Questions tagged [control-systems]

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42 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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1answer
543 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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3answers
9k views

Analyze stability of a closed-loop system with Bode

I have an open-loop system function $L(s)$ and its Bode plot is As MATLAB says, it is stable if we close the loop with unitary feedback. I thought that, seeing the Bode plots one could tell if the ...
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2answers
310 views

Why is my bode plot showing periodic behavior?

I found something very interersting when I was trying to simulate a discrete time system. So first I discretized the continuous system $G(s)$ using "c2d" function and "dbode". The resulting bode plot ...
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1answer
26 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 ...
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1answer
41 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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1answer
39 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
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
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(...
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2answers
143 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
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 ...
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1answer
38 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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1answer
323 views

Equation that describes a gravity drained tank system

I have a system like this: The upper tank has an input ($q_i$) and an output, that is the input for the lower tank ($q_{12}$). The lower tank has an output ($q_o$). Does anyone know how to get the ...
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1answer
29 views

How to tune PID parameters to track a family of reference signals?

I have a system that is controlled by a PID controller. I tune the controller to track a reference signal that is a unit step function. Is there a way to extend the obtained results to be able to ...
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1answer
304 views

AR model order selection for half second EEG fragments

I am using MATLAB to evaluate power spectral density estimates of half second EEG signals, using modified covariance method. Can anyone suggest me how to select the AR model order for this process? Is ...
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2answers
558 views

Frequency response of a (rectangular) integrator

A very simple question which can't really figure out: I have a simple discrete time rectangular integrator with Z transform H(z) = 1/(1-Z^(-1)) Plotting the frequency response with Matlab using ...
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1answer
78 views

Improving velocity estimation

I have a sensor reduction model which gives me a velocity estimate of a suspension system(velocity 1) . This suspension system estimate velocity is used to calculate another velocity(velocity 2) via ...
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2answers
237 views

How to form Kalman filtering matrices for a problem with variable acceleration?

Assuming we have time vector $T$ with constant time step $dt$ position vector $X$ velocity vector $V$ acceleration vector $A$ All vectors $X, V, A$ have noise on their measurement ( $n_x$ , $n_v$ , ...
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1answer
524 views

What is the difference between a sampled time system and a discrete time system?

I am trying to evaluate whether I should control a system in simulink using sampled data system or discrete time system. The discrete model is as follows: The sampled time system is as follows ...
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1answer
77 views

Iterative Blind Sinus Signal Suppression

There are two real signals in the form of $A_i sin(wt+p_i), i=1,2$. Suppose frequency $w$ of both the signals is the same and amplitude $A_i$ and phase $p_i$ are different. The first signal has ...
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0answers
22 views

How to integrate and differentiate sampled signals?

I am working on a control system which is defined by the equation. As you can see,the equation is in continuous state. $T_i$ = integral time and $T_d$ = differential time which are both constants ...
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0answers
16 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 $...
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0answers
11 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....
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0answers
13 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 ...
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0answers
29 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 ...
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0answers
38 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 +...
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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 ...
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0answers
32 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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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?
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0answers
56 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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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 ...
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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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2answers
342 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 ...
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2answers
198 views

Feedback systems & oscillations

The transfer function of feedback system is: $$ \frac{V_{\rm out}}{V_{\rm in}} = \frac{A}{1+Af} $$ Where $A$ is the open loop gain, and $f$ is the feedback gain. Now for oscillation to happen, $Af$ ...
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1answer
310 views

Designing observer with non-observable system

I have this state-space system \begin{align} \dot{x}&=\begin{bmatrix}1 & 0\\3 & -2\end{bmatrix}x+\begin{bmatrix}10\\0 \end{bmatrix}u\\ y&=\begin{bmatrix}1 & 0\end{bmatrix}x \end{...
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1answer
62 views

Comparing the control performance of a given closed loop system

I am having a question about comparing the control performance of a given closed loop. In this link there are some characteristic values that need to be calculated, but there is no description of what ...
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0answers
78 views

Control of pendulum (crane trolley)

I need to control crane trolley (pendulum), I have state space representation as: $ A=\begin{bmatrix} 0 & 1 & 0 & 0 \\ 0 & 0 & \frac{m_b}{m_j}g & 0 \\ 0 & 0 & 0 &...
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0answers
96 views

phase locked loop

I have seen that to get the phase angle of a signal, we have to use PLLs. this PLL is modeling in order to get the phase angle about one frequency, which is the free running frequency of the VCO. If ...
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0answers
274 views

Troubleshooting PID controller

I'm developing a PID controller to control the position of a laser beam. The position is measured using a Position Sensitive Device (PSD). I modeled the plant according to the manufacturer specs and I'...
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0answers
554 views

What is pulse train filter?

I have recently seen some code written in modelling tool like Simulink, ASCET which uses PT1 filter? Why do we use a pulse train filter? What is the difference between FIR, IIR, Chebyschev, ...
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0answers
127 views

PID Control - process variable / setpoint

I'm trying to design a PID controller but I have a problem in the following case: The process variable can only be between 0 and 1. The setpoint can be close to one, for instance 0.97. Hence the ...
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0answers
26 views

System indentification different inputs

I have peformed different form for input/output relation to determine a system, but seem to be missing some theory which input will be the most will excite enough modes such that the models which i ...
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0answers
70 views

Perfect system identification or am i doing something wrong?

I am using MATLAB to identify a system. The problem with my method is that my result is perfect. I get a nearly 100% fit, which make me wonder if what I am doing is correct. I feed a sine sweep with ...
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0answers
28 views

Stability of an unstable system using nonlinear element. Is it possible or not?

Say there is a system with open-loop transfer function G(s)=1/(s−1) . The system is definitely unstable. If I put any nonlinear system in cascade with G(s) and from the output, a negative unity ...
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0answers
50 views

construct 2-state observer

I have position $\theta(s) = \frac{s^2+1}{s^4+2s^3+3s^2+4s+5}$ and velocity $\dot\theta(s) = \frac{s(s^2+1)}{s^4+2s^3+3s^2+4s+5}$. How do I construct 2-state-observer with sampling time $T_s$? $\...
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1answer
49 views

input output read/write frequency

I am trying to identify a system based on input/output response and thereby estimate a transfer function. I generated a frequency sweep function in Mathematica which gives me the discrete values of a ...
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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.
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1answer
235 views

Step response of feedback system

We have a feedback system F(s) as in this figure: and this is the step response of G(s): and H=10. F(s): We got the root locus of the system F(s) as this: then we determined the gain at ...
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1answer
265 views

Describing Function for non-symmetric Saturation Model

Let's talk about a standard saturation model: with bounds $bound_{lower}$ and $bound_{upper}$. So in this example the output $y$ will be: \begin{equation} y(u) = \begin{cases} bound_{lower} ...
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1answer
152 views

What does variance actually mean in control theory?

The question is about the notion of variance in control theory, a college course I am taking. Ever since I can remember, in every maths or physics class, whenever a professor started teaching ...