Concept explainers
In control systems analysis, transfer functions are developed that mathematically relate the dynamics of a system's input to its output. A transfer function for a robotic positioning system is given by
where G(s) 5 system gain, C(s) 5 system output, N(s) 5 system input, and s 5 Laplace transform complex frequency. Use a numerical technique to find the roots of the numerator and denominator and factor these into the form
Where
Want to see the full answer?
Check out a sample textbook solutionChapter 7 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
Additional Engineering Textbook Solutions
Advanced Engineering Mathematics
Basic Technical Mathematics
Fundamentals of Differential Equations (9th Edition)
Elementary Statistics Using the TI-83/84 Plus Calculator, Books a la Carte Edition (4th Edition)
A Survey of Mathematics with Applications (10th Edition) - Standalone book
- for principle of öpelaliuil. Q4: A robot is used to service (load/unload) three machines in a cell, where the three machines have the same cycle time as 50 sec. the cycle time is divided as follow: Decide how this robot should service these three machines to Machine (M) Load/Unload Run M1 25 25 optimize the machine interference. M2 15 35 M3 10 40arrow_forward3. Dynamics and control of two tank in series The following system is given: A water storage Tank 1 in which water is stored at atmospheric pressure and distributed by gravity flow in a downfeed in the same type water storage Tank 2. Where: h1, h2 is water level(m), S1, S2 is squared area of botom of the tank cilinders (m²),F1 in/F2in-water inflow, F1/F2out- water outflow(m³/h), k1, k: Valve constant (m²5/h), pipe length is 2.5 ommited. F1in h1 S1 Tank 1 k1 h2 F1 out F2 in S2 k2 F2 out Tank 2 3.1 Describe the dynamic behavior of a tank 1 in terms of ordinary differential equations. 3.2 Describe the dynamic behavior of the level h2/ tank 2/, due to the input flow Flin. in terms of ordinary differential equations. 3.3 Determine the transfer function of the level h2 as output, due to the input flow Flin. 3.4 Select the strategy to control the plant / level control system / with Flin as control action and output- level h2/ tank 2 / Design the proper instrumentation and Sketch the P&ID…arrow_forwardThe Gilles & Retzbach model of a distillation column, the system model includes the dynamics of a boiler, is driven by the inputs of steam flow and the flow rate of the vapour side stream, and the measurements are the temperature changes at two different locations along the column. The state space model is given by: x = 0 00 -30.3 0.00012 -6.02 0 0 0 -3.77 00 0 -2.80 0 0 Is the system?: a. unstable b. C. not unstable x+ 6.15 0 0 0 0 3.04 0 0.052 not asymptotically stable d. asymptotically stable -1 u y = 0 0 0 0 -7.3 0 0 -25.0 Xarrow_forward
- 11. Consider a system that can be modeled as shown. The input x in (t) is a prescribed motion at the right end of spring k 2. Find X(s) the system transfer function Xeq(s)* m k₂ ww Xin The values of the parameters are m= 30 kg, k ₁=700 N/m, k 2= 1300 N/m, and b=200 N- s/m. Write a MATLAB script file that: (a) calculates the natural frequency, damping ratio, and damped natural frequency for the system; and (b) uses the impulse command to find and plot the response of the system to a unit impulse input.arrow_forwardYou are the mechatronics engineer of a manufacturing plant. You decide to perform an analysis on a robot arm of the assembly line with the objective of optimizing its performance. After taking several readings of the speed of the arm’s end effector, you approximate its velocity to the function given below. v(t) = -t4 + 5t3 - 7t2 + 3t + 0.22 0 =< t =< 3 where the velocity is in ms-1 d) Knowing that the distance travelled by an object is the area under its velocity-time graph, determine the distance travelled by the end effector on the interval 0 =< t =< 1 by using the mid-ordinate rule. Simpson’s rule correct to 3 decimal places using four intervals. e) Calculate the same distance as in (d) above by using the appropriate definite integral. f) Compare the distances you calculated in (d) and (e) above and comment on the accuracy of the two methods you used in (d)arrow_forwardYou are the mechatronics engineer of a manufacturing plant. You decide to perform an analysis on a robot arm of the assembly line with the objective of optimizing its performance. After taking several readings of the speed of the arm’s end effector, you approximate its velocity to the function given below. v(t) = -t4 + 5t3 - 7t2 + 3t + 0.22 0 =< t =< 3 where the velocity is in ms-1 Use your knowledge of differentiation to sketch the velocity-time graph, clearly marking the critical points. Using the graph sketched in (a) above, estimate the velocity when t = 1.5 s Calculate the velocity of the function when t = 1.5 s by substituting to the velocity function. Compare this value to the value you estimated in b above.arrow_forward
- Draw by hand the Bode plot of the following systems. 1. 50 G(s) : s(s² + 4s + 8) 2. 20(s + 1) s(s² + 2s + 10)(s + 5) G(s) =arrow_forwardQ3) Represent the rotational mechanical system shown below in state space representation (matrix form) where 10 6, (t) is the output. Use four state variables 10T 02 100 Kg-m 100 Kо-m 100N-m sec/rad 100 N-m/radarrow_forwardAs the control engineer on a project you are given the following information: a) The free body diagram representation of a mechanical system with the various values for the damper, spring and mass. The transfer function for the system is also provided. 28 N/m -x(1) 1 G(s): - f(1) s? +s+5.6 5 kg 5 N-s/m b) The step response plot for the system. Step Response 0.14 0.12 0.1 0.08 0.06 0.04 0.02 10 Time (sec) Your task is to analyse the system and to confirm that the diagram is for the system in a) i.e. calculate all time responses and compare your answers with the data in the graph. apnaduarrow_forward
- 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_forward2- Using Matlab, what are the step response curves of the closed-loop system, as shown in fig.1. the feedback represents the second-order dynamic system. (fill in the following table) For=0.4 Wn 1 3 6 9 10 R(S) 0.1 0.3 0.6 0.9 1 For w 5 rad/sec 3 Settling time Peak response 2 Wn s(s+23wn) Settling time Peak response C(s) Discuss the follow Which parameters or w occur on the rise time of the response? Which parameter increases the speed of response? Which parameters can be decreases the response amplitude? Which parameter decreases the steady error state? fig.2arrow_forwardll中国联通 4G 1:41 PM week 2 3. 简答题 2.10 c P2.10 By block diagram deduction find the transfer functions of following systems. G2 R GI (c) 输入答案arrow_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY