Questions tagged [control-theory]

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Examples of situations where using classical control methods are better than modern methods

I'm doing some reading on control systems at the moment and when reading pages on classical control methods, some sites state that they are preferred in industrial applications. I've read that simple ...
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Finding Derivative Gain for PD Controller

I am trying to design a PD controller $G_c(s) = K_d(s+z_c)$ with the following requirements: No overshoot, $\zeta = 1$ Settling time $T_s = 0.0002s$ The transfer function that I am currently working ...
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why do we need state feedback in H-infinity concept instead of output feedback

I have faced control of a flexible manipulator which have a zero dynamic related to flexible parts dynamic. the zero dynamic states (generalized states) are not observable in input-output dynamic and ...
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Scalability in the context of optimization and control systems

I am having a hard time trying to make sense of the phrase "Scalable optimization". I read from a few papers discussing that some global optimization solvers like BARON, ANTIGONE, etc. do ...
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51 views

Stability of a closed loop control system

I have a question regarding control theory. Say I have a closed loop feedback system and I have found the closed loop transfer function, how would I then assess the stability of my closed loop system ?...
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1answer
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Is it possible to solely use a P-controller for velocity control?

Let's say I want a robot to run at a certain speed. I have one motor attached to each robot rear wheel. The feedback value to the controller comes from an encoder, which outputs pulses per time unit, ...
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1answer
37 views

Determine Stiffness (k) and Mass (m) of a system from impulse response

I have a test sample (Piezo Diaphragm) which I am actuating with a voltage supplied to the sample to assess the impulse response. When this voltage is supplied to the sample a deformation per unit ...
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1answer
40 views

How to model this real-world system to define transfer function for stability?

The system shown is an off-axis drive system that rotates the platform to 60° via a substantially-sized NEMA 34 stepper motor. The axial force required by the stepper/ballscrew assembly has already ...
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1answer
24 views

Transfer Function

Hi Guys I am trying to evaluate the following transfer function below can anyone verify if this is correct $$e_i = -d_{r,i} + d_i $$ $$d_i = q_{i-1}-q_i$$ $$d_{r,i} =H_iq_i$$ $$Therefore, e_i = -...
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1answer
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Closed Loop transfer Function

Hi Guys wanted some help for breaking down a block diagram which can be seen below. I know that typically with feedback systems be it negative or positive you would employ using the following:- Close ...
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1answer
39 views

Determine the parameters for this given nyquist plot

I have seen quite many of this type of question and I want to find how to solve them but I haven't cracked it yet. For example this is one: My thoughts so far: Replace $$s \rightarrow j\omega$$, $$G(...
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1answer
42 views

Which way of solving from nonlinear control to choose?

I have a nonlinear system: \begin{cases} x'=f(x)+u \\ y=f(x) \end{cases} where $f(x)$ - gradient of some one-extremal function (for example $f=e^{-(x)^2}$), i.e. $\frac{df}{dx}$. Task: I want ...
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2answers
107 views

Why does accuracy of temperature PID controller drop over time and how to eliminate it?

What am I trying to control? I have a container with approximately 3*2*6 meters (width, height, length). I am controlling through PID the ...
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2answers
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High pass filter and differential equation relationship

Consider the problem stated as follows: A signal y passes through a high pass filter $\frac{s}{s + ω }$. A high pass filter with cutoff frequency ω isolates the variations of this optimized variable ...
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4answers
83 views

PID controller - Counterproductive derivative

I'm having trouble understanding the derivative part of a PID controller, because it sometimes seems to react the opposite way that I would like. Let's use a simple example where : the controlled ...
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1answer
51 views

PID Control: Is adding a delay before the next loop a good idea?

I am implementing PID control in C++ to make a differential drive robot turn an accurate number of degrees, but I am having many issues. Exiting control loop early due to fast loop runtime If the ...
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1answer
68 views

What's the difference between Fuzzy PI, PD and PID controllers?

I am investigating fuzzy control and I am a little confused, I have come across 3 models and I can't quite fathom out what is going on. In this PD+I controller, I can see the error signal being ...
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35 views

Controlling the dynamics of nonlinear systems with an unknown steady state

On the one hand, the question is simple, on the other hand, I need the help of specialists in control theory. Let's take a simple gradient dynamical system: $\frac{dx}{dt}=\frac{df}{dx}$ where $f=e^{-(...
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1answer
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What does “analytical design” mean?

What is meant by "designing analytically" ? Especially in control systems design Does it mean theoretically design?
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Is it true that points of root locus only satisfiy the angle condition?

So , I was reading a course book : ''Modern Control Engineering '' by Ogata and I came forward this statement that made me skeptical: ''The points of root locus only satisfiy the angle - condition. ...
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Complementary filter in MPU_6050 is giving me the wrong answer when the system is accelerating

So I am using a complementary filter to find the attitude in my quadcopter, doing the following $$\text{angle} = 0.98\cdot (\text{angle}+\text{dt}\cdot \text{angle_rate})+0.02\cdot \text{...
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1answer
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Feedback Control Question: Finding compensator numerator (B(s)) and denominator (A(s)) polynomials to satisfy a specific requirement

I wish to find the polynomials B(s) and A(s) in the following compensator equation: A(s)D(s) + B(s)N(s) = F(s) Given, $$N(s) = s - 2$$ $$D(s) = s^2 - 1$$ $$F(s) = s^2 + 3*s + 4$$ Condition The degree ...
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2answers
37 views

Determine the transfer function of a movement equation

The problem is the following. I have to control a spaceship (assuming no gravity, no mass, no friction / no external forces). In other words, the first equation in this question leads to $0 = 0$. My ...
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2answers
36 views

What is the output of a signal in time domain that passed through a High Pass Filter with simple transfer function

If a signal function $ U(t) = 25 – (5 – t)^2$ is passed through a high pass filter with transfer function $\frac{s}{s + ω}$. what is the output signal Y(t). I know that the transfer function $H(s) = \...
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Evaluating Steady State Error Constant for a Discrete Time Control System with Kronecker Delta Input

Hello there, hope you are doing well. I am working on a Discrete Time Control Systems homework and at a certain part of it, the question asks me to find the steady state error of the system. I ...
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35 views

How to model a double transfer function in Simulink?

I'm trying to model an actuator in Simulink based transfer functions previously derived. One of functions is $$\omega_p=G_2(K_cG_1V_c-c)$$ where $$G_1=\frac{K_e}{\tau_es+1}$$ $$G_2=\frac{1}{c+...
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1answer
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Is there any application of control engineering to the study of algorithms stability or computer science theory?

I am an undergraduate student in Electrical and Computer engineering. In our 5th semester we have a obligatory "Introduction to control systems course". I was wondering if these bunch of ...
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1answer
58 views

Feedback loop and zero - error in steady state

I need help with this exercise. I 've tried many times with pen and paper but I'm stuck. I don't want a full answer but some feedback . Here is my progess: $$\frac{dx}{dt} = Ax(t) + Bu(t) \Rightarrow ...
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45 views

Changing the quality of the transient process in a nonlinear system (in Mathematica)

I urgently need advice and help. I have a system of differential equations like this: $\begin{cases} \frac{dx}{dt} = y[t] \cdot \alpha \cdot sin(\omega t) + \frac{d}{dt}(\alpha \cdot sin(\omega t)) ...
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1answer
54 views

Numeric quadrature vs summation of running costs in model predictive control

Usually, an MPC consists of discretizing the optimal control problem in time using some numerical quadrature scheme. So the infinite-dimensional OCP reads $$\begin{aligned}J(\vec{u}) &= \varphi\...
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2answers
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How do I interpret states in the MATLAB System Identification Toolbox?

I am using the MATLAB System Identification Toolbox to estimate a 3rd order state space plant model. More precisely, the plant is a car with an Arduino mounted on it. The car takes in a PWM duty cycle ...
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Discrete measurement - continuous observer design

I have to design a controller for the above system where the two pulse generators (red blocks ) are synchronized (measurements are only available at discrete points). However, my understanding is that ...
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1answer
31 views

Fixed end points optimal control problem

Given two points $(t_0,x(t_0)=x^{0})$ and $(t_1,x(t_1)=x^{1})$ in the $(t,x)$ plane, the objective is to find an optimal trajectory $x^{*}(t)$ such that the cost function \begin{equation}\label{eq:1} ...
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1answer
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Transfer function into block diagram and matrix form

I'm reading a book on Control System Design and running into the same issue I had in Kinematic Design. When things are presented in a format without any numerical examples it just appears as gibberish ...
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1answer
54 views

Temperature controller using pt-1000 sensor

I need to control the temperature of a system with high accuracy with error value of $0.1$ degrees celsius +-. I will be using temperature sensor PT-1000. I need to know what would be the best option ...
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1answer
111 views

How to calculate the open-loop transfer function with disturbance at the input of the plant

I have the system as follows: I am trying to find the transfer function: $$ T(s) = \frac{Y(s)}{U(s)}$$ where $Y(s)$ is the output and $U(s)$ is the input of the plant. The plant is $H(s)$. I have got ...
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1answer
50 views

Differential Equation for: Locking a laser's frequency with a PI controller

I think I have a good understanding of differential equations, so I would like to first try to understand my system in terms of differential equations before transforming my system into the more ...
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2answers
99 views

What does the Lagrange Equation do for State-space systems

I'm not sure if this is a good place to ask this question, but I'm currently taking Control System Design and considering everything is this deriving of equations I'm having a hard time actually ...
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44 views

Research of transients in nonlinear systems with linear dynamic links

I am having difficulties of this nature. There is a nonlinear system of the following type: I need to analyze analytically the transient process in such a system. The analytical study of the ...
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1answer
34 views

Did I get the correct result? Block reduction problem

After solving I got $$T(s) = \frac{s^{2}+3s+3}{(s+1)(s+2)}$$ and for the stability of the system I got: $$ s_1 = -1 $$ $$ s_2 = -2 $$ So, is the system stable?
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1answer
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Adding phase error to a system based on phase margin

I have a MIMO transfer function and referring to a research work, I have found a phase margin for this MIMO system. I want to check and see the system blow when a phase error greater than the phase ...
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2answers
63 views

mass-friction-spring system with closed loop

My professor told us that it is possible to see the friction in a mass-friction-spring as the contribution of a closed loop control system. He wrote the following formulas: Transfer function: $$G(S)=\...
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1answer
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Can someone explain how the output of this control system is derived?

I understand equation (1), but I really don't see the connection between equation (2) and the picture. For starters, shouldn't the $b_0$ constant be multiplied by $$net(n)-(a_1 \cdot net(n - 1) + a_2 \...
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1answer
75 views

Gain and Phase Margins from Bode Plot

What's the interpretation of the margins when the curve of magnitude never crosses 0 dB or the phase curve never crosses the -180º? For example: $$G(s) = \frac{s+20}{(s+1)(s+7)(s+50)}$$ I know that ...
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Nyquist Stability Theorem and Clockwise/Counter Clockwise Encirclements

According to argument principle, if a contour encircles a number of poles and zeros of a transfer function, the number of origin encirclements can be deduced by : ...
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108 views

A clarifying question on Lasalle invariance principle

Given a nonlinear system \begin{equation} \dot{x}=f(x),~x(0)=x_0 \tag{1} \end{equation} where $f\in{\mathcal{C}^{1}}:D\to\mathbb{R}^{n}$. The Lasalle invariance theorem statement goes as follows: Let $...
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1answer
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designing compensator with certain specification

Ηere is an open-loop transfer function and specifications for compensator design. I defined the required poles and defined the angles according to the normal procedure of the root locus method and ...
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1answer
69 views

Zeroing a ventilator's volume measurement in the face of drifty sensors

I'm a software engineer working with http://respira.works to build an open-source ventilator for COVID-19. Notably, I'm not a controls person or a hardware person, so please forgive me. Background ...
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2answers
65 views

Control of a nonlinear static MIMO System

I am currently writing my master thesis and trying to design a controller for my system. However, the system is somewhat unconventional. It has a large number of inputs and outputs, is static, non-...
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37 views

Skew-Symmetric Gain Matrix to Encourage Exploration

I am reading a paper on controls and it has the following snippet: We propose to use the control law $$u_i = K(CV_i − p_i)$$ , where K is a (potentially time-varying) uniformly positive definite ...

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