SYSTEM DYNAMICS LL+CONNECT
3rd Edition
ISBN: 9781264201891
Author: Palm
Publisher: MCG CUSTOM
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Chapter 5, Problem 5.21P
The transfer function of a certain system is
Use two methods to obtain a state-variable model in standard form. For each model, relate the initial value of the state-variable to the given initial value
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A velocity of a vehicle is required to be controlled and maintained constant even if there are disturbances because of wind, or road surface variations. The forces that are applied on the vehicle are the engine force (u), damping/resistive force (b*v) that opposing the motion, and inertial force (m*a). A simplified model is shown in the free body diagram below.
From the free body diagram, the ordinary differential equation of the vehicle is:
m * dv(t)/ dt + bv(t) = u (t)
Where:
v (m/s) is the velocity of the vehicle,
b [Ns/m] is the damping coefficient,
m [kg] is the vehicle mass,
u [N] is the engine force.
Question:
Assume that the vehicle initially starts from zero velocity and zero acceleration. Then, (Note that the velocity (v) is the output and the force (w) is the input to the system):
A. Use Laplace transform of the differential equation to determine the transfer function of the system.
The transfer function of the following system is, G(s)
Describe the concept of a transfer function in the context of system modeling. How is it used to represent a system's behavior?
Chapter 5 Solutions
SYSTEM DYNAMICS LL+CONNECT
Ch. 5 - Prob. 5.1PCh. 5 - Obtain the transfer function Xs/Fs from the block...Ch. 5 - Obtain the transfer function Xs/Fs from the block...Ch. 5 - Draw a block diagram for the following equation....Ch. 5 - Draw a block diagram for the following model. The...Ch. 5 - Referring to Figure P5.6, derive the expressions...Ch. 5 - Prob. 5.7PCh. 5 - Prob. 5.10PCh. 5 - Obtain the state model for the reduced-form model...Ch. 5 - Obtain the state model for the reduced-form model...
Ch. 5 - Prob. 5.13PCh. 5 - Obtain the state model for the transfer-function...Ch. 5 - Obtain the state model for the two-mass system...Ch. 5 - Prob. 5.16PCh. 5 - Put the following model in standard state-variable...Ch. 5 - Given the state-variable model...Ch. 5 - Given the following state-variable models, obtain...Ch. 5 - Prob. 5.20PCh. 5 - The transfer function of a certain system is...Ch. 5 - Prob. 5.22PCh. 5 - Prob. 5.23PCh. 5 - Use MATLAB to obtain a state model for the...Ch. 5 - Use MATLAB to obtain a state-variable model for...
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- Assume F(t) is a step force input and the displacement is x(t) obtain the transfer function for the system shown below. Assume all initial conditions are zero. F(t) = 5 N, m = 0.2 kg, c = 0.3 N-s/m, k1 = 5 N/m and k2 = 4 N/m. 3. Find the global stiffness matrix, displacement at nodarrow_forwardRepresent the translational mechanical system shown in state space, where x3(t) is the output.arrow_forwardThe transfer function of a system is the ratio between _________________ and ____________ in Laplace transform. a. Output and Input b. Input and Output c. Input and Feedback d. Output and Feedbackarrow_forward
- Evaluate the following state-space system provided to find the corresponding transfer function G(s) = Y(s) / U(s)arrow_forward-Get the input-output model -Get the Transfer Function -Get representation in State Variablesarrow_forwardSketch the level response for a bathtub with cross-sectional area of 8 ft 2 as a function of time for the following sequence of events; assume an initial level of 0.5 ft with the drain open. The inflow and outflow are initially equal to2ft3/min.(a)The drain is suddenly closed, and the inflow remains con-stant for 3 min (0≤t≤3).(b)The drain is opened for 15 min; assume a time constant in a linear transfer function of 3 min, so a steady state is essentially reached (3≤t≤18) (c)The inflow rate is doubled for 6 min (18≤t≤24).(d)The inflow rate is returned to its original value for 16 min(24≤t≤40).arrow_forward
- Translational mechanical systems Get the input-output model Get the Transfer Function Get representation in State Variablesarrow_forwardThe response of a system under arbitrary force can be determined by summing the responses resulting from several elementary impulses. Choose an option: RealFalsearrow_forwardFind the transfer function,G(s)=Z1(s)/H(s) Find the state space model.arrow_forward
- Transfer function on translational mechanical systemarrow_forwardIn a tank heater with agitator, the relationship between the tank outlet temperature (T) and the heat given to the system by the heater connected to the tank (Q) is expressed by the model equation below. Accordingly, find the gain and time constant of the transfer function between temperature and heat. If the 1000 W heater power is suddenly increased by 25%, in how many minutes will the outlet temperature reach the new steady state value? (Note: The first steady state tank outlet temperature is 65 °C and the unit of time constant is minutes)arrow_forwardHow can a transfer function be derived from a system model, and what information does it provide about the system's behavior?arrow_forward
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