Control11 Digital Control

8/12/2019 Control11 Digital Control

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CHAPTER

1Introduction to Digital

Control

ObjectivesAfter completing this chapter, the reader will be able to do the following:

1. Explain the reasons for the popularity of digital control systems.

2. Draw a block diagram for digital control of a given analog control system.

3. Explain the structure and components of a typical digital control system.

In most modern engineering systems, there is a need to control the evolution withtime of one or more of the system variables. Controllers are required to ensuresatisfactory transient and steady-state behavior for these engineering systems. To

guarantee satisfactory performance in the presence of disturbances and modeluncertainty, most controllers in use today employ some form of negative feedback.A sensor is needed to measure the controlled variable and compare its behaviorto a reference signal. Control action is based on an error signal defined as thedifference between the reference and the actual values.

The controller that manipulates the error signal to determine the desired controlaction has classically been an analog system, which includes electrical, fluid, pneu-matic, or mechanical components. These systems all have analoginputs and outputs(i.e., their input and output signals are defined over a continuous time interval andhave values that are defined over a continuous range of amplitudes). In the past fewdecades, analog controllers have often been replaced by digitalcontrollers whose

inputs and outputs are defined at discrete time instances. The digital controllers arein the form of digital circuits, digital computers, or microprocessors.

Intuitively, one would think that controllers that continuously monitor theoutput of a system would be superior to those that base their control on sampledvalues of the output. It would seem that control variables (controller outputs) thatchange continuously would achieve better control than those that change peri-odically. This is in fact true! Had all other factors been identical for digital andanalog control, analog control would be superior to digital control. What then isthe reason behind the change from analog to digital that has occurred over thepast few decades?


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2 CHAPTER 1 Introduction to Digital Control

1.1WHY DIGITAL CONTROL?

Digital control offers distinct advantages over analog control that explain itspopularity. Here are some of its many advantages:

Accuracy.Digital signals are represented in terms of zeros and ones with typically12 bits or more to represent a single number. This involves a very small erroras compared to analog signals where noise and power supply drift are alwayspresent.

Implementation errors. Digital processing of control signals involves addi-tion and multiplication by stored numerical values. The errors that resultfrom digital representation and arithmetic are negligible. By contrast, theprocessing of analog signals is performed using components such as resistorsand capacitors with actual values that vary significantly from the nominaldesign values.

Flexibility.An analog controller is difficult to modify or redesign once implemen-ted in hardware. A digital controller is implemented in firmware or software,and its modification is possible without a complete replacement of the originalcontroller. Furthermore, the structure of the digital controller need not followone of the simple forms that are typically used in analog control. More complexcontroller structures involve a few extra arithmetic operations and are easilyrealizable.

Speed.The speed of computer hardware has increased exponentially since the1980s. This increase in processing speed has made it possible to sample andprocess control signals at very high speeds. Because the interval between

samples, the sampling period, can be made very small, digital controllersachieve performance that is essentially the same as that based on continuousmonitoring of the controlled variable.

Cost.Although the prices of most goods and services have steadily increased, thecost of digital circuitry continues to decrease. Advances in very large scaleintegration (VLSI) technology have made it possible to manufacture better,faster, and more reliable integrated circuits and to offer them to the consumerat a lower price. This has made the use of digital controllers more economicaleven for small, low-cost applications.

1.2 THE STRUCTURE OF A DIGITAL CONTROL SYSTEM

To control a physical system or process using a digital controller, the controllermust receive measurements from the system, process them, and then sendcontrol signals to the actuator that effects the control action. In almost all applica-tions, both the plant and the actuator are analog systems. This is a situation


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1.3 Examples of Digital Control Systems 3

where the controller and the controlled do not speak the same language andsome form of translation is required. The translation from controller language(digital) to physical process language (analog) is performed by a digital-to-analogconverter, or DAC. The translation from process language to digital controller

language is performed by an analog-to-digital converter, or ADC. A sensor isneeded to monitor the controlled variable for feedback control. The combinationof the elements discussed here in a control loop is shown in Figure 1.1. Variationson this control configuration are possible. For example, the system could haveseveral reference inputs and controlled variables, each with a loop similar to thatof Figure 1.1. The system could also include an inner loop with digital or analogcontrol.

1.3 EXAMPLES OF DIGITAL CONTROL SYSTEMS

In this section, we briefly discuss examples of control systems where digital imple-mentation is now the norm. There are many other examples of industrial pro-cesses that are digitally controlled, and the reader is encouraged to seek otherexamples from the literature.

1.3.1 Closed-Loop Drug Delivery System

Several chronic diseases require the regulation of the patients blood levels of aspecific drug or hormone. For example, some diseases involve the failure of thebodys natural closed-loop control of blood levels of nutrients. Most prominentamong these is the disease diabetes, where the production of the hormone insulinthat controls blood glucose levels is impaired.

To design a closed-loop drug delivery system, a sensor is utilized to measurethe levels of the regulated drug or nutrient in the blood. This measurement isconverted to digital form and fed to the control computer, which drives a pumpthat injects the drug into the patients blood. A block diagram of the drug deliverysystem is shown in Figure 1.2. Refer to Carson and Deutsch (1992) for a moredetailed example of a drug delivery system.

FIGURE 1.1

Configuration of a digital control system.

ControlledVariable

ReferenceInput

Computer DAC

ADC

Actuatorand Process

Sensor
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1.3.2 Computer Control of an Aircraft Turbojet Engine

To achieve the high performance required for todays aircraft, turbojet enginesemploy sophisticated computer control strategies. A simplified block diagram forturbojet computer control is shown in Figure 1.3. The control requires feedbackof the engine state (speed, temperature, and pressure), measurements of the air-craft state (speed and direction), and pilot command.

1.3.3 Control of a Robotic Manipulator

Robotic manipulators are capable of performing repetitive tasks at speeds andaccuracies that far exceed those of human operators. They are now widely usedin manufacturing processes such as spot welding and painting. To perform theirtasks accurately and reliably, manipulator hand (or end-effector) positions andvelocities are controlled digitally. Each motion or degree of freedom (D.O.F.) ofthe manipulator is positioned using a separate position control system. All the

FIGURE 1.2

Drug delivery digital control system. (a) Schematic of a drug delivery system. (b) Block diagram

of a drug delivery system.

DrugPump

RegulatedDrugor Nutrient

Computer

BloodSensor

Drug Tank

(a)

DrugPump

RegulatedDrug

or Nutrient

ReferenceBlood

Level

ADC

DACComputer

BloodSensor

Patient

(b)
http://-/?-http://-/?-


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1.3 Examples of Digital Control Systems 5

motions are coordinated by a supervisory computer to achieve the desired speedand positioning of the end-effector. The computer also provides an interfacebetween the robot and the operator that allows programming the lower-levelcontrollers and directing their actions. The control algorithms are downloadedfrom the supervisory computer to the control computers, which are typically

specialized microprocessors known as digital signal processing (DSP) chips. TheDSP chips execute the control algorithms and provide closed-loop control for themanipulator. A simple robotic manipulator is shown in Figure 1.4a, and a blockdiagram of its digital control system is shown in Figure 1.4b. For simplicity, onlyone motion control loop is shown in Figure 1.4, but there are actually nloops foran n-D.O.F. manipulator.

FIGURE 1.3

Turbojet engine control system. (a) F-22 military fighter aircraft. (b) Block diagram of an engine

control system.

(a)

AircraftState

EngineState

PilotCommand

Computer

AircraftSensors

DAC

ADC

ADC

AircraftTurbojetEngine

EngineSensors

(b)
http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-


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RESOURCES

Carson, E. R., and T. Deutsch, A spectrum of approaches for controlling diabetes, Control

Syst. Mag., 12(6):25-31, 1992.Chen, C. T.,Analog and Digital Control System Design, SaundersHBJ, 1993.

Koivo, A. J.,Fundamentals for Control of Robotic Manipulators,Wiley, 1989.

Shaffer, P. L., A multiprocessor implementation of a real-time control of turbojet engine,

Control Syst. Mag., 10(4):38-42, 1990.

FIGURE 1.4

Robotic manipulator control system. (a) 3-D.O.F. robotic manipulator. (b) Block diagram of a

manipulator control system.

(a)

Manipulator

ReferenceTrajectory

PositionSensors

VelocitySensors

ComputersSupervisoryComputer

DAC

ADC

ADC

(b)

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Control11 Digital Control