Questions tagged [control-theory]

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67 views

Space State on SEP/Ex DC-Motor

I'm currently studying DC motors and I do have some doubts about the dynamics of it. As per explained on [Guru, B.S. and Hiziroglu, H.R., 2001. Electric machinery and transformers (Vol. 726). New York:...
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1answer
168 views

How can I calculate gain margin in this transfer function and the constant K?

This is the problem statement: There is a mechanical crane whose Transfer Function is shown. If it is implemented The automatic system shown, closing the loop and adding the G1 block (s), you are ...
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100 views

PWM frequency and control system sampling frequency in dc-dc converters

I am trying to control the output voltage of a simple dc-dc buck converter, which is digitally controlled. The output voltage is sampled, and the control algorithm is run, at every \$T_s\$ seconds, ...
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2answers
950 views

I'm confused a bit on basic control stuff for a PID controller

I'm doing a PID controller demonstration project in which heat is applied to a K type thermocouple and I'm supposed to maintain the temperature read at 50 °C using a PWM signal. I know the basic ...
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0answers
60 views

Control system -- closed-loop system problem

Given a closed-loop system as shown below: Suppose that \$x(t) = u(t)\$ and \$d(t)=0.5u(t)\$. Determine the output response of \$y(t)\$ and it's steady state at \$t\rightarrow \infty\$. I've tried to ...
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3answers
62 views

Nichols plot confusion

The transfer function is \$F(p)=10/(p^2+2p+1).\$ Using Wolfram Alpha, the Nichols plot shows that the argument \$\to -\pi\$ when \$\omega \to +\infty\$. However, calculating the argument on paper ...
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33 views

Feedforward from measurable disturbance

Gff is chosen so that it completely cancels the disturbance (Gff = -Gv/P) and Lp < Lv. Is it easier to control if Tp < Tv or Tp > Tv. I am a little bit lost on how to begin here? Should I ...
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48 views

Output of a linear system with discrete feedback

I have this problem here that I had trouble with few years back and I still don't understand https://imgur.com/At2BbWe With a T period discretization on the feedback and a first order hold after it. ...
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52 views

Linearization of nonlinear plant with system identification in Matlab

I hope this question fits in here and there is someone who can maybe help me. I am new to control theory and I have a very complex Simulink model which is nonlinear. I want to have a linear ...
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1answer
84 views

Decide P controller gain K so that phase margin is 50 deg

I need help finding the gain \$K\$ so that the phase margin for the system equals 50 degrees. $$F(s) = K$$ $$G(s) = \dfrac{1}{(s+1)^2}$$ \$v\$ is a process disturbance sinusoid with amplitude 2.5 and ...
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71 views

From where does State space model equations come from?

I have a good basic understanding on classical control theory. Now I am studying modern control theory.I encountered the following equations as seen below. Online I have only been able to find ...
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64 views

fast analytical technique identifying poles/zeros using degree of freedom

I encounter some engineers who can quickly spot poles and zeros in the circuit by identifying "degree of freedom". For example, a typical technical discussion goes like : "a miller ...
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122 views

Determine range of proportional gain with given overshoot

I have given the open-loop transfer function $$ G_{ol} = 1.42 \frac{(s+3)^2+6^2}{(s-1)(s+2)((s+4)^2+4^2)} $$ The task I was given is determining the range of the proportional gain, which makes the ...
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2answers
203 views

Tuning PID without transfer function

I'm very new to control theory and I am stuck at PID tuning. I have a given Simulink model but I do not know the transfer function. I want to use a PID to provide new input from the output of the ...
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3answers
117 views

Why do I need phase margin if I know the transfer function?

What is the point of examining the phase margin (or gain margin) for a closed-loop system if I can just solve for the transfer function. The transfer function will give any poles and zeros, which can ...
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1answer
64 views

Linearization of nonlinear system

I have a nonlinear system described by: $$\begin{align} V\,\dot x_1 &= Q_1 C_1 - (Q_1+u)x_1 \\ V\,\dot x_2 &= C_2\,u -(Q_1+u)x_2 \\ y &= -\frac{\log{\left[(x_1-x_2)+|x_1-x_2|+4K\right]}...
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2answers
245 views

Steady-state Error Definition

In the textbooks and reference material which I have been using during my course on control systems, a common definition of steady-state error is as follows: $$E(s)=R(s)-C(s)$$ where E(s) is the error ...
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1answer
196 views

Finding the overall transfer function and plotting root locus of a digital control system

I have started to learn about digital control theory and struggling with a particular diagram of a digital control system. The system is presented below: \$D(z)\$ is a digital compensator, \$G_{h0}\$ ...
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2answers
362 views

Nyquist stability criterion for positive feedback

it is known that the stability of a system with negative feedback may be analized through the Nyquist stability criterion, which is based on observing the number of turns around the point (-1;0) in ...
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1answer
57 views

Layman explanation of "dynamics" or "dynamic behaviour"

I often read the term dynamics or dynamic behaviour in electrical engineering especially in control systems course What is meant by it? Is it means that the system whose internal state/properties ...
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329 views

What will be minimum number of states / state variables for these control systems in state-space model?

Consider the systems as LTI and SISO with transfer functions given below: I have read that minimum number of states for an LTI SISO system required to represent in state space analysis for any ...
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1answer
188 views

555 square wave generation with frequency feedback

Knowing that 555's behaviour varies according to temperature, I wondered: In an astable configuration, is there some way to measure output frequency, compare it with some desired value, and use this ...
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1answer
78 views

Feedback Circuit schematic to Control Theory block diagram?

I'm studying analog electronics circuit with feedback. I see that, during analysis, a useful abstraction over the schematic is the block diagram in control theory style, but I stuggle in deriving it ...
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1answer
24 views

Nomenclature for changing characteristic curve

OK, I'm at a loss for words on this one. I'm looking for a word or phrase to describe the following situation... I have an open loop control system that when I apply voltage \$A\$ I get output \$A_1\...
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272 views

Transfer function with separate time delays in each term

We've been given the problem below for our current assignment As far as I can recall, I have never seen a transfer function with time units in the function itself, added onto each separate term. I ...
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1answer
149 views

Looking for a quote on dynamic system identification

Does anyone know of a quote by an eminent control theorist or controls engineer or book author who I could reference who said something along the lines of the following: The process of control ...
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2k views

Effect of RHP zeros on stability

Why do zeros in the right half of the \$s\$ plane reduce stability (i.e., gain / phase margin)?
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1answer
1k views

Determining Number of states in State Space Modeling

I want to use state space modeling for representing the following circuit system. However, I am unable to decide the number of states. I am able to describe the system with a set of three equations. ...
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1answer
178 views

How to calculate roots using root locus method? [closed]

Find the roots of the following polynomial by use of the root locus method. 3s⁴ + 10s³ + 21s² + 24s + 30 = 0 (The root locus plot has not been given.) Can you please help me with this? This ...
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2answers
3k views

Integral only control (as opposed to PI or PID)

I am familiar with PI and PID control but I've recently been reviewing code that seems to use I (Integral) only control. What are the benefits of I control over PI control, and when should it be used /...
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1answer
172 views

Bode Plots - Absolute Value of Complex Function in Magnitude calculation

I'm struggling with one step in the magnitude calculation during manual Bode plotting. Specifically during the step of applying the absolute value to \$s = jw\$, what is the reasoning for why you can ...
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1answer
62 views

Control system error based on differential process value

In a basic PID controller, you measure the process value y (such as temperature) directly; then the error e is equal to the difference between the process value and the set point r. The error feeds a ...
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1answer
366 views

Op-amp control theory

back at it again trying to use your genius brains. I have been trying to teach myself audio amplifier design. The big road block I am getting into is the control theory part of it, meaning how does ...
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2answers
578 views

Why linearise around an equilibrium point?

In the control theory dealt in class I was taught to always linearise a nonlinear system around an equilibrium point, i.e., where $$\dot x = 0$$ However, linearization is a Taylor series expansion, ...
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1answer
1k views

Understanding the role of Pole zeros cancellation from the definition of stability

I have encountered the following theorem in a book. According to me, I can get an asymptotically stable system even if cancellations exist for the unstable poles. my example, Then Why does this book ...
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74 views

Obtaining the analytical expression using the state transformation matrix

I am trying to derive the analytical expression in the box below. T is the state transformation matrix. x_dot=A*x(t) is a second order linear system. A has 2 distinct eigenvalues s1 and s2 and ...
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603 views

Why gain crossover frequency must be lower than phase crossover frequency for stable systems?

As far as I understood from here, phase margin means the amount of phase that needs to be added in order to coincide with 0 db gain and -180 degrees phase. Likewise for the gain margin it means means ...
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2answers
63 views

limits of performance

I am trying to understand a topic on limits of performance. So there is a delay of tau between input and output so the transfer function becomes G(s)*e^-(tau *s). I am unable to understand the ...
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2answers
988 views

Should the error term of PID be normalized?

By "normalized", I mean +/-1 ~= the maximum error the system can reasonably be expected to experience, or divided by the setpoint. Background: I am working on a PID controller for an SSR heater ...
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1answer
190 views

Transfer function of a digital phase frequency detector

I'm confused about the transfer function of a digital phase frequency detector. Why can we say that the pfd output is proportional to the phase error? The pfd (with charge pump) generates current ...
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2answers
401 views

Loop bandwith and open-, closed- loop gain in ADIsimPLL

I'm want to use ADIsimPll to calculate the loop filter properties for a PLL I want to build. I read some things in the programs help topics which I find somehow strange. Maybe you guys can help me out ...
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1answer
665 views

Connection between PID, Pole placement and LQR

I am trying to control a wheeled inverted pendulum with a PID controller. I already designed a linear quadratic regulator (LQR) and a pole placement regulator (PPR). I would like to design a PID ...
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1answer
291 views

What is the mathematical difference between a transfer function and a state transition matrix?

I do know what the difference in meaning is between a transfer function (output over the input) and a state transition matrix \$\Phi\$ (describes the unforced response of the system). Yet when looking ...
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1answer
197 views

Definition of minimal phase

Let us consider a linear time-invariant system. The term minimum phase is used for a system that has stable poles and stable zeros. A system is called nonminimal phase if it is not minimum phase. ...
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1answer
69 views

The system is not completely reachable, Is state x1 reachable from x0?

The system is $$ x(k+1)=\begin{bmatrix} 1 & 1 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix} x(k)+\begin{bmatrix} 0 \\ 1 \\ 1\end{bmatrix} u(k) \\ y(k) =\begin{...
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3answers
202 views

Linear regulator loop dynamics

Given a step change in the input voltage of a standard op-amp based linear regulator, a finite amount of time is needed for the op-amp to sense the voltage difference at its input and do whatever it ...
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4answers
129 views

Why is a system description in control theory important?

If you want to control a system (with a loop controller), why actually do you need to know anything about the system itself (its dynamics or the transfer function or impulse response or whatever)? Isn'...
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1answer
313 views

Pure transport delay? (Nyquist plot)

How does pure transport delay affect the Nyquist plot, and how is it possible to find the maximum value of the delay, such that the system stays stable even after delay is introduced?
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2answers
893 views

Why can't a first-order block have an oscillatory step response?

From what I understand, multiple-order blocks can have step responses that oscillate. It's apparent that a first-order block cannot have an oscillatory step response. How come? Is it due to the ...
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3answers
9k views

Why do we use step response? [duplicate]

We tend to identify systems more often by using the step response. Why? Especially when the impulse response is directly related to the transfer function?