Homework Set 4

3. 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…

As 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. apnadu

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.

Please help me solve no. 2 below. Please provide a clear and readable solution. Thanks in advance!!! The course subject is Feedback and Control System. NOTE: The lesson is ROTATIONAL MECHANICAL SYSTEMS.

Please solve this question in mechatronics

SUBJECT: Feedback & Control Systems

Feedback & Control Systems State-Space Representation Write the state-space representation of the system below. Let the output of the mechanical system is x3 (t). 1 N-s/m x₁ (t) M3 = 1kg 1 N/m М1 -0000 1kg > X3 (t) 1 N-s/m 1 N/m oooo x₂ (t) M₂ 1kg 4 1 N-s/m² -1 N-s/m →f(t)

Rotational Mechanical System: Find the transfer function for each rotational mechanicalnetwork shown below.

Mechanical Control Engg.

solve, show solution and show matlab code for part b, vibrations

answer completely please

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.

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): 1. What is the order of this system?

The 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 X

Please solve the following WITHOUT the use of AI. Do not run the prompt through chatgpt. Using MATLAB for the required question, solve the problems. Thank you!

Please solve this exercise found in NISE, control engineering book. Please solve this using the translational mechanical system transfer fucntion method and kindly explain as well since this is an exercise to master the topic. Thank you very much!

Consider a cruise control system shown in Figure 1. Where f is the engine force, v is the velocity, fb is the friction force, and fb  = bv. Requirements: Assuming M = 2000 kg, b = 80Nsec/m, and f = 600 N: Find the transfer function of the system.

>> impulse (sys) For lab. requirements 1- 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 2 wn² s(s+23wn) Rise time Settling time Peak response C(s) Steady state Rise time Settling time Peak response Steady state fig.1

Solve this block dighrim steps  and steps

Find the Inverse Kinematic model of manipulator in Fig.1 by Graphical method.

MODELLING AND CONTROL OF SYSTEM

Control Engineering

A A flexible support system is shown (Fig. 2), For the given system, 2.1 Find the following: 2.1.1 Mathematical model 2.1.2 Transfer function matrix. 2.2 Classify the system according to: inputs/outputs and system order. 2 3 elle M₂ M₁ f(0) elle NT D₁

PLease solve the following without the use of AI. Thank You!

You 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.

You 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)

Please solve Fast i give good feedback and upvote.

Please don't provide handwritten solution.