Questions tagged [control-theory]

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22 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 $\frac{Y(s)}{U(s)}$. The plant is $H(s)$. I have gotten up until $$ \frac{Y(s)}{H(s)} = T_{\text{out}}(s) - U(s) $$ Moving $U(s)$ to the left by ...
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1answer
20 views

Determine the bandwidth of a closed loop system [closed]

The unity feedback system with loop transfer function is given as $G_c(s)G(s) = \dfrac{50}{s(s+40)}$. Determine the bandwidth of the closed loop system. options 6.4 rad/sec 3.2 rad/sec 12.8 rad/sec 1....
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1answer
20 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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13 views

Do fuzzy logic controllers create a model of a system?

I know model predictive controllers require a mathematical model of a system to operate, and fuzzy logic controllers do not. If I define a set of rules for a fuzzy logic controller, a control surface ...
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2answers
20 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
25 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
30 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
52 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
69 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
60 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
46 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
60 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
69 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
63 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
60 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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35 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
61 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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56 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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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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26 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
66 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
83 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
98 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
65 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
43 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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37 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
39 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
39 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
69 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
86 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
36 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
28 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
49 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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2answers
48 views

Chemical engineering equivalancy to the spring-mass-damper/RLC circuit

I understand the equivalency between the MSD and RLC circuits. Mass ~ resistance, spring ~ inductor, damper ~ capacitor. With the equations of the form MSD: $$ m\ddot{x} + c\dot{x}+ kx = F $$ ...
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1answer
96 views

Proportional-Derivative compensator design

I have been struggling with the following problem for a few days now and would greatly appreciate some assistance. I'm new to control systems and have very little experience with PD controllers and ...
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2answers
93 views

Increasing Kd in PID control loop

Why does increasing derivative gain $K_d$ in a PID controller loop lead to a reduction in overshoot and an increase in rise time? This is not a homework question, it is a question to improve my ...
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1answer
110 views

Does this PID-like algorithm make any sense for a solar inverter?

The application I want to implement the control of a photovoltaic inverter. The goal would be to keep the consumption of a microgrid (the power absorbed from the grid) to a constant value. Notes: I ...
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1answer
51 views

Control System; Finding resonant frequency of 3rd order

We've been requested to find the resonant frequencies of a 3rd order plant in class and were presented to the following method to do so: My question is, when using the $\ \omega_r $ formula, to find ...
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0answers
32 views

Kalman Filter by Orthogonal Projection

I'm working through the derivation for the Kalman filter using orthogonal projections. It's pretty intuitive that if we want to generate the best linear estimate for an $n$-vector $x$ using some $m$-...
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1answer
76 views

How to obtain plant parametric model of given system?

Consider the system: $$ y(s)=b\frac{e^{−sτ}}{s+a}u(s) $$ where a,b are unknown, constant parameters and $\ τ>0 $ is an unknown delay constant. How can I obtain a plant parametric model for this ...
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0answers
49 views

LQR Implementation in MATLAB

I am trying to implement a simple LQR controller in MATLAB for a purely deterministic system. The code is shown below: ...
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1answer
53 views

What are the drawbacks of inceasing the bandwidth of the system?

I have a doubt concerning the closed loop frequency responce of a control system. Suppose I have the following situation: in which is plotted the frequency response of a system with different ...
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1answer
52 views

Develop linear parametric model of a third order plant

Consider we have the third order plant described by the equation: $$ y = G(s)u $$ where $\ G(s) = \frac{b_{2}s^{2}+b_{1}s+b_{0}}{s^{3}+a_2s^2+a_1s+a_0} $ If we assume that all parameters $\ a_0,a_1,...
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1answer
44 views

Problem finding value of the gain such that the closed loop is stable

I have the following transfer function: $G(s)=\frac{-s^3 +s}{s^4+3s^3+2s^2}$ and this is a transfer function of a plant with two poles in the origin. So I want to desing a controller with two poles ...

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