The Johnson & Royce model of a distillation column is driven by the inputs of steam flow and itsflow rate; the output measurement is the temperature change. The state-space model is given by:-2x = [¯²¯¯¯7 | x + | | | u; y = [0_1]x-the system defining the model of the distillation column isa. Asymptotically stableO b. UnstableOc. Marginally stableOd. Indeterminate in relation to its stability

Step 1: By expanding the determinant, (−2−λ)(−λ)−(−7)(1)=0λ2+2λ+7=0 Step 2: Use the quadratic…

Answered: The Johnson & Royce model of a…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Get representation in State Variables
The van der Waals (vdW) equation is a cubic equation of state (CEOS) which may be used to calculate the volume or pressure conditions for a real gas: P= a = RT a v-b v² Here, v represents the molar volume of the gas, and P, R, and T' are the absolute pressure, ideal gas constant, and absolute temperature of the gas, respectively. The values a and b are component dependent an may be calculated using: 27 R²T² 64 P C and b= 1 RT 8 Pc So, when both the critical pressure (Pc) and critical temperature (Tc) are known, one can apply the vdW CEOS to give a more accurate calculate more accurate properties than the ideal gas law. One must be careful to use absolute values for the pressure & temperature (e.g., unit of K not °C) and a value for the gas constant that is consistent with the unit desired (such as R = 0.0083144598 L·bar/K·mol) Do the following: a) Calculate the molar volume (L/mol) of nitrogen gas (Pc = 33.96 bar, Tc = 126.19 K) at 5 bar and 30°C using both the ideal gas law & using…
1. Reduce the following differential equation to the state space equation form. a. y" (t) + 3y' (t) + 2y (t) = u(t) b. y" (t) = u(t) — b₁y' (t) — boy (t) c. 4y" (t) cos (t) y' (t) + sin (t) y (t) = u(t)
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1 Problem You are given the following data (below) showing the steady-state output response, x(t), of a mass-spring-damper (stable, LTI) system to a sinusoidal input u(t) = A sin(wt). This snapshot is the response after all the transients have decayed (the time is shifted to start at zero for conve- nience). x 0.5225 Displacement pu(t) Sinusoidal force input x 0.1041 1.5 1 Y2 х 0.2783 Y1.372 0.5 h ok -0.5- -1 -1.5 x(t) M Assume: bl u(t) x(t) Horizontal Plane (no gravity) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Time (sec) www k Using only the data provided above (the blue line is the input u(t) and the red line is the output x(t)), determine: 1. The frequency of the input in rad/s 2. The amplitude of the input, A 3. The frequency of the output in rad/s 4. The output-input ratio |G(iw)| = max(x(t)) max(u(t))' at the particular input frequency shown. 5. The phase (also called phase lag) of the output, $, at the particular input frequency shown in degrees. Note the phase is generally…
Fill in the Blank Question: Simulations that have time derivative terms in their governing equations are considered to be _________ in nature?
(2) A mechanical system is modeled by the system of ODE's. For this system choose [x₂] [y] -0-0 = X3 18 2 consider the output to be y, and do the following: Determine the state-space matrices A, B, and C ● Determine the characteristic equation mÿ+k₁y+k₂(y−z)=F c₂ż−k₂(y-z)=0
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If a system, * + 10x + 21x = 4f(t) is converted into a state-space model, what would be the state (A), input (B), and output (C) matrices? [where input = f (t) and output = x(t)] %3D A) A = | [-21 l, B = | and C = [0 1] В -10 1 B) A = 21 ol, B = and C = [1 0] %3D C) A = = Al and C = [1 0] В %3D -21 D) None of the above
In this problem, you will have to first create a Python function called twobody_dynamics_first_order_EoMS. Given a time t and a state vector X, this function will return the derivatives of the state vector. Mathematically, this means you are computing X using some dynamics equation X = f(t, X). Once you have this function in Python, you can solve the differential equations it contains by using solve_ivp. The command will be similar to, but not necessarily exactly, what is shown below: solve_ivp(simple_pendulum_first_order_EoMS, t_span, initial_conditions, args=constants, rtol 1e-8, atol 1e-8) which integrates the differential equations of motion to give us solutions to the states (i.e., position and velocity of a satellite). In the above, t_span contains the initial time to and final time tƒ and it will compute the solution at every instant of time (you will define this later in Problem 1.3 below). The integration is done with initial state vector Xo which defines the initial position…
1) Obtain a state space model of the system. 2) Given m =1 kg, k = 1 N/m and b = 1 N.s/m is the system Controllable? 3) For what values of k,m,b the system is stable? Explain your answer?
3. Consider the mechanical system shown in Fig. 3. Let V3(t) be the input and the acceleration of the mass be the output. Derive the state equations and the output equation using linear graphs and normal trees. V,(t) В m k2 101 k, Figure 3: A mechanical system with an across-variable source

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