MrYouMath
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3 answers
3 votes
157 views
Determining the transfer function of cruise control given characteristic equations
1 votes

If you take the Laplace transform of the system you obtain: $$msV_0(s)+FV_0(s)=U(s)$$ $$U(s)=K\left[V_0(s)-V_\text{r}(s) \right]$$ Plug the second equation into the first equation and solve for $...

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1 answers
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108 views
Why do we use linear transformation of states in linear control technique
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2 votes

The examples in which it is useful are already given in your PDF file. The first reason is modal decomposition (use $x=Vz$, in which $V$ is the matrix containing the eigenvectors of the matrix $A$). ...

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2 answers
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79 views
How to solve system's general stability from transfer function?
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You did answer both questions correctly. You could also consider solving the both questions by using the Hurwitz criterion. The first one is directly solvable with the Hurwitz criterion the second one ...

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1 answers
1 votes
433 views
An Argument from Kelvin’s Circulation Theorem
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Normally you would apply Kelvin's circulation theorem on the whole system such that everything that is important is enclosed by the contour for all times $t$ (note, that the author also expanded the ...

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1 answers
1 votes
282 views
Proving Kelvin’s Circulation theorem
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1 votes

The circulation is given by $$\Gamma = \oint_{C(t)}\boldsymbol{u}d\boldsymbol{r}.$$ Now, take the material derivative of this expression (remember to use the product rule because our contour is time-...

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1 answers
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499 views
Block Diagram using Integrator (Linear Systems Theory - Hespanha)
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You can use the following block diagram. Note that your $\boldsymbol{D}=\boldsymbol{0}$. If you really want to have all the states you could draw it like the following picture. You can neglect all ...

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2 answers
4 votes
75 views
How to determine the region in a state plane where the equilibrium state is asymptotically stable
4 votes

As you might already know your system is nonlinear, which means that it is not trivial at all. See below for the plot of the system. The linearization around $(0,0)$ gives you the information that the ...

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2 answers
1 votes
182 views
Does the order of the states in a state vector matter?
3 votes

A linear state space model is given by $$\dot{\mathbf{x}}=\mathbf{A}\mathbf{x}+\mathbf{B}\mathbf{u},$$ in which $\mathbf{x}=[x_1,x_2,\ldots,x_n]^T$. The reason why we write it in matrix notation is ...

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1 answers
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2k views
Control Systems: Why is this system unstable?
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2 votes

Your system is open loop stable as the poles are at $s=-1$, $s=-3$ and $s=0$. Note, that if the order of the pole at $s=0$ is greater then 1, then the open loop system is also unstable. But closing ...

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3 answers
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91 views
Graphene distribution over a sphere
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2 votes

The volume $V$ needed to cover the surface is equal to the spherical shell volume with $d_{\text{inner}}=5 \text{ inch}=0.127\text{ m}$ and $d_{\text{outer}}=d_{\text{inner}}+2\cdot 35 \cdot 10^{-9}\...

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2 answers
1 votes
152 views
Can buckling failure at the first critical load be avoided by "instantaneous" loading?
1 votes

Euler's buckling is the behavior of static loads and not time-dependent loads. You would need to look at nonstatic beam deflections but I doubt that instantaneous loading will prevent buckling. In ...

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1 answers
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75 views
Using electromagnetic induction to fire a neuron
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Your goal is to move the electrons in a neuron with a magnetic field. If we assume a homogeneous magnetic field $\mathbf{B}$, then this will generate an electrodynamic force $$\mathbf{F}=q\mathbf{v}\...

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3 answers
1 votes
1k views
Equation for finding the thickness of material required for tubes under radial stress
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Assuming a very long cylinder (to neglect effects at the top and bottom of the cylinder) with a small wall thickness $t$ (to assume that the stress is constant across the thickness of the wall) and ...

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1 answers
1 votes
177 views
Two angular velocities on two segments connected by a hinge joint differ only by the joint angle velocity
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0 votes

What is the joint angle velocity? The joint angle velocity is the angular velocity of you joint, because we are acutally dealing with a 2D problem. This will become clear if you look at your ...

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3 answers
13 votes
1k views
Does good electrical conductivity imply good thermal conductivity?
11 votes

Beryllium oxide is a very good electrical insulator but at the same time the best non-metal (except diamond) thermal conductor. So to summarize. In general, good thermal conductivity is correlated ...

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1 answers
2 votes
50 views
Acoustic transmission through houseboat hulls
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As @SolarMike pointed out the acoustic waves might harm the fish because the sonic speed in water is approximate $1484 \frac{\text{m}}{\text{s}}$ (at $20° \text{ C}$), this is quite high compared to ...

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2 answers
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Center line of cut-off periodic signal
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The problem that you describe comes from the fact that you calculating the average of the vector with numerical values. In order to calculate the exact mean of $\sin(x)$ or other functions, you should ...

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2 answers
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2k views
Transfer Function of Spring-Damper System
2 votes

First, create the free body diagram for this system. If you cut through the spring $k_1$ and the damper $b_1$ you will get two forces $F_{k_1}=k_1(x_i-x_0)$ and $F_{b_1}=b_1(\dot{x}_i-\dot{x}_0)$ ...

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3 answers
1 votes
280 views
How can a car can be lifted using hydraulic press?(Pascal's Law)
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The main idea of the hydraulic press is that we use a piston for which we have to apply a small force $F_1$ and small area $A_1$ to displace a specific volume of the incompressible fluid. Imagine we ...

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1 answers
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5k views
How to calculate the power/torque/force needed to move a 4 wheeled vehicle?
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3 votes

The force required $F_{\text{r}}$ for driving a wheeled vehicle with mass $m$ is given the following formula (I will neglect slip): $$F_{\text{r}}=F_{\text{tire}}+F_{\text{aero}}+F_{\text{acc.}}+F_{\...

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1 answers
1 votes
139 views
Find transfer function from step response and root locus?
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I think you did mix this up with proportional feedback. The transfer function is given by $$G(s)=K\frac{(s+5)(s-4)}{(s+10)(s+6)(s+3)},$$ in which $K$ is a parameter that needs to be determined. ...

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1 answers
1 votes
54 views
Why does secondary flow occur?
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Secondary flow can result from obstacles, viscosity effects and because of changes in the size and orientation of the cross section. In general these causes lead to nonvanishing convective terms in ...

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1 answers
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433 views
What is the best resolution obtainable by ultrasonic non destructive testing?
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The resolution depends on the material you are using and the frequency $f$ applied. An approximation for the resolution is given by half of the wavelength $$\lambda = \frac{c}{f}.$$ The sonic speed $...

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1 answers
2 votes
79 views
is a cylindrical pylon just as sturdy as a cubical one of the same volume?
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3 votes

I assume that both pylons are composed of the same material. If you have a cylindrical pylon with height $h$ and volume $V$ then the radius can be calculated by $V = hA_{\text{base}} =h\pi r^2 \...

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1 answers
4 votes
365 views
Otto Cycle Efficiency
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According to my reference book on thermodynamics, the efficiency is given by: $$\eta = 1-\frac{1}{\varepsilon^{\varkappa-1}}.$$ The heat capacity ratio is given by $\varkappa$ and $\varepsilon$ is ...

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2 answers
4 votes
675 views
Medieval wooden screw press tonnage
1 votes

I can only try to give you an approximate answer. The principle is simple. We give rotational energy $E_{\text{rot}}$ into the system and we get axial force $F_{\text{ax}}$ times displacement $\Delta ...

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7 answers
2 votes
4k views
What is the opposite of "parallel" in engineering?
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In general, we can distinguish four cases. Case: parallel --> If you take the curvature into account, the pillars cannot be treated as parallel. While I would guess that the error is pretty small on ...

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1 answers
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273 views
Pressure distribution on an inclined plate
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This task is not trivial at all. In order to get a crude estimate of the pressure distribution, we will assume inviscid flow. The flow is separated by a streamline in the middle (red line in the ...

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3 answers
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103 views
Will water level of remain level between two points
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This is answering the second part of your question to get a mathematical relationship for the parameters that are involved. We write down the continuity equation in integral form. $$\int_{V}\dfrac{\...

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3 answers
7 votes
13k views
Force required to empty a syringe
-1 votes

You could try to analyze this problem with doing very complicated fluid dynamics analytically or numerically. The problem is nonstationary and the convective terms do not vanish, hence very difficult ...

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