T H R E E
Modeling in the Time Domain
SOLUTIONS TO CASE STUDIES CHALLENGES
Antenna Control: StateSpace Representation
. Ea(s) 150 For the power amplifier, V (s) = s+150 . Taking the inverse Laplace transform, ea +150ea = p 150vp. Thus, the state equation
F O U R
Time Response
SOLUTIONS TO CASE STUDIES CHALLENGES
Antenna Control: OpenLoop Response
The forward transfer function for angular velocity is, 0(s) 24 G(s) = V (s) = (s+150)(s+1.32) P a. 0(t) = A + Be150t + Ce1.32t 24 b. G(s) = 2 . Therefore, 2n
F I V E
Reduction of Multiple Subsystems
SOLUTIONS TO CASE STUDIES CHALLENGES
Antenna Control: Designing a ClosedLoop Response
a. Drawing the block diagram of the system:
Pots
Pre amp
Power amp
Motor, load and gears
ui +
10
K
150 s+150

0.16 s (s+1.32)
S I X
Stability
SOLUTIONS TO CASE STUDIES CHALLENGES
Antenna Control: Stability Design via Gain
From the antenna control challenge of Chapter 5, 76.39K T(s) = 3 s +151.32s2+198s+76.39K Make a Routh table: s3 s2 s1 s0 1 151.32 29961.3676.39K 151.32 76.39K
S E V E N
SteadyState Errors
SOLUTIONS TO CASE STUDIES CHALLENGES
Antenna Control: SteadyState Error Design via Gain
76.39K a. G(s) = s(s+150)(s+1.32) . System is Type 1. Step input: e() = 0; Ramp input: 1 2.59 = 76.39K = K ; Parabolic input: e() = . 15
N I N E
Design via Root Locus
SOLUTIONS TO CASE STUDIES CHALLENGES
Antenna Control: LagLead Compensation
76.39K a. Uncompensated: From the Chapter 8 Case Study Challenge, G(s) = s(s+150)(s+1.32) = 7194.23 1 6.9 s(s+150)(s+1.32) with the dominant poles a
E I G H T
Root Locus Techniques
SOLUTIONS TO CASE STUDIES CHALLENGES
Antenna Control: Transient Design via Gain
a. From the Chapter 5 Case Study Challenge: 76.39K G(s) = s(s+150)(s+1.32) 1 Since Ts = 8 seconds, we search along  2 , the real part of poles
T E N
Frequency Response Techniques
SOLUTION TO CASE STUDY CHALLENGE
Antenna Control: Stability Design and Transient Performance
First find the forward transfer function, G(s). Pot: K1 = Preamp: K Power amp: 100 G1(s) = s(s+100) Motor and load: Kt 1 1 1 J
E L E V E N
Design via Frequency Response
SOLUTIONS TO CASE STUDIES CHALLENGES
Antenna Control: Gain Design
a. The required phase margin for 25% overshoot ( = 0.404), found from Eq. (10.73), is 43.49o. 50.88K From the solution to the Case Study Challenge
O N E
Introduction
ANSWERS TO REVIEW QUESTIONS
1. Guided missiles, automatic gain control in radio receivers, satellite tracking antenna 2. Yes  power gain, remote control, parameter conversion; No  Expense, complexity 3. Motor, low pass filter, inertia
T W E L V E
Design via State Space
SOLUTION TO CASE STUDY CHALLENGE
Antenna Control: Design of Controller and Observer
a. We first draw the signalflow diagram of the plant using the physical variables of the system as state variables.
Writing the state e
T W O
Modeling in the Frequency Domain
SOLUTIONS TO CASE STUDIES CHALLENGES
Antenna Control: Transfer Functions
Finding each transfer function: Vi(s) 10 = ; i(s) Vp(s) PreAmp: V (s) = K; i Ea(s) 150 Power Amp: V (s) = s+150 p Pot: 50 Motor: Jm = 0.05 + 5
T H I R T E E N
Digital Control Systems
SOLUTIONS TO CASE STUDIES CHALLENGES
Antenna Control: Transient Design via Gain
a. From the answer to the antenna control challenge in Chapter 5, the equivalent forward transfer function found by neglecting the dyna