Questions tagged [control-theory]
The control-theory tag has no usage guidance.
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1answer
47 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 ...
0
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1answer
19 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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0answers
20 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 ...
0
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1answer
68 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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0answers
22 views
How to treat poles with imaginary part when using root locus angle criteria - what is the angle to use?
Context: In the process of designing a phase-lead compensator for a system, I have used the design requirements to find the ideal locations for my closed-loop (CL) poles, have picked a place for a new ...
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4answers
116 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)?
0
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1answer
82 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. ...
0
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0answers
126 views
Design of a lead compensator with root locus in matlab
For the transfer function G(s), I tried to design a lead compensator for the function to have a response to the step with the following specifications: Overshoot= 10%; Ts (2%) = 5s.
When I simulate ...
0
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1answer
111 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 ...
3
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2answers
671 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 /...
0
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1answer
45 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
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1answer
48 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 ...
0
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1answer
141 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 ...
1
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1answer
89 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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0answers
372 views
Speed of response and crossover frequency relationship
In SISO(Single Input Single output) cases, My professor keeps mentioning the speed of response and crossover frequency interchangeably. I don't really understand what the speed of response means also ?...
1
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1answer
496 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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0answers
53 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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0answers
148 views
Why does the gain and phase margin need to be positive for a stable system?
As far as I understood, 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 the amount ...
1
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2answers
62 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 ...
2
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2answers
379 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 ...
1
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1answer
124 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 ...
0
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2answers
170 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 ...
1
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1answer
186 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 ...
0
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1answer
105 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.
...
1
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1answer
61 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{...
1
vote
3answers
101 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 ...
1
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4answers
119 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'...
0
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1answer
175 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?
0
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2answers
174 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 ...
11
votes
3answers
5k 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?
0
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0answers
115 views
Tips for solving difficult block diagrams?
I've gotten the hang of solving block diagrams, i.e. condensing them to a transfer function. I'm aware that one may be solved in multiple ways.
For simple diagrams, it's fairly straightforward to see ...
3
votes
6answers
510 views
Are oscillators always non linear?
From linear systems theory, self-excited sustained oscillations are only possible by means of a marginally stable system, where poles are located exactly on the imaginary axis. However, such a ...
0
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1answer
97 views
Get transfer function from state space
The following system is given and I'm asked to find the transfer function $$\frac{Y(s)}{U(s)}=G(s)$$ $$\bar {\dot x}=\begin{bmatrix} 0 & 1 & 0 & 0 &0 \\0 & 0 & 1 & 0 & ...
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0answers
72 views
Design controller to get this response
We have the following closed loop system where a is from 1 to 10 and p from 0 to 1(excluding 1).
We want to design controllers H(s) and C(s) so that the step response is inside this area
This is ...
0
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0answers
263 views
Calculate K for best settling time?
I'm practising on compensators and the root locus. A very common problem in my textbook is to find the value of a variable for the minimum settling time of the system.
I have no trouble drawing the ...
1
vote
1answer
136 views
Root locus problem
The problem consists of two questions: a) Find k so that one of the roots is at s=-2 $$(s+1)^5+k=0$$ b) for the value of k you just found find the rest roots using root locus.
Regarding the first ...
0
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1answer
1k views
Overshoot percentage of a critically damped system
My textbook explains how we recognize an underdamped , overdamped or a critically damped system and all their characteristics.
Later on, in another chapter, without going into much detail I'm given ...
1
vote
2answers
451 views
Closed loop transfer function problem
Let's say we have the basic feedback system of the picture
We know that the closed loop transfer function is given by $$T(s)=\frac{G(s)}{1+G(s)H(s)}$$ Now, the diagram above is equivalent to an open ...
0
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1answer
433 views
How do I get a closed-loop PID controller from a transfer function?
I have the transfer function below:
$$T_c(s) = \frac{s+k_i}{m_0s^3+s+k_i}$$
It is assumed that \$k_p=1\$ and \$k_d=0\$. I am given that \$x_l(t)=[x_l(t),y_l(t)]^T\$ is the trajectory and the ...
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1answer
243 views
Doubts about stability control theory
I have some questions about theory of stability:
Can a system be stable and have poles in the right semiplane of s plane?
If a system has poles in the right semiplane, what should happen in GH ...
0
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1answer
180 views
doubt on application of stability criteria
I have only seen systems with this transfer function treated in stability criteria with this general form:$$\frac{KG(s)}{1\pm KG(s)}$$ so the $$\lvert H(s)\rvert =1$$
is it possible to apply criteria ...
1
vote
3answers
659 views
Steps to hand draw Bode magnitude plot for a particular transfer function
Can anyone guide me through how to hand draw a correct Bode magnitude plot for
$$G(s) = \dfrac{48000}{s(s+0.1)(s+100)}$$
Don't even need phase plot, just need correct magnitude plot
As few ...
0
votes
2answers
102 views
MATLAB: Pole at 0.1 rad/s contributing to nothing on the Bode Plot - Why?
Consider the transfer function
$$G(s) = \dfrac{48000}{s(s+100)}$$
The Bode plot is given as
Now observe that the gain at frequency w = 1 Hz is 53.6244 dB. Completely reasonable, because this is ...
2
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4answers
600 views
Intuitively, why does gain margin and phase margin infer instability in feedback system?
On MATLAB https://www.mathworks.com/help/control/ref/margin.html, gain margin and phase margin are additional gain in the system and additional delay in the phase of the system such that the system ...
0
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2answers
238 views
Is the Nyquist plot a plot of Re(G(s)) v.s. Im(G(s) or Re(G(jω)) v.s. Im(G(jω))
It seems that people in control theory are divided over whether the Nyquist Plot/Diagram (that is the plot, not the contour!) is a plot of $$\text{Re}(G(s)) \text { v.s. } \text{Im}(G(s))$$ or $$\text{...
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2answers
1k views
Sensorless driving of 3 phase BLDC motor for gimbal applications?
I have started to work on a project of mines, which consists in implementing the stabilization of a single axis gimbal using a generic microcontroller (STM32 or
Arduino Uno).
The gimbal axis is ...
1
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0answers
61 views
Digital PLL reference noise rejection
I have a fully digital implementation of a PLL.
The problem that I have is the white noise coming from the PFD (you can view it as input jitter). I would like to filter it a lot, but an implementation ...
-2
votes
1answer
277 views
Object tracking project [closed]
I have to create a system that can track an object in the air and shoot a projectile at it. This in on a small scale. I want to use an ultrasonic sensor because I know nothing about vision algorithms. ...
1
vote
2answers
1k views
Stability & error from nyquist POLAR plot?
I have been given the following Nyquist polar plot of an unknown transfer function, along with the fact that this system is openloop stable:
Now I can directly see this is a type 1 system. - So there ...
0
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2answers
73 views
Stochastic optimal control different in finance and engineering [closed]
What is the different between stochastic optimal control approach in finance and engineering?
Why methodes used in finance approach like Ito calculus are not used in engineering?
