0195136047.pdf

16.3 DIGITAL CONTROL SYSTEMS 813

ω(kT) and then compute the next value of control,u[(k+1)T]. After calculation of the control,
the microprocessor waits for another interrupt from the timer before it outputs the control at
t=(k+ 1 )T.Anassembly-languageprogram can be developed for the implementation of the
PI controller.
The control of a dc motor can be achieved with a PI controller discretized for microprocessor
programming. The starting point is that the PI controller is described by a differential equation.
The latter is discretized at the sampling instants by one of the numerical approximation methods,
and then is programmed in the microprocessor machine language.
Practical limitations of microprocessor-based control systems stem from the following
considerations:

• Finite-word-length characteristic, that is, an 8-bit word would only allow 2^8 =256 levels
  of resolution.


• Time delays encountered in executing the data handling, which may have a significant effect
  on the system response.


• Quantization effects, which affect accuracy and stability.

Adaptive Control

Another type of control system that makes use of the computer is known asadaptive control,
which is functionally represented in Figure 16.3.11. While the blockGprovides the system
output for the system input, the feedback is provided byHand is converted to a digital signal.
This digital signal is processed by the digital processor to effect the necessary control. The
characteristic feature of the adaptive control is that the characteristics of the blockGare
changed with time so that, for a given input, the desired output is obtained. Based on the
prediction of the performance of the system, the digital processor determines howGis to be
changed.
Figure 16.3.12 illustrates the adaptive control process as applied to a motor-speed control
system, which is based on adjustments of the armature resistance. Using all of the data inputs,
the computer computes the optimum value ofRasuch that the motor speed is appropriate to
the load. The signal corresponding to the computed value ofRais in turn used to position the
potentiometer arm of the variable resistance. The actual armature resistance is then controlled by
the position of the potentiometer arm, which in turn may be controlled by a sampled-data version
of the position-control system.
The speed and power of the digital computer (in predicting the response to a wide range of
changes that affect the system) are the main reasons for the use of adaptive systems in industrial
control. Large-scale systems may have multiple inputs applied simultaneously, and control is
successfully achieved because the process of predicting the desired response, and comparing
with the actual response, can be accomplished in a relatively short time compared to the response
time of the system to be controlled.

Digital processor

Output

Input

H

G

Figure 16.3.11Functional representation of

an adaptive control system.