Questions tagged [control-systems]

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2answers
349 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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1answer
227 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
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 ...
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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
225 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
659 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 ...
3
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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
80 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
61 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
88 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
547 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 ...
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1answer
49 views

Books on delay / lag compensation

Which books do you recommend that provide comprehensive overview of delay compensation techniques in control systems?
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1answer
326 views

In the context of transfer functions, what is the relationship between the terms “proper”, “causal”, and “realizable”?

I am thinking about these terms in the context of linear control. A transfer function is proper if the degree of the numerator is not greater than the degree of the denominator. I've read often that ...
3
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2answers
482 views

Control design: under what conditions can closed-loop poles be placed arbitrarily?

Say we have a single-input linear system $\dot{\mathbf{x}} = A\mathbf{x}+Bu$. With full-state feedback ($u=-G\mathbf{x}$), it is straightforward to arbitrarily place the $n$ closed-loop poles (i.e., ...
2
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1answer
303 views

Control systems and convolution

I think i am not understanding the concept of convolution well. Lets say we are given a system impulse response in the S-domain, and we have implemented a controller $G_c(s)$ that will adjust the ...
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2answers
5k views

What is the difference between a lag filter and “PI” control?

A lag filter/compensator has the form $$G_c(s) = \frac{s+z}{s+p}$$ with $-z < -p < 0$. In practice, the effect of lag compensation in feedback control is to increase the DC gain of the open-...
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2answers
199 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, $Af$ ...
2
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1answer
382 views

How can a system be unstable if $L(j\omega)$ is never exactly $-1$?

Say we have a linear system with unity feedback, with loop transfer function $L(j\omega)$. The closed-loop transfer function from reference to output is $T(j\omega) = \frac{Y(j\omega)}{R(\omega)}=\...
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1answer
139 views

Orthogonal signal generator using integer arithmetic

I have a problem with implementing an orthogonal signal generator (OSG) algorithm on a microcontroller using integer arithmetic. I use this algorithm for a single-phase phase-locked loop (PLL) ...
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2answers
4k views

Why oscillations in PI control?

When integral control is added to proportional controller (i.e. PI control), why steady state error becomes 0 and why oscillations appear , how actually the integrator works ?
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1answer
327 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
208 views

Regarding the choice of cost function in adaptive control - squared error vs absolute error

I did search the question database regarding this question, and although one or two questions came close, they didn't really address my specific question. In adaptive control based on minimizing ...
2
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1answer
72 views

Control theory: how do you initialize input for a model predictive controller?

Although I think this is a pretty popular algorithm, I posted this question on electronics stacksexchange but received no response. I am posting it here to see if there are many signal/control experts ...
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0answers
2k views

Deriving the transfer functions of a heating system

I'm tying to develop a model for a heated system that consists of a small steel block (~25 sq. in.) with a heating element embedded in it. The block acts as a sort of hot-plate that is used to deform ...
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0answers
33 views

Perturbation test for a real plant

How should we conduct a perturbation test for an LTI unknown system by perturbing the input to see the output response i.e. How many different perturbation step size should be given to the input?
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1answer
316 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
352 views

Nyquist with only poles at the origin

I need to solve this three exercises: $$G_1(s) = \frac{1}{s}$$ $$G_2(s) = \frac{1}{s^2}$$ $$G_3(s) = \frac{1}{s^3}$$ This is what I did: For the single pole ($1/s$), magnitude of A is $\infty$ and ...
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2answers
101 views

Mathematically speaking, is a “signal” a function or the set of outputs from a function

In engineering it is well known that we abuse the notation of a function $f: A \to B$ with the image of that function $f(t) = \left\{y \in B\mid f(t) = y, t \in A\right\}$ When we say: let $f(t) = \...
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1answer
177 views

How do I test stability of a MIMO system?

Let's say I have a system similar to two interconnected IIR filters described like this: \begin{align} x_1(t)&=a_{11} x_1(t-1)+a_{12} x_1(t-2) +a_{13} x_2(t-1) + a_{14} x_2(t-2)+y_1(t)\\ x_2(t)&...
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2answers
944 views

How to establish transfer function of a speaker?

I'm working on a signal processing project about vocal system, and I'm trying to use controlling theories to solve the problem. I need to get the transfer function, $H(s)$, of a speaker, from ...
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1answer
67 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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1answer
227 views

Is there a strategy for discrete control of a system with dynamics near sample rate?

I'm trying to control a system where the controller sample rate is physically fixed and the plant has significant dynamics on the same order as the sample rate. I understand that one would prefer to ...
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1answer
64 views

How to create a control loop using a 100Msps digital signal as input

I would like to know what type of microcontroller should I buy for this control loop task. Scenario: I have a digital signal coming from the following equipment: $\boxed{\text{Ultrasonic}\\\text{...
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3answers
3k views

What are the advantages of LTI ( Linear Time Invariant ) systems over other systems? [duplicate]

In our engineering academics, there is one subject named "signals and systems". In this subject only LTI system is discussed. I want to know what are the advantages of LTI systems over other ...
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1answer
1k views

Measuring the open loop transfer function in closed loop: what's the better approach?

Considering the closed loop system; $C$,$G$, and $H$ all linear and stable transfer functions, If I chose to excite $\bf r$ and measure $\bf e$, I get the Sensitivity Function, $S$ $$S=\frac{1}{1+CGH}...
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1answer
32 views

Are there theories to manage states of signal volatility around a limit

Assume input signal and discrete output. The signal can cross the limit at 1000 times per second, but it is desired that the discrete output changes at the most once every 15 seconds. See image below:...
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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 ...
2
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1answer
381 views

How to do this root locus by hand?

I have an open-loop system function $$L(s)=6\frac{(s-2)^2}{s(s-20)^2}$$ and I wanted to to the root locus diagram for it. I did it in MATLAB and got the following graph What I don't know how to do ...
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1answer
96 views

Kalman for 3D position and 1D orientation

Is the following state correct for a Constant Acceleration (CA) model KF applied for tracking an object which moves in (x, y, z) and have the freedom of rotation $\phi$ around the $z$ axis? \begin{...
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3answers
4k views

Closed loop vs. Open loop

When analyzing a control system via Bode, Nyquist and Root-Locus, are we using open or closed loop information? I'm not being able to understand when the poles of the open loop are used and when the ...
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1answer
44 views

Problems calculating Z-transform

I am trying to solve a class exercise in which I am given the following, in Laplace domain: $$G(s)=\dfrac{e^{-Ts}}{s+3}$$ $$H(s)=\dfrac{1}{s}$$ And I need to calculate $\dfrac{C(z)}{R(z)}$, which is ...
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1answer
348 views

Designing a root-locus compensator to attain design requirements

I am working with Matlab to design a compensator capable to make a system attain the design requirements ($\omega_n\geq 0.3$ rad/s & $\xi\geq 0.5$). In order to do so I have a discrete-time ...
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1answer
584 views

What is the Reference in Control Theory?

I've started studying Control and I've come across some concepts that I'm finding a bit difficult to understand. For example, in the system showed here, there is a signal called "reference" as well ...
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1answer
214 views

Can bandwidth of the closed loop be bigger than bandwidth of individual elements in it?

This is a question from control theory but I hope you can help me with it. I was pointed to this community. So in my control loop I have elements that have cut-off frequency of 3-5kHz and I designed ...
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1answer
87 views

Showing a system is always controllable?

I need to show that the following system is always controllable: \begin{align}A &= \begin{bmatrix} -\alpha_1I_{k\times k}& -\alpha_2I_{k\times k}& \cdots &-\alpha_{n-1}I_{k\times k}&...
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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
74 views

Parameter identification for PI controller

I have a PI temperature controller being used in experiments, which I am also trying to simulate. However, using the proportional gain and integral time as used in the experiments gives different ...
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1answer
153 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 ...
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1answer
30 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 ...