Questions tagged [control-systems]
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0
votes
1answer
25 views
Cascade filter realization equivalence? [closed]
Given
$$H(z) = \frac{11 +4.6z^{-1} -26z^{-2}-3.75z^{-3}}{1-z^{-1}-8.75z^{-2}}$$
I'd like to know whether this realization:
Is equivalent to this one?
In short, is the direct form realization ...
3
votes
1answer
78 views
SRF-PLL discretization problem
So I've been working on how to digitally implement a static reference frame PLL (SRF-PLL), which is a quite popular PLL used for extracting three-phase grid angle.
This PLL works by using the DQ0 ...
0
votes
0answers
15 views
Finding gain on root-locus
I have to design a compensator using root locus for the system $G(s) = \frac{1}{s\cdot(s-4)}$ that follow the following criteria:
$op\% \le 5\%$
$t_{2\%} \le 4s$
So I started computing $\zeta$ and $...
0
votes
0answers
10 views
What is difference between natural response and zero-input response of a system and how to find natural response? [duplicate]
In most books it is said that natural response is another name to zero-input response while in some resources is is mentioned that the classification is based on poles of transfer function and input....
1
vote
1answer
37 views
What is the type number of a discrete time system given $H(z)$?
Given a continuous time impulse response $h(t)$, if I take the Laplace transform and count the no. of poles at origin, that gives the type number of the system. For e.g., $$H(s) = \frac{2}{s(s+2)}$$ ...
0
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0answers
9 views
Comparison Between Mahoney Filter and Kalman Filter in Euler Angles (Yaw, Pitch, Roll) Estimation
What are the advantages of Mahoney Filter over Kalman Filter for Euler Angle (Yaw, Pitch, Roll) estimation?
Could anyone compare them for Angular State Estimation?
Resources
Mahoney Filter ...
0
votes
0answers
20 views
Block diagram reduction with multiple inputs
I need to reduce the diagram, when each input is 0, I can do when d=0, however i'm finding it a little difficult when r=0.
I have solved the exercise using a signal flow diagram and the solution is ...
0
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0answers
37 views
On $H_\infty$ norm for transfer function
For a given scenario in the context of control system, I'm trying to investigate how the $H_\infty$ norm can be calculated for a transfer function as follows:
$$G(s)= \frac{w_n^2}{s^2 +2\zeta w_ns +...
0
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0answers
23 views
How to move a linear block before an Integrator block?
I have the following discrete time blocks which acts as a decimation filter. My objective is to linearize the piecewise linear outputs using $O$ and $G$; the purpose of these two variables is ...
0
votes
1answer
40 views
Implementation of gain scheduling for a PI controller
I'm designing a PI controller for a boost converter. I was able to find a set of gains that fit for all situations, but I get a slow response at full-load.
I was thinking instead of using gain ...
0
votes
0answers
31 views
system identification: MATLAB tfestimate gives different results for different Fs
So I have an experimental data; A is a chirp signal (sweep sine wave) and B is the response of the system. I identify the system as follows in MATLAB:
...
0
votes
1answer
38 views
Calculating an in-loop signal as part of a hierarchical control loop
I've got a control system with two feedback paths, with each path going to a different actuator that corrects the error in the system. One feedback path provides feedback at low frequencies, and the ...
1
vote
1answer
57 views
State space equations
I am stuck on this exercise. I don't know how to deal with this squared y in the denominator. What am I supposed to do to obtain state space equations?
ex.1
Simplified dynamic model of the steel ball ...
1
vote
2answers
30 views
Discrepancy in stability conditions when calculating via RH criterion and Nyquist criteria
I have the following open loop transfer function for a unity feedback system.
$$G(s)=\frac{K(s+20)^2}{s^3}$$
1.When using RH criterion it can be easily proved that the closed loop transfer function ...
0
votes
1answer
41 views
Routh's stability criterion: zeros of the auxiliary polynomial and of its derivative
When using RH criterion and using the auxiliary equation special case, which of the following is true?
The auxiliary equation $A(s)=0$ gives some(or all) of the symmetrical poles.
The differentiated ...
0
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0answers
15 views
What are simple direct adaptive control algorithms?
I am going into this blind. Was wondering if someone can point out some resource on direct adaptive control algorithms?
1
vote
0answers
51 views
How general are adaptive-filtering techniques? [closed]
How often do problems arise that let you use adaptive filters? Unless I am understanding something incorrectly it seems the requirement that the input signal be stationary(or even WSS) is too strong ...
0
votes
1answer
42 views
Transfer function of open loop system
Suppose i have the system equation
$Y(s) = G(s)X(s)+ 3T(s)$
Then what is the transfer function of the system?
I know that the transfer function is $Y(s)/X(s)$, but i can't get that expression.
0
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0answers
51 views
How to compare the similarity of 2 transfer functions
I'm working on a power systems where I have 2 linearized transfer functions. The first transfer function corresponds to the no-load case and the second transfer function corresponds to the full-load ...
0
votes
3answers
99 views
Discrete state space model - Why are we calculating $x[k+1]$ instead of $\dot{\textbf{x}}(t)$?
A continuous state space model is defined as follows.
$$
\dot{\textbf{x}}(t)=\textbf{A}\textbf{x}(t)+\textbf{B}\textbf{u}(t) \\
\textbf{y}(t)=\textbf{C}\textbf{x}(t)+\textbf{D}\textbf{u}(t)
$$
If we ...
1
vote
0answers
36 views
How can I design a PI controller for a closed loop system, which requires a bandwidth equal to the natural frequency and a set Phase Margin?
For a school project I have to hand in a small report on a this problem. I've been studying so much for it but right now I'm just mixing up everything I've seen and just don't know where to start. I'd ...
1
vote
3answers
252 views
Why use transfer functions than differential equations?
I have some simple questions regarding DSP and Control Systems, but found no simple answers. I just need simple and easy to understand answers, not complex answers with huge maths.
Why we use ...
1
vote
1answer
148 views
Eigenfunction property for LTI sinusoidal and the sinusoidal steady-state response
All LTI systems possess the eigenfunction property for complex exponential inputs. That is (restricting our attention to periodic complex exponentials), if $e^{j\omega_k t}$ is an input to the LTI ...
5
votes
4answers
283 views
Make a signal that fits another the best possible with a limitation in the 2nd derivative
Consider this step function:
The signal that "fits" this should look like the following (in green):
The corners are now smooth because the maximum second derivative allowed is not infinite anymore.
...
0
votes
1answer
36 views
Confused about applying Routh Hurwitz to $s^2 +s + k$
I have a closed loop transfer function
$$G_{\rm cl}(s) = \frac{k}{s^{2} + s + k}$$
I am trying to find the critical gain of the system. From using the Routh Hurwitz criterion I get a $k = 0$.
0
votes
1answer
32 views
Proof $GM$ (in dB) of $2nd$ order system is $\infty$
How can we prove that the Gain Margin $[GM]$ of $2nd$ order system is $\infty\quad ?$
My Approach:
Let us consider a $2nd$ order open loop system : $$G(s)= \frac{k}{(s+1)(s+2)}$$
Now, we know: $GM(...
0
votes
3answers
183 views
How do I stabilize my oscillating system?
I have two scalars $x$ and $y$ that vary with time $t$ such that
\begin{align}
\frac{dx}{dt} &= ay + b + dx\\
\frac{dy}{dt} &= cx
\end{align}
but $a, b, c$ are unknown.
If $d$ is too small, ...
2
votes
1answer
89 views
Transient response of system with single pole $0 \le p < 1$
$G(z) = \frac{1-p}{z-p}$
If the value of p satisfies $ 0 \leq p < 1$ there are no oscillations
in the transient response.
Question: Why is that $\uparrow$ true? I know roughly what a ...
0
votes
2answers
315 views
What does G(1) = 1 say about a system?
This is a line from a paper I've been reading:
The static gain of the closed loop system must be $1$ ($G(1) = 1$) [...]
First of all: I know what gain is, but isn't gain dependent upon frequency? ...
0
votes
2answers
138 views
How to make bode plot when output signal changes amplitude?
When I do frequency analysis on my feedback controlled system and the controller is really tightly tuned, I get a frequency response that looks like this:
Blue is excitation signal and green is ...
0
votes
1answer
45 views
Compensating effects of a system with a known transfer function
Suppose we have a system which we want to know the exact transient times. In ideal case, we can extract the transient times, but in practice it will be affected by another system with a known transfer ...
1
vote
2answers
187 views
What are poles and zeroes (with respect to the inputs and outputs of a system)?
I get it, about poles and zeroes, when we talk in terms of the transfer function.
But, if the transfer function is the ratio of the output to the input, then if the input signal is zero, then the ...
2
votes
1answer
55 views
Controllable realisation of $\frac{s^4+1}{4s^4+2s^3+2s+1}$ is both controllable and observable?
I am trying to find the controllable realization of the following transfer function:
$$H(s)=\frac{s^4+1}{4s^4+2s^3+2s+1}$$
I approach this by first using polynomial division to assure that $H(s)$ is ...
3
votes
2answers
703 views
Is this system time invariant?
I've been working at this problem for a while now, and can't seem to come to a solid conclusion - is this system time invariant?
$y(t) = \int_{-\infty}^{t} e^{-9(t-\tau)} x(\tau)d\tau $
My reasoning ...
1
vote
1answer
92 views
Time invariance of a System
I have this small question about the time invariance of a system. Which is follows:
- If the current output is multiplies by the current input (see both are variables) will the system be time variant ...
0
votes
1answer
37 views
How can I translate what I have learnt in Transfer Functions to differential equations?
I have gone through the entirety of K. Ogata's Modern Control Engineering, and I do not understand how can I translate all the transfer function models into differential equations? For example, how ...
0
votes
0answers
39 views
Analog to digital controller- What sampling rate?
I'm studying about the design of controller in digital control systems. Right now I see the method in which I design my controller in the s domain and then convert it to the z domain.
However, in ...
2
votes
1answer
446 views
Exponential decaying step response in LTI System
I'm attempting to better understand the relationship between step responses, impulse responses, and convolutions. Say that I have a system where if I apply a constant input, my output decays from a ...
5
votes
2answers
461 views
Does the impulse response of a system have any physical meaning?
In other words, what does the impulse response tell us about the characteristics of the system? For simplicity, let's assume we deconvolve a discrete output and a discrete input to obtain an impulse ...
0
votes
1answer
531 views
Z transform of a function with delay?
i have this open loop system , and i've been asked to find out the response $C(kT)$ due to a unit step input.
I am able to find the transfer function without the delay unit i.e $$\frac{C(z)}{R(z)}=\...
1
vote
1answer
42 views
Time Delay Margin
I have a question regarding the time delay margin. I know the definition of time delay margin now I want to know that for the stability of the system is it good to have large time delay margin or ...
1
vote
1answer
695 views
What is $H_2$ and $H_{\infty}$ control? [closed]
I can create a Linear Quadratic Gaussian Integral(LQGI) controller very easy by using GNU Octave. LQGI is in the area of Optimal Control Theory.
But there is something called Robust Control Theory. ...
0
votes
0answers
43 views
Which equation should I use to compute the Extended Kalman Filter?
Compute the Extended kalman filter can be done in several ways.
The first one compute the convariance matrix $P(t)$ from the Riccati Equation:
$$\dot{P} = F(t)P(t) + P(t)F^T(t) - P(t)H^T(t) R^{-1}H(...
0
votes
1answer
42 views
Does a closed loop system with a reference of its previous iteration always reach a point in which it adventually loops, even if that loop is stable?
For example you have a $F(\cdot)$ which starts off taking some input $a$, which describes some set of objects and their states, and creating a output $F(a)$, which can be renamed $F_1$, that also ...
0
votes
2answers
335 views
Design discrete controller for zero steady state error
I have the following system
where $$G(s)=\frac{0.5}{s+1}+\frac{5}{s+10}$$
How can I design the C(z) controller so that the steady state error for a step input r(t)=1(t) is zero?
I know that this ...
0
votes
1answer
212 views
Step response of a differentiating system
Consider I can find the step response of a system with the following method:
We can easily find the step input of a system from its transfer function. Given a system with input $x(t)$, output $y(t)$ ...
1
vote
0answers
45 views
How can I find the transfer function from this Bode diagram?
I've been given this bode diagram :
I've been asked to find the transfer function only by using the bode diagram.
It's the first time I'm doing this so here's what I thought.
The starting value is ...
-1
votes
1answer
63 views
What means ideal integrator in this MIMO system state diagram?
Can someone explain me what ideal integrator is as simple as possible? Which meaning it has in this diagram?
$A,B,C$ and $D$ are matrices. $u$ is input and $y$ is output.
1
vote
1answer
210 views
Under what conditions do the phase margin and Nyquist criteria give the same results?
When designing feedback systems, I often evaluate stability by thinking about phase margin: the closed loop system $$T(s) = \frac{L(s)}{1+L(s)}$$ is stable if $L(s)$ has positive phase margin, i.e.,
$...
3
votes
1answer
642 views
Determining the final value of the output of a discrete system
I'm going through an exam question where I've been told that the samples $f(kT)$ of the following function
\begin{equation}{F\left(z\right)=\frac{1}{1-0.819z^{-1}}} \end{equation}
are applied to a ...
