Process Dynamics and Control-pages-14

4. For the fluid system in Fig 6 construct the linear graph, identify the state variables, and derive the state equations. The output variables are the pressure p₁ and på at the tanks. C₁ Aut I,R 0,01) - Figure 6: An fluid system R₂ V (t) ww Rs ERL L V (1) Figure 7: A tuning circuit for radio

The governing equation of motion for a base motion system is given by (assume the units are Newton) mä(t)+ci(t)+kx(t) =cY@, cos(@,t) +kY sin(@t) %3D Given that m = 180 kg, c = 30 kg/s, Y = 0.02 m, and о, — 3.5 rad/s %3| 1. Use Excel or Matlab to find the largest value of the stiffness, k that makes the transmissibility ratio less than 0.85 2. Using the value of the stiffness obtained in part (1), determine the transmitted force to the base motion system using Matlab or Excel. 3. Display and discuss your results.

lail - Ahmed Amro Hussein Ali A x n Course: EN7919-Thermodynamic x Homework Problerns(First Law)_S x noodle/pluginfile.php/168549/mod_resource/content/1/Homework%20Problems%28First%20Law%29_SOLUTIONS.pdf UTIONS.pdf 4 / 4 100% Problem-4: When a system is taken from a state-a to a state-b, the figure along path a-c-b, 84 kJ of heat flow into the system, and the system does 32 kJ of work. (i) How much will the heat that flows into the system along the path a-d-b be, if the work done is 10.5 kJ? (Answer: 62.5 kJ) (ii) When the system is returned from b to a along the curved path, the work done on the system is 21 kJ. Does the system absorb or liberate heat, and how much? (Answer:-73 k]) (iii) If Ua = 0 andU, = 42kJ , find the heat absorbed in the processes ad and db. (Answer: 52.5 kJ, 10 kJ)

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1. The following diagram shows a model of a river. a. Give a dynamic systems model for h1, hz and h3 (does not need to be in state-variable matrix form). The system inputs are qmi and qm2. b. In steady state, what is the flow out of the tank on the right? Use the following values: qm1 = qm2 = 20 kg/s, A1 = Az=1 m², p = 1 kg / m³, r = 1, R = 1 / m-s; use g = 10 m/s². [Hint: This can be solved without much work. Don't spend too much time on this part.] Im2 Iml A R | A2 R R

Please provide steps on how to derive the output of each container.

hey can i get help with these two questions please. thank you.

Here I'm finding final kinetic energy KE2, given initial kinetic energy, initial force, alpha N/m^3 and beta N representing F(x). I integrated F(x)dx though I'm not sure how to integrate Fo with respect to X. I tried just finding the integrand ouput of 7.5x10^4m and subtracting the initial force, since the initial force would count as x=0, or I assumed. I then followed the regular approach of adding over the initial KE1 to isolate the unknown KE2 which I keeo getting as 1.07x10^10 which seems to be off. Again, I suspect where I'm going wrong is integrating the initial force -3.5x10^6N with respect to x, but other than what I've already done, that doesn't make sense to me.

Q3) 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/rad

Telecommunications 3.- Find and graph the first derivative for the

Pls help with Dynamics Homework

The equation of motion of a simplified model mechanical system is given below. of a m, o X₁ ki+k₂ k₂ O +1 NA 1/2 FU 10 ma -k₂ k₂ | k₂ = 10,000 N m₁ = 40 kg / m₂ = 130 kg, k₁ = 20,000~ m 0 a) Natural Freequency b) Find the mass normalized mode shapes of the system. c) Drave the mass normalized mode shapes.

1 An object of mass 125 kg is released from rest from a boat into the water and allowed to sink. While gravity is pulling the object down, a buoyancy force of times the weight of the object is pushing the object up (weight = mg). If we assume that water 40 resistance exerts a force on the object that is proportional to the velocity of the object, with proportionality constant 10 N-sec/m, find the equation of motion of the object. After how many seconds will the velocity of the object be 90 m/sec? Assume that the acceleration due to gravity is 9.81 m/ sec2. Find the equation of motion of the object. X(t) = %3D

'p' (liquid density 'A' (tank cross sectional area) Qin' (Input Flow Rate) P 'R' (restriction coefficient) dh Qin = A + dt '' (head of liquid) Figure 1 The single tank system (Figure 1) has been modelled by the first order differential equation given as equation. The equation describes the relationship between the input flow rate entering the tank and the head of liquid in the tank. Pi R h 5 m equation + The following constants are provided: R = 40 Kpa s m², 4 = 10 m², p= 1001 kg m², and g = 9.81 m s A pump is suddenly switched on and provides a step input flow rate of 0.5 m³s¹¹. (1) Using Laplace Transforms, solve equation and provide an expression to show how the level in the tank will vary in time after the step input has been applied. (ii) Build a Simulink model and validate the results from Part 1 (i).

'p' (liquid density 'A' (tank cross sectional area) 'Qin' (Input Flow Rate) "Que P 'R' (restriction coefficient) '' (head of liquid) dh Qin = A + dt Figure 1 The single tank system (Figure 1) has been modelled by the first order differential equation given as equation. The equation describes the relationship between the input flow rate entering the tank and the head of liquid in the tank. ph R 5 m equation The following constants are provided: R = 40 Kpa s m², 4 = 10 m², p= 1001 kg m², and g = 9.81 m s A pump is suddenly switched on and provides a step input flow rate of 0.5 m³s¹. (1) Using Laplace Transforms, solve equation and provide an expression to show how the level in the tank will vary in time after the step input has been applied.

Modeling in states space a) Find the equations over time and define state variables b) State modeling matrices

H2: What actually happens in a cylinder in an internal combustion engine? Your input : Number of carbon atoms in a molecule of the fuel, x: 5 Amount of fuel added, m br : 45 mg The temperature after compression, t,: 320 ° C Calculate : The mass of clean air in the cylinder, mair : Number (g) Amount of heat supplied during combustion, Q, : Number (J) Average molecular weight after combustion, M m: Number (kg/kmol) The temperature after combustion, t: Number (°C) NOTE : Use the point as a decimal separator and the units that appear after the answer boxes! The maximum permissible error in the answers is + 0.5% except for M m where the maximum permissible error is + 0.1%.

Q 6(a) Find the linearized incremental state-variable model for the system shown in Figure 8. Use the linearized pump relationship Wp = Wp - (P₂ - P₁) Note that w(t) Pa C₁ P₁ Wo Wp P2 - Pa Figure 8 Pa C₂ P2 R Wor Pa

1 Overview In this project, you'll use several robot datasets for estimation and you will implement a Kalman Filter (KF) for state estimation. Consider the vehicle depicted in Fig. 1 with m = 0.5, k = 3.5, b = 2. The position s and velocity v represent the state x of the system and the input ƒ (t) is the force often denoted with u. F b m Figure 1: Robot cart 0 s(t) f(t) 1. Write the system in state space form and consider additive Gaussian white noise to the model n N (0, Q). Discretize the system state space form using Euler approach (30 points).

Please show steps

k₁ B₁ Fs(t) ww k2 12 m B2 Figure 4: A translational system 2. Consider a translational system shown in Fig. 4. Answer the following questions. (a) Draw a linear graph and write down all the elemental equations. (Don't draw the normal tree yet.) (b) From the elemental equation you write down, identify three variables that can potentially serve as state variables and explain why. (c) Are these potential state variables independent of each other? If not, use either conti- nuity or compatibility equation to prove it. How would you choose your state variables? (d) Draw a normal tree to see if there is any dependent energy storage element. What are the state variables according to your normal tree? Are they consistent with the explanation in the Part (c)?

For the model defined in Question 1, is the closed loop system with the negative feedback control law? 0 0 0 ;]* X 0 u=-Kx= O a. O b. O c. unstable 0 1 0 asymptotically stable not unstable O d. not asymptotically stable

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

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Manufacturing process with two variables x1,x2 described by the empirical model:   y=bo +b1 x1 + b2 x2 + b12 x1 x2 + b3 (x1)^2 +b4  (x2)^2    please refere to the image attached

Simulink Assignment- Filling a Tank In fluid mechanics, the equation that models the fluid level in a tank is: dh 1 -(min Ap - mout) dt h is the water level of the tank A is the surface area of the bottom of the tank pis the density of the fluid Mim and mout are the mass flow rates of water in and out of the tank, the flow out is a function of the water level h: 1 mout Vpgh Ris the resistance at the exit. Assume that the exit is at the bottom of the tank. g is the gravitational acceleration What to Do: 1. Build a model in Simulink to calculate the water level, h, as a function of time. Your model should stop running as soon as the tank is full. 2. Assuming the height of the tank is 2 meters, after how many seconds does the tank fill up? Use the following constants to test your model: • A: area of the bottom of the tank = 1 m? • p: the density of fluid = 1000 kg/ m? • R: the resistance at the exit = 3 (kg.m)-1/2 • ho: Initial height of the fluid in the tank = 0 m • g: the gravitational…

An object attached to a spring undergoes simple harmonic motion modeled by the differential equation d²x = 0 where x (t) is the displacement of the mass (relative to equilibrium) at time t, m is the mass of the object, and k is the spring constant. A mass of 3 kilograms stretches the spring 0.2 meters. dt² Use this information to find the spring constant. (Use g = 9.8 meters/second²) m k = + kx The previous mass is detached from the spring and a mass of 17 kilograms is attached. This mass is displaced 0.45 meters below equilibrium and then launched with an initial velocity of 2 meters/second. Write the equation of motion in the form x(t) = c₁ cos(wt) + c₂ sin(wt). Do not leave unknown constants in your equation. x(t) = Rewrite the equation of motion in the form ä(t) = A sin(wt + ), where 0 ≤ ¢ < 2π. Do not leave unknown constants in your equation. x(t) =

I need help with my MATLAB code. I am trying to propagte 10 different initial state vectors. In the end, I get 1 state matrix. I need to get 10 different state matrices for the 10 different initial state vectors. How do I store each state matrices seperately in MATLAB?   R = 6378.0; %km mu = 398600.4415; %km^3/s^2     r = [7000, 0, 0, 0, 7.5, 0; 7100, 0, 0, 0, 7.6, 0; 7200, 0, 0, 0, 7.4, 0; 7300, 0, 0, 0, 7.3, 0; 7400, 0, 0, 0, 7.2, 0; 7500, 0, 0, 0, 7.1, 0; 7600, 0, 0, 0, 7.0, 0; 7700, 0, 0, 0, 6.9, 0; 7800, 0, 0, 0, 6.8, 0; 7900, 0, 0, 0, 6.7, 0];   % Initialize cell array to store results for each initial state results = cell(size(r, 1), 1);   for i = 1:length(r) % Finding Period T_orbit = 2 * pi * sqrt((norm(r(i, :))^3) / mu); time_span = [0, T_orbit];   state_init = r(i, :);   % Numerical integration using ODE solver options = odeset('RelTol', 1e-12, 'AbsTol', 1e-12); [t, state] = ode45(@(t, state) orbital_dynamics(t, state, mu), time_span, state_init, options);   end       %%…

The attached image is of the Runge-Kutta method. I want to know if there are any errors with the equations. I think I saw an error on k2 equation. It should be k2 = ax0 + h_step/2 * k1, right? Please let me know if there is anything else wrong with it