torques are unable to overcome stiction. Although there
are many other common nonlinearities that appear in control systems, we will only
mention one more, the quantization nonlinearity that appears whenever a continuous
plant is digitally controlled.

d z

Plant

y

u

actuators sensors

Fig. 3 The plant with sensors
and actuators indicated