Questions tagged [control-theory]

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1answer
20 views

Animation of system response with python [closed]

I am trying to animate the root locus for a tranfer function G as kp, changes. This is my code: ...
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1answer
16 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
24 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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0answers
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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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0answers
27 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
35 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 ...
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1answer
36 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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0answers
40 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
46 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
65 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 ...
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0answers
31 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 ...
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1answer
29 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
33 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 ...
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1answer
51 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
49 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
35 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
34 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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0answers
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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
32 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
26 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 ...
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2answers
55 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
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 \...
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1answer
66 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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1answer
67 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 : ...
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2answers
87 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
71 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 ...
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1answer
64 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
62 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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0answers
36 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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1answer
73 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)\...
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0answers
62 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{...
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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 : \...
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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 ...
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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 ...
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1answer
104 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) ...
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3answers
140 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) =...
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1answer
78 views

Physical interpretation of a Bode plot

I have a few questions regarding the physical interpretation of the information presented on a Bode plot. I believe it is one of those cases where I "don't know what I don't know", so please bear with ...
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0answers
25 views

How to create a Complementary Filter for a linearly accelerating vehicle to obtain estimate of orientation in quaternion?

A complementary filter (CF) uses orientation obtained calculated from gyroscope, accelerometer and magnetometer to find a more accurate measurement of orientation. However, when my sensor is ...
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1answer
64 views

Why phase margin and gain margin should be positive?

In many textbooks it's given that gain margin (in db) and phase margin of the system needs to be positive for the system to be stable. I could not find the reason behind this. Could someone explain ...
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0answers
38 views

Mathematical transformation of a heading angle to a roll angle

I'm trying to understand a function in a SIMULINK example of a path following UAV simulation. The gist is that, the UAV Waypoint Follower block provides a required heading from a list of waypoints and ...
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1answer
40 views

Order of a system

I can find it when the transfer function is written in standard form but I don't know how to find it if it is written differently. For example $G(s)=\dfrac{1}{s(s+1)^3}$, is this order three or four?
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1answer
40 views

Using Integral gain for motor positioning

I'm struggling to see how Integral gain is used for motor positioning. Suppose we have an AC motor (with a 2048PPR encoder on the shaft) connected to a winch which drives an object forwards and ...
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1answer
74 views

Passivity in State Space Systems

Suppose I have the state space system $a\dot{x} = -x + \frac{1}{k}h(x) + u$, and output $y = h(x)$, where $a,k > 0$. The only information I'm given about $h(x)$ is that $h\in[0,k]$. I want to show ...
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1answer
39 views

Bounds to prove exponential stablity for given Lyapunov function

Problem 3.6 in Khalil's Nonlinear Control: Use given Lypunov candidate function to prove that the origin is exponentially stable. The system is $$\dot{x}=\begin{bmatrix}x_2\\-h(x_1)-2x_2\end{bmatrix},...
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0answers
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avoidance with LQR

I'm interested in using linear quadratic regulators (LQR) to model prey avoidance behaviors. I want to adapt the LQR algorithm to incorporate dynamics and state costs that maximize the distance from a ...
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2answers
89 views

How to obtain transfer function of control diagram with Internal Model Control?

I want to design a robust control system using the internal model design specifications. The block diagram is the one shown below: I am trying to obtain the transfer function $\ \frac{Y(s)}{R(s)} $ ...
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1answer
37 views

Tuning a cascaded attitude and attitude rate PID controller

Assume that I have an object in 3D, and I want to have a controller that stabilizes its orientation (also referred to as "attitude"). To be sure we are clear: attitude is measured in "degrees" or "...
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2answers
40 views

Applying full state feedback on DC motor with torque load

I tried to apply full state feedback on DC motor (with no load) and it works fine in the simulation on Simulink But the question is if I have a load applied on the motor (let’s say constant load or ...
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1answer
29 views

Noise sensitivity transfer function

Consider we have a second order system (plant) described by the following transfer function: $$ P(s) = \frac{b_0}{s^2+a_1*s+a_2} $$ which is controller by a PD-controller: $$ C(s) = K_p+K_ds $$ ...
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1answer
59 views

How to reduce oscillations (rapid changes of control signal) when controlling a real system, which occur due to noise in measurement from sensors?

I have a real mechanical system (ball & beam) which I want to control. The system is approximated by the second order transfer function: $$ T(s) = \frac{b_0}{s^2+a_1s+a_2} $$ and in state-space ...

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