# 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.

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### Open loop transfer function - explaination

Assume there is a simple closed-loop control system with G(s) representing the plant and H(s) representing the feedback element: Could any one explain what exactly is open-loop transfer function ? ...
51 views

### About controllable and observable discrete-time LTI systems

Consider the discrete-time LTI system with the following state-space representation: \begin{align} {x}_{k+1}&={A} {x}_k+{B} {u}_k &;{A} \in \mathbb{R}^{n \times n}, {B} \in \mathbb{R}^{n \...
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### For the equation below, how would I calculate the gain required for a settling time of 1 s?

The equation is: $G=\dfrac{k(s+4)}{(s+1)(s^2+6s+13)}$ How would I calculate the gain (k) required for a settling time of 1 s? By using $ts=\dfrac{4}{(ωζk)}$ the closest value I got was ...
173 views

### Isolation Topology in SMPS

I have been researching SMPS designs as a hobby recently and finally have the courage to build one for theoretical and practical understanding. I have chosen an isolated design looking at several ...
96 views

### Order of Complexity

Generally, number of independent state variables (order of complexity of a system) is equal to the number of reactive elements in RLC network. But, if capacitor and voltage source loops are present ...
101 views

### Derive state space from initial value problem

I am given the following initial value problem $y^{(4)} - y = u$ with $y^{(3)}(0)=0, \ddot{y}(0)=1, \dot{y}=1, y(0)=10$ and am supposed to calculate the state space in the usual form \begin{...
741 views

### Assign Bode plots to Nyquist diagrams

How do I assign the following Bode plots to their corresponding Nyquist diagram? Can i tell the number of poles of the transfer function of the nyquist plot, by looking at w→infinity (from which of ...
1 vote
357 views

### Deriving a transfer function from Nyquist plot

I am given a half Nyquist plot and exercise as below I know how to plot a Nyquist curve for a given transfer function but I have trouble doing it the other way. I stumbled upon this post Deriving ...
250 views

### Compensator design for control systems

Currently, I'm working on linear control course from Nise's book. In the root-locus design chapter, some methods were explained for lag and lead compensator design which uses root-locus properties. ...
54 views

### Routh Hurwitz Criterion for Stability

What do the rows of the Routh table represent? What is the significance of writing the powers of 's' in the zeroth column?
1 vote
43 views

### Confused about how Loop 2 is defined

In one of my exercises, I am presented with the following circuit: We are asked first to write some loop equations for the circuit. Naturally, they are given to be defined as: What I cannot ...
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### Finding closed loop interval of stability with open loop frequency response data

I have the following open-loop frequency response data of a system: Frequency (rad/s) Gain (dB) Phase (degrees) 0.0628 9.3080 -137.4711 0.1257 8.2370 -126.3069 0.2513 7.8477 -151.0235 0.6283 9....
1 vote
361 views

### What are the gain and phase margins from this Bode plot?

I thought I had a decent grip on how Bode plots work yet for this model that I am working on, I need to implement a lead or a lag compensator. A lead compensator, which I was thinking about ...
898 views

### 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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332 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, ...
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269 views

### Laplace of third-order lead-lag filter

For Butterworth low-pass filters, the Laplace function of the third-order filter is $$H(s)= \frac {1}{\left(1+\frac{s}{\omega_c}\right)\left(1+\frac{s}{\omega_c}+\frac{s^2}{\omega_c^2}\right)}$$ ...
295 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 ...
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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 ...
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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
4k views

### 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 ...
544 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, ...
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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 ...
72 views

### 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 ...
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1 vote
428 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 ...
50 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 ...
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### Meaning of "Dynamics" in terms of control systems?

What is meant by "dynamics" in context of control systems? For example what is difference between the dynamics of an aeroplane and a car? This question below answers to some extent my ...
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### 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 ...
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### Decide P controller gain K so that phase margin is 50°

I need help finding the gain $K$ so that the phase margin for the system equals 50°. $$F(s) = K$$ $$G(s) = \dfrac{1}{(s+1)^2}$$ $v$ is a process disturbance sinusoid with amplitude 2.5 and ...
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### 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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### 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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### 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 vote
1k 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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238 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 ...
1 vote
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### 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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### Nyquist stability criterion for positive feedback

it is known that the stability of a system with negative feedback may be analyzed through the Nyquist stability criterion, which is based on observing the number of turns around the point (-1;0) in ...
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1 vote
106 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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560 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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### 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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1 vote
109 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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