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Questions tagged [control-theory]

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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?
5
votes
2answers
154 views

Types and regulation schemes LDOs

LDOs, or low-dropout linear regulators, come in various types, but it can be difficult to distinguish them, and to the novice engineer, this regulator is often made to seem deceptively simple. Some ...
3
votes
6answers
514 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 ...
3
votes
2answers
725 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 /...
3
votes
1answer
187 views

I want to find \$\frac{\hat{\theta}}{\hat{T}}\$

I have the following block diagram, and I want to find the transfer function \$\frac{\hat{\theta}}{\hat{T}}\$. I am not sure how to do this, I've got the rules of connection in a series or parallel, ...
2
votes
4answers
608 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 ...
2
votes
2answers
391 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
vote
2answers
458 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 ...
1
vote
3answers
665 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 ...
1
vote
4answers
120 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'...
1
vote
2answers
919 views

What happens when P controller's gain equals zero?

For example, I use Routh-Hurwitz Cirterion to examine the following system with P controller gain \$K\$: $$\frac{{K\left( {2 - s} \right)}}{{{s^3} + 3{s^2} + 5s + 3}}$$ I closed loop it with \$H=1\$ ...
1
vote
1answer
126 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 ...
1
vote
1answer
4k views

Difference between a controller (e.g PD) and a compensator(e.g Lead)?

Really.What is it?Can't find anything anywhere related to it...Please don't give fancy examples.Just tell me the difference
1
vote
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
vote
1answer
90 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, ...
1
vote
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 ...
1
vote
3answers
102 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
vote
1answer
137 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 ...
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 ...
1
vote
3answers
186 views

Bode plot of transfer function?

I am having trouble where to start an attempt at sketching the Bode plot for the following transfer function: I know I need to rewrite it into its proper form, making both the lowest-order term in ...
1
vote
1answer
1k views

What is the difference between disturbance and noise for dynamic systems?

In most references from dynamic system theory, the following linear continuous dynamic system is considered. $$\frac{\text{d}x(t)}{\text{d}t}=Ax(t)+Bu(t)+Dd_{1}(t)\quad (1)$$ $$y(t)=Cx(t)+Ed_{2}(t) \...
1
vote
1answer
50 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 ...
1
vote
1answer
520 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 ...
1
vote
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
0answers
62 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 ...
1
vote
0answers
111 views

a linear system is a bilinear transformation of anyone its circuit elements

I am reading about dissection theorem and the part below is a bit confusing. Could anyone one explain it? Any transfer function of a linear system is a bilinear transformation of anyone its ...
1
vote
1answer
194 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
votes
3answers
111 views

PID Control: Controller of the type \$\dfrac{1}{s+k}\$

In PID control an integrator action is represented by \$\dfrac{1}{s}\$ Does anyone know what would be the effect of using \$\dfrac{1}{s+k}\$ instead of \$\dfrac{1}{s}\$, where \$k\$ is a constant? ...
0
votes
1answer
113 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 ...
0
votes
2answers
175 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 ...
0
votes
1answer
46 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
2answers
104 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 ...
0
votes
2answers
245 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{...
0
votes
1answer
2k views

How to find system overshoot (Mp) from Bode diagram

In some questions (in linear control theory) it is desired to design a controller to change the system overshoot (Mp), my question is: Is it possible to find Mp or damping factor directly from Bode ...
0
votes
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 ...
0
votes
4answers
139 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
votes
1answer
89 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
votes
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
votes
1answer
107 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. ...
0
votes
1answer
183 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
votes
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 ...
0
votes
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?
0
votes
0answers
41 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 ...
0
votes
1answer
20 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\...
0
votes
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
votes
0answers
24 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 ...
0
votes
0answers
152 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
votes
1answer
144 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 ...
0
votes
0answers
390 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 ?...
0
votes
0answers
54 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 ...