Questions tagged [control-systems]
Questions on the use of Mathematica to analyze, design, and simulate continuous- and discrete-time control systems.
218
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28
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How to plot the input to a state-space closed loop model?
I have a mathematica notebook to build the state-space model of a system from its differential equations, calculate LQR gains and simulate the system response.
...
- 101
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0
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27
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How to use the OutputResponse function with multiple inputs?
I have a state-space model with 2 inputs and 2 outputs.
The documentations of mathematica to obtain the output response define the usage as ...
- 101
0
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0
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37
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How to set reference value a State-Space Model with simulating the reponse?
I have a mathematica notebook to build the state-space model of a system from its differential equations, calculate LQR gains and simulate the system response.
...
- 101
0
votes
0
answers
29
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Problem in visualization of control variable from the NDSolveValue solution
I am trying to solve some optimal control problem with free endpoint and bounded control in the switching environment.
First of all, it would be great if someone will check the code and the logic ...
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-1
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1
answer
59
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How to Paste Complex Transfer Function Equation to Excel [closed]
I am trying to paste this transfer function to Excel, is it possible?
0
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1
answer
69
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How can i derive this using StateSpaceModel?
Please how can I solve this using StateSpaceModel.
eqns := {(lp \[Theta]''[t]) + m g Sin [\[Theta][t]] + c \[Theta]'[t] -
Sin [\[Theta][t]] y0''[t] == 0};
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4
votes
1
answer
71
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Discontinuous ODE results in NDSolve::ndinid warning, initial condition is not in the range specified by the discrete variable (internal variable)
The equations and code are below.
The short version is:
I know the error is because NDSolve is doing something in the background to handle the discontinuous ODE. ...
- 53
2
votes
1
answer
52
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Matrix Rank Error
I have a linear State Space model and was trying to tell if it was completely controllable. When I get the matrix with ControllabilityMatrix and then calculate the rank I get an incorrect matrix rank ...
- 21
3
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1
answer
106
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0
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0
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29
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Set the MPC tracker arguments
I have an affine system $\dot x(t)=X(x(t))+u(t) Y(x(t))$ with one input $u$ and two outputs (corresponding to the state $x=(x_1,x_2)$ of the system) and I would like to start from ...
- 496
1
vote
2
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122
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NDSolve with piece-wise function and BVP
How to numerically solve a system of differential equation with boundary conditions and piece wise affine functions ?
Consider the following system of differential equations from some optimal control ...
- 11
1
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0
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55
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Phase unwrapping of transfer function model for calculating group delay [duplicate]
Suppose that I have a transfer function model
...
- 31
0
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2
answers
125
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Plotting horizontal lines on Bode plot
I have an array of transfer functions and plotted multiple Bode plot. Now I need to add a horizontal line to show where all these Bode plots attain a gain of -8db. I know that previously people ...
- 31
2
votes
1
answer
181
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The nonlinear state-space model of a spherical pendulum cannot be linearized and cannot be controlled?
I am attempting to model and control a spherical pendulum. I have derived the equations as follows:
...
- 23
5
votes
3
answers
328
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Calculating the n derivative of state space equations
I have a nonlinear model ${\bf{\dot x}} = f\left( {\bf{x}} \right) $
which is represented as follows:
$$\begin{array}{l}{{\dot x}_1} = {x_2}\\{{\dot x}_2} = {x_3} - \alpha {x_4}{x_2} + \frac{\alpha }{...
- 51
2
votes
2
answers
204
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Why does this PhaseRange not work?
Any idea why this PhaseRange does not work?
BodePlot[-(1/(s + 1000)), PlotLayout -> "Phase",
PhaseRange -> {0, 2 \[Pi]}]
- 2,822
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1
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187
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Solve Riccati Equations by hand
I'm in the midst writing a bit about LQR problems and would like to show that some things in mathematica can be tested by trying to write such problems out by ones self, However I cannot seem to find ...
- 2,923
1
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1
answer
164
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How to excite a transfer function with continuous white noise
I'm trying to get the output response of linear system represented by transfer function, once the white noise is given as an input. Here's the code:-
For generating continuous noise, I'm getting help ...
- 13
6
votes
1
answer
131
views
What does BodePlot actually calculate?
I'm using Mathematica v12.3 student edition, running on Windows 10 Home (AMD Ryzen 5 4500U with Radeon Graphics 2.38 GHz).
I'm trying to get a Bode plot of an example function. I try to do it with the ...
- 63
0
votes
1
answer
87
views
Asymptotic bode plot [closed]
Is it possible to plot an asymptotic bode plot. I am interested in verifying my straight line bode plot approximations done by hand by using mathematica but the bodeplot function generates the curved ...
1
vote
0
answers
193
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Linearization of the ODE system: Problems
I have summarized the issues covered in the topics:
Linearization of ODE without an equilibrium
I ask for help with commands TransferFunctionModel + StateSpaceModel
Plot3D + WhenEvent + NDSolve
...
- 2,304
1
vote
1
answer
74
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I ask for help with commands TransferFunctionModel + StateSpaceModel
Given system of ODE:
$\begin{cases} \dot{x}=G+u_1 \\ \dot{z}=-z+\frac{df}{dt} \\ \dot{G}=-G+z \cdot u_2 \end{cases}$
where $f=-x^2$,
$u_1=\frac{d}{dt}(\alpha \sin(\omega \cdot t))$ and $u_2=\alpha \...
- 2,304
-1
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1
answer
188
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Problem with Lagrangian and Matrix Calculus in Mathematica
Continuing the questions:
Lagrangian of three-mass system with Mathematica
Equations of motion for two-mass torsional oscillator with the gear train
Derivation of equations of motion for a multi-body ...
- 2,304
2
votes
2
answers
71
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Removing transient part in equation and solving for a general form
I have the following code that I run:
...
- 1,911
3
votes
1
answer
248
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Equations of motion for two-mass torsional oscillator with the gear train
This is my first topic and I continue work on that: Lagrangian of three-mass system with Mathematica
I found interesting problem here, and try reproduce results.
Assumption: $d_1=0$
Algorithm:
Write ...
- 2,304
1
vote
1
answer
151
views
How can I solve this system please?
I need to solve the following impulsive heat equation:
$$
\left\{\begin{array}{ll}
\partial_{t} \psi(x,t)-\partial_{xx} \psi(x,t)=0, & (x,t)\in (0,1) \times((0, 2) \backslash\{1\}) \\
\...
- 99
1
vote
3
answers
407
views
BodePlot to calculate the amplitude and phase at a specific frequency
I have transfer function:
$W=\frac{1}{s+1}$
tf = TransferFunctionModel[{{1/(s + 1)}}, s]
BodePlot[tf, {.01, 100}]
It is very simple to construct a Bode diagram, ...
- 2,304
1
vote
1
answer
94
views
Asymptotic Output Tracking: Compensator properties
Asymptotic Output Tracking: Code Issues
The question is, rather, of a theoretical nature (practical applications can be viewed in the topic at the link).
Asymptotic Output Tracking is said to be based ...
- 2,304
2
votes
1
answer
65
views
OutputResponse numerical error?
It shoud approach to 1 and remains at 1, but when time over 20s it deteriorates.
Mathematica 12.1
...
- 121
1
vote
0
answers
72
views
Multidimensional obstacle avoidance in ODE. Part II
Multidimensional obstacle avoidance in ODE (Visualization)
https://math.stackexchange.com/questions/4146255/multidimensional-obstacle-avoidance-in-ode
For some time, I studied this question more ...
- 2,304
1
vote
2
answers
77
views
Notation parse rule does parse when it acts as a argument
https://reference.wolfram.com/language/Notation/tutorial/NotationSymbolizeAndInfixNotation.html
Notation[boxes ⟹ expr] set boxes to be parsed to expr
I want a simplified notation for entering a ...
- 121
4
votes
1
answer
136
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Multidimensional obstacle avoidance in ODE (Visualization)
A simple 3-dimensional ODE system is given:
$F=\begin{cases} \dot{x}=g+g_{U_{rep}} \\ \dot{g}=-g+\frac{df}{dx} \\ \dot{h}=-h+\frac{d^2f}{d^2x} \end{cases} $
Task: Make the variable $g$ move so that ...
- 2,304
1
vote
1
answer
206
views
Tuning the optimal control synthesized according to the Pontryagin maximum/minimum principle and choosing the cost function
I continue to study the topic I started here: Problem with optimal control and Pontryagin's maximum principle
A simple ODE system $(1)$ is given:
$F=\begin{cases} \dot{x}=g \\ \dot{g}=-g+\frac{df}{...
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6
votes
1
answer
650
views
Problem with optimal control and Pontryagin's maximum principle
For dynamic system:
$\dot{x}=\frac{df}{dx}+u$
where $f=e^{-x^2}$
It is necessary to develop optimal control, minimizing criterion:
$J= \int_{0}^{t_f} ((\frac{df}{dx})^2+u^2) \,dt $
Algorithm:
We ...
- 2,304
1
vote
0
answers
59
views
Nonlinear system with time-optimal control
Given nonlinear system:
\begin{cases} \dot{x_1}=x_3+u \\ \dot{x_2}=-x_2+\dot{f} \\ \dot{x_3}=-x_3+x_2 \cdot \alpha \sin(\omega t) \\ \dot{x_4}=-x_4+x_2 \cdot (\frac{16}{\alpha^2}(\sin(\omega t)-\frac{...
- 2,304
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0
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50
views
Asymptotic Output Tracking - How to Track?
Asymptotic Output Tracking: Code Issues
Abstract state-space:
\begin{cases} \dot{x_1}=x_3 \\ \dot{x_2}=-x_2+\frac{df}{dt} \\ \dot{x_3}=-x_3+x_2 \cdot \alpha \sin(\omega t) + u \\ \dot{x_4}=-x_4+x_2 \...
- 2,304
2
votes
1
answer
43
views
AsymptoticOutputTracking for output with boundary condition
I want to try asymptotic output tracking, but with inequality.
There is a differential equation:
$\frac{dx}{dt}=\frac{d}{dx}(-x^4)$
With output $y=\frac{d}{dx}(-x^4)$,
The output should strive for $0$,...
- 2,304
1
vote
1
answer
74
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AsymptoticOutputTracker to Matlab-Simulink
What is the structural scheme for AsymptoticOutputTracker in Mathematica? I need this in order to transfer the feedback signals received with the help of ...
- 2,304
5
votes
1
answer
129
views
Is there a better way to simulate quadratic cost MPC problems?
Question
I would like to know if there is a more straightforward or a better way to simulate MPC problems in terms of code length and accuracy as compared to what I am doing. I am looking to know if ...
- 215
1
vote
1
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56
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Comparison of NDSolve and Asymptotic Output Tracking results: Problem identified
My question is a continuation of the topic:
Asymptotic Output Tracking: Code Issues
Edit: Take system of ODE for example:
$\begin{cases} \frac{dx}{dt}=H \cdot \alpha \sin(\omega t)+\alpha \omega \cos(\...
- 2,304
2
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0
answers
66
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Affine state-space: Nonlinear output
I am using a system of equations to experiment:
$\begin{cases} x_1'=x_2 \\ x_2'=x_1^2-x_2+u \end{cases} $
As an output, I want to use the following non-linear output:
$y=e^{-x_1^2}$
...
- 2,304
2
votes
1
answer
180
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Asymptotic Output Tracking: Code Issues
My question is a continuation of the topic Which way of solving from nonlinear control to choose?, and in the future I plan to expand this question.
I want to try to apply this article https://www....
- 2,304
1
vote
0
answers
38
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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. $\frac{df}{dx}$.
I want to construct a ...
- 2,304
0
votes
0
answers
207
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NDSolve Error - There are fewer dependent variables, than equations, so the system is overdetermined
I have a program in which I am simulating the motion of two-wheel vehicle. I have four global parameters xo (position x of rear wheel), yo (position y of rear wheel), teta (the angle of inclination of ...
- 1
3
votes
1
answer
102
views
How to code a Sum Block when working with Transfer Functions?
I am working using transfer functions models with Mathematica and i am missing a basic feature like the ability to use a Sum Block.
How could the model above be modeled?
Considering:
...
- 107
1
vote
0
answers
86
views
Do Loop contained in a function defined within a custom package doesn’t work as expected but works fine when function is defined directly in a script
Below is my code and I am having problems running the StdMPC function that I am trying to define. Running my code gives me the error that the matrix A and Xopt[[i]] are not of compatible shapes for ...
- 215
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0
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91
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How to solve this linear complementarity problem with NDSolve or other functions? The arguments should be ordered consistently
I want to find a numerical solution of $\omega(t,q)$, where $t\in[0,T]$ and $q\in[0,N]$. $q_t$ is a determinstic w.r.t $t$, other unmentioned parameters can be fullfilled or given by the user.
I met ...
- 71
1
vote
1
answer
56
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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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2
votes
1
answer
118
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How to combine Manipulate and OutputResponse to manipulate a transfer function
The webpage on Manipulate provides an example on section Examples > Applications of how to manipulate two parameters (the initial conditions) of an Initial Value Problem (ODE with initial ...
- 453
3
votes
1
answer
309
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State Space Model in Controllable Canonical Form
Mathematica by default puts state space model realizations in controllable companion form, as seen here:
...
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