Questions tagged [control-theory]

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11
votes
3answers
7k 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
169 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 ...
4
votes
2answers
2k 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
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6answers
715 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
1answer
191 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
2answers
225 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 ...
2
votes
4answers
807 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
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
2
votes
2answers
354 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, ...
2
votes
2answers
724 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 ...
2
votes
2answers
162 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 ...
2
votes
1answer
797 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 ...
2
votes
1answer
435 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 ...
1
vote
2answers
579 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
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3answers
1k 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
126 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
1k 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
163 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
2answers
2k 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
3k 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 ...
1
vote
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 ...
1
vote
3answers
170 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
155 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
214 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
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0answers
62 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 ...
1
vote
0answers
52 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 ...
1
vote
1answer
50 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]}...
1
vote
1answer
36 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 ...
1
vote
1answer
64 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
67 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
67 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
118 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 ...
0
votes
3answers
119 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
159 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
407 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
3answers
997 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
118 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
82 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 ...
0
votes
3answers
69 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 ...
0
votes
1answer
265 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
2answers
119 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
285 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
97 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}\$ ...
0
votes
1answer
126 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
1answer
496 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
54 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
2answers
346 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 ...
0
votes
1answer
153 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. ...