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Questions tagged [control-systems]

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0answers
22 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 ...
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1answer
35 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 ...
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0answers
16 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: ...
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1answer
34 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 ...
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1answer
52 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 ...
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2answers
24 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 ...
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1answer
19 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 ...
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0answers
12 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?
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0answers
45 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 ...
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1answer
40 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.
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0answers
35 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 ...
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3answers
96 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 ...
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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 ...
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3answers
161 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
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1answer
113 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 ...
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4answers
270 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
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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 $k = 0$.
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1answer
31 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(...
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3answers
158 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
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1answer
75 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 ...
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2answers
247 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? ...
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2answers
116 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 ...
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1answer
43 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 ...
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2answers
171 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 ...
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0answers
52 views

Transfer Function of VCO and Counter combination

I have a VCO which operates for (0-100KHz) for VIN =0-10V, the output of VCO is connected to a 10 bit counter. I want to know the procedure to derive transfer function of the combo in the form Kvco/S. ...
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0answers
40 views

Quadcopter's simulation vs. empirical response

As part of my PhD, I am designing a controller for a quadcopter. However, I was able to tune 3 PID controllers to control and stabilize the roll, pitch, and yaw channels of the quadcopter, which is ...
2
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1answer
48 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 ...
4
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2answers
530 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 ...
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1answer
78 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
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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 ...
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0answers
37 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
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1answer
317 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 ...
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2answers
344 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
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1answer
400 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)}=\...
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1answer
37 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 ...
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1answer
485 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. ...
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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(...
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1answer
41 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 ...
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2answers
256 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
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1answer
183 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 $y(t)$ ...
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0answers
42 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 ...
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1answer
57 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.
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1answer
169 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., $...
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1answer
611 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 ...
4
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1answer
1k views

Find transfer function from root locus and step response diagram?

I am given the response of a step of magnitude of 3 and the root locus and I have to find the transfer function of the system. The function I find gives me the step response(magnitude of 3 again) of ...
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1answer
72 views

When can the $\mathcal Z$-transform be inverted? When not?

What are the conditions that must be satisfied to be able to invert the $\mathcal Z$-transform?
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1answer
60 views

(How to ask a Homework Question): Define poles by using proportional controller

Given is a process with the transfer function $$G(s) = \frac{s - 1}{s^2 + 3s + 2}$$ I want to create a controller so that the poles of the controlled system are $$p_{1,2} = -4 \pm i$$ Is it ...
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1answer
54 views

Why do these 2 methods give different solutions?

I need to solve what is underlined in red for $x_i$, nut currently I'm interested in the right side of the equation only. On the left I sarted by doing the Laplace transform of $x_u'$ and $x_u$, and ...
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1answer
80 views

Why the bandwidth of the system with the minimum-order observer is higher than the full-order observer?

In Ogata's Modern Control Engineering (5th Ed., page 786) it says: The bandwidth of the system with the minimum-order observer is higher than that of the system with the full-order observer, ...
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2answers
448 views

Is a filter/control transfer function with positive phase “causal”?

In control we often use transfer functions with positive phase, i.e., a "lead filter" has transfer function $$G_c(s) = \frac{\alpha \tau s+1}{\tau s+1}$$ (with $\alpha>1$). Since the zero occurs ...