Questions tagged [control-theory]
For questions about control theory as it relates to electrical engineering, which provides tools to design electronics so that a system's output(s) are driven to the correct state for given input(s) by ensuring stability, reducing steady state error, overshoot, etc. Consider using in conjunction with related tags such as "transfer-function", "stability", "feedback", "frequency-response", "step-response", "nyquist-plot", "phase-margin", etc., if applicable.
84
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Contradictory relationship between quality factor and damping
I am studying control theory and mechanical vibrations.
From control theory aspect, I know that bandwidth and response time is inversely proportional, which means bandwidth and damping as well.
The ...
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3
votes
1
answer
174
views
What is the practical advantage of root locus method in control system engineering? [closed]
Recently I learned about the topic.
Decades ago, when no computational power was available for engineers, it was surely helpful in some way. But I do not understand what the advantage is nowadays, ...
- 361
0
votes
2
answers
89
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Laplace of third-order lead-lag filter
For Butterworth low-pass filters, the Laplace function of the third-order filter is
$$
H(s)= \frac {1}{\left(1+\frac{s}{\omega_c}\right)\left(1+\frac{s}{\omega_c}+\frac{s^2}{\omega_c^2}\right)}
$$
...
- 3
0
votes
0
answers
17
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How to create a LPV Plant model for a DC Motor?
Currently I'm learning about LPV systems and long-story-short I intend to create a simple LPV plant model for a DC motor.
Imagine a simple 2x2 matrix for its space-state:
$$
\begin{bmatrix}\
\dot x_1 \...
0
votes
2
answers
86
views
Why is closed loop frequency response hard to determine?
I'm learning about frequency domain control design and one of its advantages is said to be that: one can deduce the closed loop behaviour of a system by (experimental) data on frequency response on ...
- 103
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votes
0
answers
73
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How to design a 2nd order LP active filter with differents responses?
I have been asked to design and simulate a 2nd order analog low pass filter having the responses of Butterworth, Chebyshev and Bessel.
Im looking for guidance and suggestions,since I understand the ...
- 431
0
votes
3
answers
139
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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:...
1
vote
1
answer
741
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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 ...
- 343
0
votes
0
answers
175
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, ...
- 41
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votes
2
answers
998
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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 ...
- 183
2
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0
answers
64
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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 ...
- 21
1
vote
3
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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 ...
- 55
0
votes
0
answers
40
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 ...
- 51
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0
answers
72
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 ...
- 21
0
votes
1
answer
225
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}$$
\$v\$ is a process disturbance sinusoid with amplitude 2.5 and ...
1
vote
0
answers
79
views
From where does State space model equations come from?
I have a good basic understanding on classical control theory. Now I am studying modern control theory.I encountered the following equations as seen below.
Online I have only been able to find ...
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1
vote
0
answers
72
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fast analytical technique identifying poles/zeros using degree of freedom
I encounter some engineers who can quickly spot poles and zeros in the circuit by identifying "degree of freedom". For example, a typical technical discussion goes like : "a miller ...
- 389
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0
answers
241
views
Determine range of proportional gain with given overshoot
I have given the open-loop transfer function
$$
G_{ol} = 1.42 \frac{(s+3)^2+6^2}{(s-1)(s+2)((s+4)^2+4^2)}
$$
The task I was given is determining the range of the proportional gain, which makes the ...
- 1
1
vote
2
answers
387
views
Tuning PID without transfer function
I'm very new to control theory and I am stuck at PID tuning.
I have a given Simulink model but I do not know the transfer function. I want to use a PID to provide new input from the output of the ...
- 21
0
votes
3
answers
148
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Why do I need phase margin if I know the transfer function?
What is the point of examining the phase margin (or gain margin) for a closed-loop system if I can just solve for the transfer function. The transfer function will give any poles and zeros, which can ...
- 426
1
vote
1
answer
86
views
Linearization of nonlinear system
I have a nonlinear system described by:
$$\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]}...
2
votes
2
answers
262
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 ...
0
votes
1
answer
242
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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2
votes
2
answers
475
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 ...
- 3,276
0
votes
1
answer
64
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 ...
- 437
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votes
0
answers
426
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 ...
- 435
0
votes
1
answer
219
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 ...
- 165
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vote
1
answer
82
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 ...
- 325
0
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1
answer
48
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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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0
votes
0
answers
362
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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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0
votes
1
answer
155
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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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4
answers
3k
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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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1
answer
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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. ...
user172541
0
votes
1
answer
225
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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 ...
5
votes
2
answers
4k
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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0
votes
1
answer
224
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 ...
0
votes
1
answer
77
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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1
answer
451
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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2
votes
2
answers
651
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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2
votes
1
answer
1k
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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 ...
- 213
0
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0
answers
81
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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0
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777
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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 ...
- 213
1
vote
2
answers
66
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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votes
2
answers
1k
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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 ...
- 249
1
vote
1
answer
217
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 ...
- 115
0
votes
2
answers
453
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 ...
- 115
2
votes
1
answer
873
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 ...
- 204
1
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1
answer
446
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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 ...
0
votes
1
answer
211
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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.
...
- 204
1
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1
answer
73
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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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