Control Systems Engineering
7th Edition
ISBN: 9781118170519
Author: Norman S. Nise
Publisher: WILEY
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Textbook Question
Chapter 6, Problem 42P
Find the range of K to keep the system shown in Figure P6.9 stable. [Section: 6.4]
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Get the input-output model
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32. For the rotational mechanical system with gears
shown in Figure P2.18, find the transfer function,
G(s) = 03(s)/T(s). The gears have inertia and bear-
ing friction as shown. [Section: 2.7]
T(t)
to
|N1
小D
N2
N3
2, D2
Jz, D3 03(1)
N4
J4. D4
J5. D5
FIGURE P2.18
sair
Find a state space representation for the network shown below when the output is the displacement at M3.
Chapter 6 Solutions
Control Systems Engineering
Ch. 6 - Prob. 1RQCh. 6 - Prob. 2RQCh. 6 - What would happen to a physical system chat...Ch. 6 - Why are marginally stable systems considered...Ch. 6 - Prob. 5RQCh. 6 - Prob. 6RQCh. 6 - Prob. 7RQCh. 6 - Prob. 8RQCh. 6 - Prob. 9RQCh. 6 - Why do we sometimes multiply a row of a Routh...
Ch. 6 - Prob. 11RQCh. 6 - Prob. 12RQCh. 6 - 13. Does the presence of an entire row of zeros...Ch. 6 - Prob. 14RQCh. 6 - Prob. 15RQCh. 6 - Prob. 16RQCh. 6 - Tell how many roots of the following polynomial...Ch. 6 - Tell how many roots of the following polynomial...Ch. 6 - Using the Routh table, tell how many poles of the...Ch. 6 - Prob. 4PCh. 6 - Determine how many closed-loop poles lie in the...Ch. 6 - Determine how many closed-loop poles lie in the...Ch. 6 - MATLAB ML 7. Use MATLAB to find the pole location...Ch. 6 - Symbolic Math SM 8. Use MATLAB and the Symbolic...Ch. 6 - Determine whether the unity feedback system of...Ch. 6 - Use MATLAB to find the pole locations for the...Ch. 6 - Consider the unity feedback system of Figure P6.3...Ch. 6 - In the system of Figure P6.3, let Gs=Ks+1ss2s+3...Ch. 6 - Given the unity feedback system of Figure P6.3...Ch. 6 - Using the Routh-Hurwitz criterion and the unity...Ch. 6 - Given the unity feedback system of Figure P6.3...Ch. 6 - Repeat Problem 15 using MATLAB.Ch. 6 - Prob. 17PCh. 6 - For the system of Figure P6.4, tell how many...Ch. 6 - Using the Routh-Hurwitz criterion, tell how many...Ch. 6 - Determine if the unity feedback system of Figure...Ch. 6 - For the unity feedback system of Figure P6.3 with...Ch. 6 - In the system of Figure P6.3, let Gs=Ksassb Find...Ch. 6 - For the unity feedback system of Figure P63 with...Ch. 6 - Find the range of K for stability for the unity...Ch. 6 - For the unity feedback system of Figure P6.3 with...Ch. 6 - find the range of K for stability. [Section: 6.41]...Ch. 6 - Find the range of gain, K, to ensure stability in...Ch. 6 - Using the Routh-Hurwitz criterion, find the value...Ch. 6 - Use the Routh-Hurwitz criterion to find the range...Ch. 6 - Prob. 32PCh. 6 - Given the unity feedback system of Figure P63 with...Ch. 6 - Repeat Problem 33 for [Section: 6.4]...Ch. 6 - For the system shown in Figure P6.8, find the...Ch. 6 - Given the unity feedback system of Figure P6.3...Ch. 6 - For the unity feedback system of Figure P6.3 with...Ch. 6 - For the unity feedback system of Figure P6.3 with...Ch. 6 - Given the unity feedback system of Figure P6.3...Ch. 6 - Using the Routh-Hurwitz criterion and the unity...Ch. 6 - Find the range of K to keep the system shown in...Ch. 6 - Prob. 43PCh. 6 - The closed-loop transfer function of a system is...Ch. 6 - Prob. 45PCh. 6 - Prob. 46PCh. 6 - An interval polynomial is of the form...Ch. 6 - A linearized model of a torque-controlled crane...Ch. 6 - The read/write head assembly arm of a computer...Ch. 6 - A system is represented in state space as...Ch. 6 - State Space SS 52. The following system in state...Ch. 6 - Prob. 54PCh. 6 - A model for an airplane’s pitch loop is shown in...Ch. 6 - Prob. 57PCh. 6 - Prob. 58PCh. 6 - Prob. 59PCh. 6 - Prob. 60PCh. 6 - Prob. 61PCh. 6 - Look-ahead information can be used to...Ch. 6 - Prob. 63PCh. 6 - It has been shown (Pounds, 2011) that an unloaded...Ch. 6 - Prob. 65PCh. 6 - The system shown in Figure P6.16 has G1s=1/ss+2s+4...Ch. 6 - Prob. 67PCh. 6 - Prob. 68PCh. 6 - Hybrid vehicle. Figure P6.l8 shows the HEV system...Ch. 6 - Prob. 70P
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- For the following state-space representation,define the:– State Vector– System Matrix– Feedforward Matrix– Input Matrix & Input Vector– Output Matrix & Output Vectorarrow_forward38. Given the rotational system shown in Figure P2.24, find the transfer function, G(s) = 06(s)/01(s). [Section: 2.7]arrow_forwardThis question asks for matrix form and NOT state space, but I don't understand what the difference between the two are.arrow_forward
- Question 5: A model for a single joint of a robotic manipulator is shown in Figure below. The usual notation is used. The gear inertia is neglected and the gear reduction ratio is taken as 1:r (Note: r < 1). a) Draw a linear graph for the model, assuming that no external (load) torque is present at the robot arm. b) Using the linear graph derive a state model for this system. The input is the motor magnetic torque Tm and the output is the angular speed o, of the robot arm. What is the order of the system? Jm m (viscous) 1:r Motor Robot Arm Gear Box (Light)arrow_forwardMATLAB PROBLEMarrow_forwardGet representation in State Variablesarrow_forward
- P4.7 A robot uses feedback to control the orientation of each joint axis. The load effect varies due to varying load objects and the extended position of the arm. The system will be deflected by the load carried in the gripper. Thus, the system may be represented by Figure P4.7 O, where the load torque is Ta (s) = D/s. Assume R(s) = 0 at the index position. (a) What is the effect of Ta(s) on Y(s)? (b) Determine the sensitivity of the closed loop to k2. (c) What is the steady-state error when R (s) = 1/s and Ta(s) = 0? Load disturbance T (s) R(s) Controller Y(s) Desired k2 Actual k1 joint angle joint angle s(TS + 1) kz + k4s Figure P4.7 Robot control system.arrow_forward3. Consider the system shown below. The outputs of the system are the angular displacement of the upper gear (positive about the x-axis) and the Contact force between the upper and lower gear. Assume that the initial conditions for all state variables are zero and that the gears are massless. There are two inputs Ti(t) acting on the top gear and T₂(t) acting on the rightmost disk. If you let • 9₁ denote the state variable for the spring 92 denote the state variable for the rightmost disk. u₁ denote T₁. u₂ denote T₂. You should expect to get the following state space representation and 9= KR + 0₁ 0 LIR -1. 7/2 Ti(t) Jun 0:0⁰ 40² T₂(t) 03 Figure 3: System for problem 3 21 (a) Derive the state-space model (state equation and output equation) in vector form. (b) For the system parameters I = 8 kg m², k = 1 N m,b=2 N s m/rad, R₁ = 1 m, and R₂ = 3 m: i. Use MATLAB to determine the transfer function matrix [G(s)]. ii. What is the ristic equation AS the system? iii. What are the values of the…arrow_forwardUse MATLAB to obtain a state model for the following equations; obtain the expressions for the matrices A, B, C, and D. In both cases, the input is f(t); the output: is y. a. 5d³yd²y +7. b. dy +3 dt³ dt² dt Y(s) 5 = F(s) s² +7s+4 - +6y=f(t)arrow_forward
- Derive the state-space representation of the following system where the input is f(t) and the outputs isthe y1 =X1, y2=X2, y3=X3arrow_forwardFind the transfer function X(s)/G(s) of the block diagram below.arrow_forwardReduce the block-diagram shown, to find the transfer function C(s)/R(s).arrow_forward
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