6
votes
Accepted
Which equations of a state space model influence the poles and zeroes?
Half of your statement is correct: If we are considering the following system:
$$G : \begin{aligned} \dot{x} &= Ax+Bu \\ y &= Cx \end{aligned}$$
then $A$, $B$, and $C$ all influence the zeros ...
- 1,220
6
votes
Accepted
How does load force impact load inertia?
Let's first compute the model. The control design is a separate effort.
The torque applied to the drum is $n T_M $, where n is the gear ratio and $T_M$ is the output produced by the motor. $T_M= K_T ...
- 1,951
5
votes
Accepted
Square wave transfer function?
I thought I would expand a little on the answer offered by Karlo.
Long story short, I would not try to calculate the analytical time response of a system to a square wave. That would be a serious ...
5
votes
Accepted
Determine the range of values for a PI controller
There is a mistake in your expressions. The coefficient of $s$ is $2+k_p$.
The conditions are: $$\frac{1}{3} \left(3 \left(k_p+2\right)-k_i\right)>0$$ $$k_i>0$$ $$k_p>0$$
This simplifies ...
- 1,951
5
votes
What do the zeros of the transfer function tell you about a system?
Zeros are very important when you are looking at how to control a system. A good way to look at this is to examine a root locus plot. There are several rules on how to sketch a root locus, but the ...
- 725
5
votes
Frequency Response of a Discrete System
If you want to evaluate a continues time transfer function at a specific frequency $\omega$ in rad/s you substitute $s$ with $j\,\omega$. For a discrete time transfer function you substitute $z$ with $...
- 1,653
5
votes
Accepted
How do I interpret the following Bode, Nyquist and Nichols diagrams?
Your systems shows extremely close pole-zero cancellation. So much even that it nearly removes 4 poles and zeros. Lets look at why, starting with the Bode plot:
The magnitude plot is constantly ...
- 1,069
4
votes
How does load force impact load inertia?
Stretch in the spring delta $ Y = A.sin(\omega.t) = A.sin\sqrt(k/m) . t $
So the delta Y is not constant but if you are interested in delt Y_max
delta $Y max = m/k$, by Hooks law.
Because your ...
- 22.1k
4
votes
What are the Singular Values of a dynamic system and how are they calculated in the *sigma* function in Matlab?
For a MIMO system $y(s) = G(s)d(s)$, with $m$ inputs and $l$ outputs.
Consider a fixed frequency $\omega$ where $G(j\omega)$ is a constant $l \times m$ complex matrix.
For the sake of simplicity the ...
- 884
4
votes
How can I extract transfer function an unknown nonlinear system?
As I remember (learned it 15 yrs ago) You need to have an experimental data, which will help you to find "linear" sections and the their limits (with taking into account the things like hysteresis), ...
4
votes
Accepted
PI controller for second order system
Step 1: Draw the root locus of the system.
Here you can see the two poles of your plant $G(s)$ (marked with an x), at $p_1=-9$ and $p_2=-1$, the pole of your controller $C(s)$ at $p_c = 0$ and the ...
- 884
4
votes
How do I find the minimum/maximum stable value of scalar gain for a closed loop transfer function?
The forward path of your control diagram consists of the following transfer functions connected in series:
$$ \begin{align*} G(s) &= \frac{s+8}{s^2-2s-3}\rightarrow \text{Plant}\\
K(s) &= K \...
- 1,019
3
votes
Accepted
How to solve system's general stability from transfer function?
I would like to extent the already given answer by MrYouMath.
So question 1 is pretty straight forward and you already got it right. If there's no right half plane (RHP) pole then it doesn't matter ...
- 1,734
3
votes
Accepted
Is lead filter same as PD combined with a low pass filter?
A lead filter implies that the zero has a lower frequency than the pole. While a PD controller with a low-pass-filter does not necessarily imply that order. Also a lead filter (usually) does not have ...
- 1,653
3
votes
Practical examples of LTI transfer function
Why would a linear, time-invariant system require initial conditions to be zero? This is completely incorrect.
A linear, time-invariant system is any system that is linear (no state terms ...
- 3,575
3
votes
Unexpected Results from my Transfer Function
Checking the units is an excellent way to double check your work; kudos for doing so. However, the next step in checking to see if your results make sense is to check limits. In your case, you can ...
- 6,386
3
votes
How to find closed loop transfer function and use it to identify τ and k?
The general form of a transfer function for a first order system is the following:
$$ T(s) = \frac{K}{\tau s+1} $$
where:
$\ K \rightarrow $ DC Gain of the system
$\ \tau \rightarrow $ Time ...
- 1,019
3
votes
Accepted
Help understanding a control system represented by coefficients of theta?
In mathematics,which are very closely related and broadly applied in control engineering, the derivatives with respect to time are often notated using the so-called: dot notation. You can check this ...
- 1,019
3
votes
Accepted
mass-friction-spring system with closed loop
Based on the information you've given, I believe your professor is suggesting that a friction term can be represented as shown in the following block diagram.
The transfer function $G(s)$ relates ...
- 1,220
3
votes
Accepted
How to get a transfer function from this block diagram?
You are going in the right direction! Lets take these two equations:
$$(1) \quad in = \alpha+a_1\alpha z^{-1}+a_2\alpha z^{-2}$$
$$(2) \quad out = b_0\alpha+b_1\alpha z^{-1}+b_2\alpha z^{-2}$$
now ...
- 1,069
2
votes
Practical examples of LTI transfer function
Imagine hitting a pendulum by a hammer with same force and same direction. The pendulum's response will be always same, yesterday, today, tommorow, and 1 year after. It means, between your impact ...
- 354
2
votes
What do the zeros of the transfer function tell you about a system?
I would refer you to "Poles and Zeros of Linear Multivariable Systems: A Survey of the Algebraic, Geometric and Complex Variable Theory", A. G. J. Macfarlane, N. Karcanias for a very detailed analysis ...
- 1,951
2
votes
What do the zeros of the transfer function tell you about a system?
You can think of poles as low pass filters and zeros as high pass filters. They are in some way two sides of the same coin. You can't decide stability solely by looking at poles, any more than ...
- 11.4k
2
votes
How can I calculate the z-transformation of this transfer function of a time-discrete controller?
Observe that $G(s)$ is formed by $$\frac{1}{s^2} \to \frac{1}{(s+1)^2}$$ with the corresponding Z-transform/Laplace pairs $$\frac{1}{s^2} \to \frac{Tz}{(z-1)^2}$$ and $$\frac{1}{s+a} \to \frac{z}{z-e^{...
- 121
2
votes
How can I calculate the z-transformation of this transfer function of a time-discrete controller?
In order to solve it, you have to divide $ G_s(s)$ by s first and then you have it in the form on which you can perform the Z-transform.
- 21
2
votes
Accepted
Closed loop response of a discrete system
The plant and controller:
$$\text{sys}=\frac{4700 s^2+4393 s+3.245\times 10^8}{s^4+7.574 s^3+120200. s^2}$$
$$pid=0.287\, +0.008 s+\frac{0.5}{s}$$
The closed-loop system obtained as $\frac{pid*sys}{...
- 1,951
2
votes
Transfer function of a temperature controlled incubation system
The transfer function you provide is merly a model of the egg incubation system it is not a controller. In addition a lot of assumptions are made, for instance, heat does spread evenly through the egg ...
- 131
2
votes
How does load force impact load inertia?
I realize this is an old thread, and I am not sure how deep of a dive you finally took on this, but one thing I don't see accounted for in your equations is drum/cable friction. This will be small, ...
- 21
2
votes
Transfer Function of Spring-Damper System
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 $F_{b_1}=b_1(\dot{x}_i-\dot{x}_0)$ ...
- 1,036
2
votes
Square wave transfer function?
You want to look for the Laplace transform of a square wave.
Note: The transfer function $H(s)$ is the ratio of the Laplace transforms of output $Y(s)$ and input $U(s)$:
$Y(s)=H(s)\cdot U(s)$
If ...
- 540
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