Questions tagged [control-theory]
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293
questions
0
votes
1answer
35 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 ...
0
votes
1answer
20 views
Transfer Function
Hi Guys I am trying to evaluate the following transfer function below can anyone verify if this is correct
$$e_i = -d_{r,i} + d_i $$
$$d_i = q_{i-1}-q_i$$
$$d_{r,i} =H_iq_i$$
$$Therefore, e_i = -...
0
votes
1answer
32 views
Closed Loop transfer Function
Hi Guys wanted some help for breaking down a block diagram which can be seen below. I know that typically with feedback systems be it negative or positive you would employ using the following:-
Close ...
0
votes
1answer
33 views
Determine the parameters for this given nyquist plot
I have seen quite many of this type of question and I want to find how to solve them but I haven't cracked it yet. For example this is one:
My thoughts so far:
Replace $$s \rightarrow j\omega$$, $$G(...
0
votes
1answer
36 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 ...
2
votes
2answers
100 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 ...
1
vote
2answers
41 views
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 ...
2
votes
4answers
78 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 ...
0
votes
1answer
48 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 ...
2
votes
1answer
63 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 ...
0
votes
0answers
31 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^{-(...
1
vote
1answer
24 views
What does “analytical design” mean?
What is meant by "designing analytically" ?
Especially in control systems design
Does it mean theoretically design?
0
votes
1answer
28 views
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. ...
0
votes
1answer
25 views
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
$$\text{angle} = 0.98\cdot (\text{angle}+\text{dt}\cdot \text{angle_rate})+0.02\cdot \text{...
0
votes
1answer
32 views
Feedback Control Question: Finding compensator numerator (B(s)) and denominator (A(s)) polynomials to satisfy a specific requirement
I wish to find the polynomials B(s) and A(s) in the following compensator equation:
A(s)D(s) + B(s)N(s) = F(s)
Given,
$$N(s) = s - 2$$
$$D(s) = s^2 - 1$$
$$F(s) = s^2 + 3*s + 4$$
Condition
The degree ...
0
votes
2answers
33 views
Determine the transfer function of a movement equation
The problem is the following. I have to control a spaceship (assuming no gravity, no mass, no friction / no external forces). In other words, the first equation in this question leads to $0 = 0$. My ...
1
vote
2answers
33 views
What is the output of a signal in time domain that passed through a High Pass Filter with simple transfer function
If a signal function $ U(t) = 25 – (5 – t)^2$ is passed through a high pass filter with transfer function $\frac{s}{s + ω}$. what is the output signal Y(t). I know that the transfer function $H(s) = \...
1
vote
0answers
23 views
Evaluating Steady State Error Constant for a Discrete Time Control System with Kronecker Delta Input
Hello there, hope you are doing well.
I am working on a Discrete Time Control Systems homework and at a certain part of it, the question asks me to find the steady state error of the system. I ...
0
votes
0answers
32 views
How to model a double transfer function in Simulink?
I'm trying to model an actuator in Simulink based transfer functions previously derived.
One of functions is $$\omega_p=G_2(K_cG_1V_c-c)$$ where $$G_1=\frac{K_e}{\tau_es+1}$$ $$G_2=\frac{1}{c+...
1
vote
1answer
39 views
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 ...
2
votes
1answer
52 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:
$$\frac{dx}{dt} = Ax(t) + Bu(t) \Rightarrow ...
0
votes
0answers
44 views
Changing the quality of the transient process in a nonlinear system (in Mathematica)
I urgently need advice and help.
I have a system of differential equations like this:
$\begin{cases} \frac{dx}{dt} = y[t] \cdot \alpha \cdot sin(\omega t) + \frac{d}{dt}(\alpha \cdot sin(\omega t))
...
0
votes
1answer
53 views
Numeric quadrature vs summation of running costs in model predictive control
Usually, an MPC consists of discretizing the optimal control problem in time using some numerical quadrature scheme. So the infinite-dimensional OCP reads
$$\begin{aligned}J(\vec{u}) &= \varphi\...
1
vote
2answers
67 views
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 ...
1
vote
0answers
33 views
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 ...
1
vote
1answer
30 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}
...
0
votes
1answer
44 views
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 ...
0
votes
1answer
52 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 ...
-1
votes
1answer
79 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 ...
1
vote
1answer
48 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 ...
-1
votes
2answers
70 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 ...
0
votes
0answers
43 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 ...
-1
votes
1answer
33 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?
1
vote
1answer
29 views
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 ...
0
votes
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:
$$G(S)=\...
0
votes
1answer
75 views
Can someone explain how the output of this control system is derived?
I understand equation (1), but I really don't see the connection between equation (2) and the picture.
For starters, shouldn't the $b_0$ constant be multiplied by
$$net(n)-(a_1 \cdot net(n - 1) + a_2 \...
-1
votes
1answer
70 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 ...
-1
votes
1answer
145 views
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 : ...
6
votes
2answers
100 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 $...
-1
votes
1answer
73 views
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 ...
1
vote
1answer
65 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
...
-1
votes
2answers
64 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-...
0
votes
0answers
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 ...
-1
votes
1answer
96 views
How to find the transfer function of a control system?
I have a linear control system defined by the following equations:
\begin{array}{l}\dot{x}_{1}(t)=-\frac{1}{2}\left(x_{1}(t)-x_{2}(t)\right) \\ \dot{x}_{2}(t)=\frac{1}{10}\left(2 x_{2}(t)-10 x_{1}(t)\...
2
votes
0answers
63 views
Converting nonlinear system into equivalent nonlinear of the Byrnes-Isidori normal form
I have a nonlinear system (Ball & Beam) which is described by the following equations of motion:
$$ \ddot{y} + \frac{mg}{a} \sin(θ) -\frac{m}{a}y\dot{θ}^2 = 0 $$
$$ \ddot{θ} + \frac{2m}{b}y\dot{...
1
vote
0answers
43 views
Lyapunon candidate function to derive parameters estimation law
I have a system and a reference model represented in state space in the following form:
\begin{gather}
\dot{x} = Ax+Bu \\\
u = \hat{K}(t)x+\hat{k}_r(t)r \\\
\\
A_m = A+BK \\\
Bk_r = B_m \\\
K,k_r : \...
0
votes
0answers
27 views
What does “Coupling Effect” refer to in MIMO systems?
Here is the block diagram of the system.
G11 relates the input R1 to the output Y1, G12 relates the input R1 to the output Y2 similarly for R2.
What is the effect of coupling-which is as I know is ...
2
votes
1answer
67 views
Input-output representation to state space
How do you create a state space representation of the following input/output equation:
$$ \dot{y} = -ky + u + a\sin(ωt) $$
where the parameters $k$, $a$, and $ω$ are unknown.
The end goal is to ...
1
vote
1answer
145 views
Root Locus and Routh–Hurwitz stability criterion
A satellite launcher has a unit feedback system, whose TF global open loop is given by:
$$G_c(s)G(s) = \frac{K(s^2-4s+18)(s+2)}{(s^2-2)(s+12)} $$
a) Draw the root locus for this function
b) ...
1
vote
3answers
259 views
Determine the gain K from a root locus
I'm studying Root Locus method and I still confused. The question below exemplifiques my doubt.
Determine the $K$ gain so that the dominant roots have a damping factor equal to $0.5$, where
$$G(s) =...
