Questions tagged [control-theory]

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43 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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41 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
77 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
67 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
47 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
222 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
88 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
148 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
34 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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0answers
109 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
154 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
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 ...
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1answer
22 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
99 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
122 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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3answers
875 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
425 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
158 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
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 /...
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1answer
112 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
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 ...
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1answer
229 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
308 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
778 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
61 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
296 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
674 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
161 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
335 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
410 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
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. ...
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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{...
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3answers
163 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
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'...
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1answer
254 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
377 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
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?
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0answers
143 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 ...
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6answers
706 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 ...
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1answer
162 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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74 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 ...
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0answers
463 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 ...
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1answer
153 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 ...
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1answer
2k 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 ...
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2answers
566 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 ...
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1answer
509 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
248 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 ...
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1answer
195 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 ...
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3answers
993 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 ...