Control Systems Engineering
7th Edition
ISBN: 9781118170519
Author: Norman S. Nise
Publisher: WILEY
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Chapter 4, Problem 73P
Find an equation that relates 2% settling time to the value of fvfor the translational
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Find a state space representation for the network shown below when the output is the displacement at M3.
Represent the translational mechanical system shown in state space, where x3(t) is the output.
Problem 1: Write the transfer function of the systems.
Problem 2: Write the differential equation and state space equation describing the following system.
Please answer both the problems.
Chapter 4 Solutions
Control Systems Engineering
Ch. 4 - Prob. 1RQCh. 4 - What does the performance specification for a...Ch. 4 - Prob. 3RQCh. 4 - In a system with an input and an output, what...Ch. 4 - Prob. 5RQCh. 4 - Prob. 6RQCh. 4 - 7. What is the difference between the natural...Ch. 4 - Prob. 8RQCh. 4 - Prob. 9RQCh. 4 - Prob. 10RQ
Ch. 4 - List five specifications for a second-order...Ch. 4 - Prob. 12RQCh. 4 - What pole locations characterize (1) the...Ch. 4 - Prob. 14RQCh. 4 - How can you justify pole-zero cancellation?Ch. 4 - Prob. 16RQCh. 4 - 17. What is the relationship between , which...Ch. 4 - Name a major advantage of using time-domain...Ch. 4 - Prob. 19RQCh. 4 - What three pieces of information must be given in...Ch. 4 - 21. How can the poles of a system be found from...Ch. 4 - Prob. 1PCh. 4 - Prob. 2PCh. 4 - MATIAB ML 3. Plot the step responses for Problem 2...Ch. 4 - Find the capacitor voltage in the network shown in...Ch. 4 - For the system shown in Figure P4.3, (a) find an...Ch. 4 - Prob. 8PCh. 4 - MATLAB ML 9. Use MATLAB to find the poles of...Ch. 4 - Find the transfer function and poles of the system...Ch. 4 - MATLAB ML 11. Repeat Problem 10 using MATLAB....Ch. 4 - Write the general form of the capacitor voltage...Ch. 4 - Solve for x(t) in the system shown in Figure P4.5...Ch. 4 - Prob. 15PCh. 4 - Prob. 16PCh. 4 - Calculate the exact response of each system of...Ch. 4 - Prob. 18PCh. 4 - Prob. 19PCh. 4 - For each of the second-order systems that follow,...Ch. 4 - MATLAB ML 21. Repeat Problem 20 using MATLAB. Have...Ch. 4 - GUI Tool GUIT
22. Use MATLAB’s LTI Viewer and...Ch. 4 - Prob. 23PCh. 4 - Find the transfer function of a second-order...Ch. 4 - For the system shown in Figure P4.7, do the...Ch. 4 - For the system shown in Figure P4.8, a step torque...Ch. 4 - Prob. 28PCh. 4 - Prob. 29PCh. 4 - Prob. 30PCh. 4 - Prob. 31PCh. 4 - Prob. 32PCh. 4 - Prob. 33PCh. 4 - Prob. 34PCh. 4 - Prob. 35PCh. 4 - Prob. 36PCh. 4 - State Space SS 38. A system is represented by the...Ch. 4 - Prob. 39PCh. 4 - Prob. 40PCh. 4 - State Space SS 41. Given the following system...Ch. 4 - State Space SS 42. Solve the following state...Ch. 4 - Prob. 43PCh. 4 - Prob. 44PCh. 4 - Prob. 46PCh. 4 - Prob. 47PCh. 4 - Prob. 48PCh. 4 - Prob. 53PCh. 4 - Prob. 54PCh. 4 - A MOEMS (optical MEMS) is a MEMS (Micro...Ch. 4 - Prob. 56PCh. 4 - Prob. 59PCh. 4 - Prob. 60PCh. 4 - Prob. 61PCh. 4 - Prob. 63PCh. 4 - Prob. 67PCh. 4 - Figure P4.l6 shows the step response of an...Ch. 4 - Figure P4. I 7 shows the free-body diagrams for...Ch. 4 - Find an equation that relates 2% settling time to...Ch. 4 - Prob. 74PCh. 4 - Prob. 75PCh. 4 - 76. Find J and K in the rotational system shown in...Ch. 4 - Given the system shown in Figure P4.22, find the...Ch. 4 - Prob. 78PCh. 4 - Find M and K, shown in the system of Figure P4.24,...Ch. 4 - If vi(t) is a step voltage in the network shown in...Ch. 4 - Prob. 81PCh. 4 - Prob. 82PCh. 4 - For the circuit shown in Figure P4.26, find the...Ch. 4 - Prob. 84PCh. 4 - Prob. 86P
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- This question asks for matrix form and NOT state space, but I don't understand what the difference between the two are.arrow_forwardObtain the state space model of the system shown below. Use equations for control theory state space modeling.arrow_forwardFind the state-space equation of the following mass-springdamper system. Assume that the bottom surface is frictionless. The input is external forcef(t)and the output is displacementx1(t)arrow_forward
- Get the input-output model Get the Transfer Function Get representation in State Variablesarrow_forwardFor the given close-loop system transfer function, determine its stability using Routh-Hurwitz Test for Stability.1. What is the stability of the system? (Stable, Unstable, Marginally Stable)arrow_forwardMATLAB PROBLEMarrow_forward
- Obtain the following requirements for a simple mass-spring-damper system with input of force f, output of displacement x, and translational motion only along the horizontal axis.a) Equation of motion,b) state space model,c) transfer function G(s),d) the time domain expression of the output according to the unit step function input,e) permanent regime error to be observed at the output according to the unit step function input,f) pole and zero positions in the complex plane,g) its absolute stability,h) the undamped natural frequency,i) damping ratio,j) damped natural frequency,k) open loop/static/dc gain,l) maximum overshoot (Mp),m) peak time (tp),n) settling time (ts, 2% tolerance).arrow_forwardFind the transfer function,G(s)=Z1(s)/H(s) Find the state space model.arrow_forwardDerive the state-space representation of the following system where the input is f(t) and the outputs isthe y1 =X1, y2=X2, y3=X3arrow_forward
- Translational mechanical systems Get the input-output model Get the Transfer Function Get representation in State Variablesarrow_forwardFor the following state-space representation,define the:– State Vector– System Matrix– Feedforward Matrix– Input Matrix & Input Vector– Output Matrix & Output Vectorarrow_forwardFor the system shown in the figure. the system parameters, the length of the rod, l is 2 m, mass of the rigid rod, m is 7, and the stiffness of the springs, k, is the last two digits of 57. Derive the equation of motion, b) Find the transfer function between force input (F) and angular displacement (θ) of the system c) Find the step response of the system, and show time-domain characteristics of the system d) Find the frequency response function, and draw frequency response graphs, and draw bode diagrams, show frequency-domain characteristics.arrow_forward
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