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1 year ago

a) find the state-space representation of the system. b) is the system controllable? why? c) is the system observable? why

1 answer:

5 0

If a controlled input can transfer (alter) the control system's initial states to some other desired states in a finite amount of time, the control system is said to be controllable.

Using Kalman's test, we can determine whether a control system is controllable. The evolution model for the state variables (time-varying unknowns) and the observation model, which connects the observations to the state variables, make up the state space representation of a dynamical system. The capacity to move a system about in its full configuration space using just specific permitted actions is generally referred to as controllability. The precise definition changes slightly depending on the model type or framework used.

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An insulated, vertical piston-cylinder device initially contains 10kg of water, 6kg of which is in the vapor phase. The mass of

Alexeev081 [22]

Answer:

a)120C

b)29kg

Explanation:

Hello!

To solve this exercise follow the steps below

1. we will call 1 the initial state, 2 the steam that enters and 3 the final state

2. We find the quality of the initial state, dividing the mass of steam by the total mass.

$q1=\frac{6kg}{10kg} =0.6$

3 Find the internal energy in the three states using thermodynamic tables

note:Through laboratory tests, thermodynamic tables were developed, these allow to know all the thermodynamic properties of a substance (entropy, enthalpy, pressure, specific volume, internal energy etc ..)

through prior knowledge of two other properties such as pressure and temperature.

u1=IntEnergy(Water;x=0,6(quality);P=200kPa) =1719KJ/kg

u2=IntEnergy(Water;t=350;P=5000kPa) =2808KJ/kg

u3=IntEnergy(Water;x=1;P=200kPa) =2529KJ/kg

4. use the internal energy and pressure to find the temperature in state 3, using thermodynamic tables

T3=Temperature(Water;P=200kPa;u=u3=2529KJ/kg)=120C

5. Use the first law of thermodynamics in the system, it states that the initial energy in a system must be equal to the final

m1u1+m2u2=(m1+m2)u3

where

m1=inital mass=10kg

m2=the mass of the steam that has entered.

solve for m2

(m1)(u1-u3)=(m2)(u3)-(m2)(u2)

$m2=m1\frac{u1-u3}{u3-u2} =10\frac{1719-2529}{2529-2808} =29kg$

7 0

3 years ago

A two-dimensional flow field described by

Oduvanchick [21]

Answer:

the answer is

Explanation:

<h2> We now focus on purely two-dimensional flows, in which the velocity takes the form </h2><h2>u(x, y, t) = u(x, y, t)i + v(x, y, t)j. (2.1) </h2><h2>With the velocity given by (2.1), the vorticity takes the form </h2><h2>ω = ∇ × u = </h2><h2> </h2><h2>∂v </h2><h2>∂x − </h2><h2>∂u </h2><h2>∂y </h2><h2>k. (2.2) </h2><h2>We assume throughout that the flow is irrotational, i.e. that ∇ × u ≡ 0 and hence </h2><h2>∂v </h2><h2>∂x − </h2><h2>∂u </h2><h2>∂y = 0. (2.3) </h2><h2>We have already shown in Section 1 that this condition implies the existence of a velocity </h2><h2>potential φ such that u ≡ ∇φ, that is </h2><h2>u = </h2><h2>∂φ </h2><h2>∂x, v = </h2><h2>∂φ </h2><h2>∂y . (2.4) </h2><h2>We also recall the definition of φ as </h2><h2>φ(x, y, t) = φ0(t) + Z x </h2><h2>0 </h2><h2>u · dx = φ0(t) + Z x </h2><h2>0 </h2><h2>(u dx + v dy), (2.5) </h2><h2>where the scalar function φ0(t) is arbitrary, and the value of φ(x, y, t) is independent </h2><h2>of the integration path chosen to join the origin 0 to the point x = (x, y). This fact is </h2><h2>even easier to establish when we restrict our attention to two dimensions. If we consider </h2><h2>two alternative paths, whose union forms a simple closed contour C in the (x, y)-plane, </h2><h2>Green’s Theorem implies that </h2><h2> </h2><h2> </h2><h2> </h2><h2> </h2><h2> </h2><h2></h2><h2></h2>

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3 years ago

When is a handrail required for stairs?

Leviafan [203]

Answer:

after 8 stepshddnffuddbnggkbdbkloyr

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3 years ago

The National Park Service is waiting on your recommendation.

maksim [4K]

The hypothesis that would help restore equilibrium is reintroduce wolves in the park or into the forest.

<h3>What is reintroduce?</h3>

To reintroduce, is a term that means to revive, reinstate, or bring back something.

Note that based on the right recommendation needed by National Park Service, one can say that the best hypothesis that would help restore equilibrium is reintroduce wolves in the park or into the forest as it will help restore balance.

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8 0

2 years ago

You are designing a system for a real-time application in which specific deadlines must be met. Finishing the computation faster

makvit [3.9K]

Answer / Explanation:

To proper understand the answers that is given to the question, we need to understand some basic terms that has been used in the question.

Energy: This can be refereed to as the quantitative property that is transferred to an object for the purpose of the object working or to heat up the object. It can also be referred to as conserved quantity that is energy can be converted from one form or state to another but cannot destroyed.

Power: This can be defined as the rate of doing work or transferring heat per unit time from one state to another. The SI Units of power is watt which is equal to one joule per second.

Hence, the formula that links energy and power is:

Energy = Power x Time

Now. referring back to the question (a) asking how much energy do we save if we execute at the current speed and turn off the system when the computation is complete: The answer is = 50%. That is 50% of the energy is saved.

(b) If we recall the formula for calculating energy,

we have:

Energy = 1 /2 Load x V²

Changing the frequency does not affect the energy.However, it affects the power.

So therefore, the new energy is 1 / 2 Load x ( 1/2 V)² ,

reducing it to about 1 /4 of the old energy.

6 0

3 years ago