Control Systems Engineering
7th Edition
ISBN: 9781118170519
Author: Norman S. Nise
Publisher: WILEY
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Chapter 3, Problem 25P
Experiments to identify precision grip dynamics between the index finger and thumb have been performed using a ball-drop experiment. A subject holds a device with a small receptacle into which an object is dropped, and the response is measured (Fagergren, 2000). Assuming a step input, it has been found that the response of the motor subsystem together with the sensory system is of the form
Convert this transfer function to a state-space representation.
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1. Verify Eqs. 1 through 5.
Figure 1: mass spring damper
In class, we have studied mechanical systems of this
type. Here, the main results of our in-class analysis are
reviewed. The dynamic behavior of this system is deter-
mined from the linear second-order ordinary differential
equation:
where
(1)
where r(t) is the displacement of the mass, m is the
mass, b is the damping coefficient, and k is the spring
stiffness. Equations like Eq. 1 are often written in the
"standard form"
ď²x
dt2
r(t) =
= tan-1
d²r
dt2
m.
M
+25wn +wn²x = 0
(2)
The variable wn is the natural frequency of the system
and is the damping ratio.
If the system is underdamped, i.e. < < 1, and it has
initial conditions (0) = zot-o = 0, then the solution
to Eq. 2 is given by:
IO
√1
x(1)
T₁ =
+b+kr = 0
dt
2π
dr.
dt
ل لها
-(wat sin (wat +)
and
is the damped natural frequency.
In Figure 2, the normalized plot of the response of this
system reveals some useful information. Note that the
amount of time Ta between peaks is…
A mechanical system is presented as
below. There are four simulation
graphs for different values for m, b
and c tested for a step response.
Identify the graph for m=4 kg, b=0.3
N.s/m and k=1 N/m (Hint: you may
need to use matlab simulation to find
it).
m
1.8
1.6
1.4
b
·f(t)
Step Response
Needs Complete typed solution with 100 % accuracy. Otherwise skip if you can't give complete solution don't use chat gpt or ai i definitely upvote you.
Chapter 3 Solutions
Control Systems Engineering
Ch. 3 - Prob. 1RQCh. 3 - State an advantage of the transfer function...Ch. 3 - Define state variables.Ch. 3 - Define state.Ch. 3 - Define state vector.Ch. 3 - Define state space.Ch. 3 - What is required to represent a system in state...Ch. 3 - 8. An eighth-order system would be represented in...Ch. 3 - If the state equations are a system of first-order...Ch. 3 - Prob. 10RQ
Ch. 3 - What factors influence the choice of state...Ch. 3 - What is a convenient choice of state variables for...Ch. 3 - If an electrical network has three energy-storage...Ch. 3 - Prob. 14RQCh. 3 - Prob. 1PCh. 3 - Represent the electrical network shown in Figure...Ch. 3 - Prob. 3PCh. 3 - Represent the system shown in Figure P3.4 in state...Ch. 3 - Represent the rotational mechanical system shown...Ch. 3 - Represent the system shown in Figure P3.7 in state...Ch. 3 - 8. Show that the system of Figure 3.7 in the text...Ch. 3 - Find the state-space representation in...Ch. 3 - MATLAB ML 10. Repeat Problem 9 using MATLAB....Ch. 3 - For each system shown in Figure P3.9, write the...Ch. 3 - MATLAB ML
12. Repeat Problem 11 using MATLAB....Ch. 3 - 13. Represent the following transfer function in...Ch. 3 - Find the transfer function G(s) = Y(s)/R(s) for...Ch. 3 - MATLAB ML
15. Use MATLAB to find the transfer...Ch. 3 - 17. A missile in flight, as shown in Figure P3.10,...Ch. 3 - Given the dc servomotor and load shown in Figure...Ch. 3 - Prob. 20PCh. 3 - Prob. 23PCh. 3 - Experiments to identify precision grip dynamics...Ch. 3 - State-space representations are, in general, not...Ch. 3 - Figure P3.16 shows a schematic description of the...Ch. 3 - Prob. 28PCh. 3 - A single-pole oil cylinder valve contains a spool...Ch. 3 - Figure P3.17 shows a free-body diagram of an...Ch. 3 - 33. Parabolic trough collector. A transfer...
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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Similar questions
- Harmonic oscillators. One of the simplest yet most important second-order, linear, constant- coefficient differential equations is the equation for a harmonic oscilator. This equation models the motion of a mass attached to a spring. The spring is attached to a vertical wall and the mass is allowed to slide along a horizontal track. We let z denote the displacement of the mass from its natural resting place (with x > 0 if the spring is stretched and x 0 is the damping constant, and k> 0 is the spring constant. Newton's law states that the force acting on the oscillator is equal to mass times acceleration. Therefore the differential equation for the damped harmonic oscillator is mx" + bx' + kr = 0. (1) k Lui Assume the mass m = 1. (a) Transform Equation (1) into a system of first-order equations. (b) For which values of k, b does this system have complex eigenvalues? Repeated eigenvalues? Real and distinct eigenvalues? (c) Find the general solution of this system in each case. (d)…arrow_forwardanswer completely pleasearrow_forwardPlease try to give type solution fast i will rate for surearrow_forward
- For the undamped linear system with two degree-of-freedom system, the initial conditions are shown as below. Please determine the mode of the motion. x₁(0) = x(0) = 1, x(0)=x₂ (0) = 0, X1 k k ww m ww X2 2k 24 2m wwarrow_forwardVibrationsarrow_forward1) Obtain the Mechanical system equivalent to the above electrical System (show it as a diagram). In addition, provide the mathematical model of the obtained mechanical system. 2) What is the output of the system in terms of Matrices C and D (if exist).arrow_forward
- 1. For the linkage system show, Link 1 moves along the vertical direction via a linear motor. Link 2 and 3,,dependent on the motion of Link 1, will move accordingly. Perform position analysis using Chace Mehod: Draw the loop closure vectors for the problem. (a) (b) Determine the unknowns. (c) Determine which kinematic case it is (d) Determine equations for the unknowns as function of known variables. (e) Assume link 1 is located 3 inches above the x-y coordinates, and link 2 has a length of 5 inches. Determine the numerical values of the two unknowns for this specific configuration. Link 1 X Link 2 Link 3arrow_forwardExample # 1 For the mechanical system shown, a force of 2 lb( step input) is applied to the system, the mass oscillates, as shown in fig. determi from this response curve. The displacement x is measured from the equilibrium position m, b, k of the system 0.0095 ft 0.1 ft 4 5 (b)arrow_forwardIn a standing posture, the masses of head, upper torso, hips, and legs and the elasticity/ damping of neck, spinal column, abdomen, and legs influence the response characteristics. Develop a sequence of three improved approximations for modeling the human body.arrow_forward
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