A linearized model for the water level in a system of two interconnected water tanks is 2 * = [ -1 -²] * + [i] * x u 0-2 a) Find the transfer function for the system with input u when the output, y, is the level of water in the lower tank. [Hint: you should be able to decide which state that represents the level in the lower tank from the dynamic equations.] b) Assume that we wish to control the level of water in the lower tank with a proportional controller U(s) = K (R(s) - Y(s)). What K> 0 will result in oscillations following a step response? c) What will be the period of the oscillations when K = 5? d) We now set K = 2 and assume that initially the system is at rest with x₁(0) = x₂(0) = 0. What is the maximal size of a step (i.e. r(t) = al(t) where 1 is the heaviside function) that we can make without water spilling from the lower tank which has a capacity to hold 1 unit of water? (We assume that the upper tank has unlimited capacity.)

A linearized model for the water level in a system of two interconnected water tanks is 2 * = [ -1 -²] * + [i] * x u 0-2 a) Find the transfer function for the system with input u when the output, y, is the level of water in the lower tank. [Hint: you should be able to decide which state that represents the level in the lower tank from the dynamic equations.] b) Assume that we wish to control the level of water in the lower tank with a proportional controller U(s) = K (R(s) - Y(s)). What K> 0 will result in oscillations following a step response? c) What will be the period of the oscillations when K = 5? d) We now set K = 2 and assume that initially the system is at rest with x₁(0) = x₂(0) = 0. What is the maximal size of a step (i.e. r(t) = al(t) where 1 is the heaviside function) that we can make without water spilling from the lower tank which has a capacity to hold 1 unit of water? (We assume that the upper tank has unlimited capacity.)

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter4: Numerical Analysis Of Heat Conduction

Section: Chapter Questions

Problem 4.6P

See similar textbooks

Similar questions

A proposed hypersonic plane would climb to 100,000 feet, fly 3800 miles per hour, and crossthe Pacific in 2 hours. Control of the aircraft speed could be represented by the model in Figure.Find the sensitivity of the closed-loop transfer function T(s) to a small change in the parameter
A liquid storage system is shown below. The normal oper-ating conditions are q1=10 ft3∕min,q2=5ft3∕min,h=4ft.The tank is 6 ft in diameter, and the density of each stream is 60 lb/ft3. Suppose that a pulse change in q1 occurs as shown inFig.(a)What is the transfer function relating H′ to Q′1?(b)Derive an expression for h(t) for this input change.(c)What is the new steady-state value of liquid level h?(d)Repeat (b) and (c) for a change in q1 from 10 to 20 (at t=0) to 15 ft3/min at t=12
Figure 1 shows an electrical system comprising a series RLC circuit and input voltagesource ein(t).(a) Derive the input-output equation with output y = I and input u = ein(t). (b) Using the derived input-output equation, drive the system transfer function G(s)that relates output to input. Use the following numerical values for the electrical systemparameters: resistance R = 2Ω, inductance L = 0.25H, and capacitance C = 0.4F. (c) Using the derived transfer function, derive the time-domain ordinary differentialequation for the input-output equation of this electrical system. (d) Draw the complete block diagram of this series RLC circuit using the derived transferfunction.
Can you solve this without the transformation matrix and if thtas not possible explain what they do. Also can you explain why you need to change from the J2000 state to geocentric equatorial frame. also would this code work to solve the problem?: % Step 1: Define the initial state vector at burnout r0 = [5210.345121, -549.481941, 4300.883291]; % Position vector [km] v0 = [-1.451280 7.391098 2.690198]; % Velocity vector [km/s] % Step 2: Calculate the initial velocity magnitude and specific angular momentum v0_mag = norm(v0); % Initial velocity magnitude [km/s] h0 = cross(r0, v0); % Specific angular momentum vector [km^2/s] h0_mag =…
MATLAB PROBLEM
1) (Derive equation of motion for a givensystem.) 2)(Obtain transfer function. Find the state space model of the system in the format given below.) (Format shared as pictures.)
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?
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)If the system has a transfer function of the form G_P (s)=H(s)/(V_m (s) )=μ/(1+Ts) where µ is the gain and T is the time constant, calculate values for µ and T for the case where the valve is at position 3. Hints: Use the constants and information in table 1. The dynamics of the water tank can be found by applying the continuity equation: qin - qout = rate of change in water tank
root locus electrical engineering Don't overthink and reject. Complete the solution as per the given transfer function. No need of quadratic equation just simplify for the exact given transfer function.
For 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.
The ratio of output to input of a system in Laplace domain is known as Transfer function . Select one: True False