Feedback Control

100

Solutions Manual
6th Edition

Feedback Control of Dynamic Systems
. .

Gene F. Franklin
.

J. David Powell
.

Abbas Emami-Naeini
. . . .

Assisted by: H.K. Aghajan H. Al-Rahmani P. Coulot P. Dankoski S. Everett R. Fuller T. Iwata V. Jones F. Safai L. Kobayashi H-T. Lee E. Thuriyasena M. Matsuoka

Chapter 1

An Overview and Brief History of Feedback Control
1.1 Problemsand Solutions

1. Draw a component block diagram for each of the following feedback control systems. (a) The manual steering system of an automobile (b) Drebbel’ incubator s (c) The water level controlled by a ‡ and valve oat (d) Watt’ steam engine with ‡ s y-ball governor In each case, indicate the location of the elements listed below and give the units associated with each signal. theprocess the process output signal the sensor the actuator the actuator output signal The reference signal Notice that in a number of cases the same physical device may perform more than one of these functions. Solution: (a) A manual steering system for an automobile: 101

102CHAPTER 1. AN OVERVIEW AND BRIEF HISTORY OF FEEDBACK CONTROL

(b) Drebbel’ incubator: s

(c) Water level regulator:

(d)Fly-ball governor:

1.1. PROBLEMS AND SOLUTIONS

103

(e) Automatic steering of a ship:

(f) A public address system:

2. Identify the physical principles and describe the operation of the thermostat in your home or o¢ ce. Solution: A thermostat is a device for maintaining a temperature constant at a desired value. It is equipped with a temperature sensor which detects deviation fromthe desired value, determines whether the temperature setting is exceeded or not, and transmits the information to a furnace or air conditioner so that the termperature in the room is brought back

104CHAPTER 1. AN OVERVIEW AND BRIEF HISTORY OF FEEDBACK CONTROL
S to ra g e chest M a c h in e chest S creen s H eadbox a n d c le a n e rs P re sse s D r y in g s e c tio n R eel

R e f in e r

Wire T h ic k s to c k C o n s is te n c y m e te r M o is tu re m e te r

CV W h ite w a te r

C o n tro lle r

Figure 1.1: A paper making machine From Karl Astrom, (1970, page 192) reprinted with permission.

to the desired setting. Examples: Tubes …lled with liquid mercury are attached to a bimetallic strip which tilt the tube and cause the mercury to slide over electrical contacts. Abimetallic strip consists of two strips of metal bonded together, each of a di¤erent expansion coe¢ cient so that temperature changes bend the metal. In some cases, the bending of bimetallic strips simply cause electrical contacts to open or close directly. In most cases today, temperature is sensed electronically using,for example, a thermistor, a resistor whose resistance changes withtemperature. Modern computer-based thermostats are programmable, sense the current from the thermistor and convert that to a digital signal. 3. A machine for making paper is diagrammed in Fig. 1.12. There are two main parameters under feedback control: the density of …bers as controlled by the consistency of the thick stock that ‡ ows from the headbox onto the wire, and the moisture content of the …nalproduct that comes out of the dryers. Stock from the machine chest is diluted by white water returning from under the wire as controlled by a control valve (CV). A meter supplies a reading of the consistency. At the “dry end” of the machine, there is a moisture sensor. Draw a signal graph and identify the seven components listed in Problem 1 for (a) control of consistency (b) control of moistureSolution: (a) Control of paper machine consistency:

1.1. PROBLEMS AND SOLUTIONS

105

(b) Control of paper machine moisture:

4. Many variables in the human body are under feedback control. For each of the following controlled variables, draw a graph showing the process being controlled, the sensor that measures the variable, the actuator that causes it to increase and/or decrease, the...