Questions tagged [control-systems]

Questions on the use of Mathematica to analyze, design, and simulate continuous- and discrete-time control systems.

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Phase unwrapping of transfer function model for calculating group delay [duplicate]

Suppose that I have a transfer function model ...
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2 answers
71 views

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 ...
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2 votes
1 answer
108 views

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: ...
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5 votes
3 answers
307 views

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 }{...
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2 answers
193 views

Why does this PhaseRange not work?

Any idea why this PhaseRange does not work? BodePlot[-(1/(s + 1000)), PlotLayout -> "Phase", PhaseRange -> {0, 2 \[Pi]}]
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LQGRegulator Design Syntax and import to Systemmodeler

In learning how to import models to and from systemmodeler, I have taken a system I have built, and imported this into MMA and already created a statespacemodel. ...
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1 answer
96 views

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 ...
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1 vote
1 answer
61 views

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 ...
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6 votes
1 answer
129 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 ...
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1 answer
65 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 ...
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1 vote
0 answers
125 views

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 ...
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1 answer
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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 \...
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-1 votes
1 answer
157 views

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 ...
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2 votes
2 answers
66 views

Removing transient part in equation and solving for a general form

I have the following code that I run: ...
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3 votes
1 answer
209 views

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 ...
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1 vote
1 answer
150 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\}) \\ \...
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1 vote
3 answers
163 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, ...
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1 vote
1 answer
91 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 ...
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2 votes
1 answer
61 views

OutputResponse numerical error?

It shoud approach to 1 and remains at 1, but when time over 20s it deteriorates. Mathematica 12.1 ...
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1 vote
0 answers
69 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 ...
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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 ...
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4 votes
1 answer
126 views

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 ...
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1 vote
1 answer
166 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
502 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 ...
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1 vote
0 answers
45 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{...
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0 votes
0 answers
46 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 \...
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2 votes
1 answer
40 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 $0$,...
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1 vote
1 answer
69 views

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 ...
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5 votes
1 answer
111 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 ...
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1 vote
1 answer
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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(\...
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2 votes
0 answers
46 views

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: $y=e^{-x_1^2}$ ...
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2 votes
1 answer
170 views

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....
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1 vote
0 answers
38 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. $\frac{df}{dx}$. I want to construct a ...
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0 votes
0 answers
143 views

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 ...
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3 votes
1 answer
68 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: ...
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1 vote
0 answers
84 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 ...
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0 answers
71 views

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 ...
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1 vote
1 answer
55 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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2 votes
1 answer
91 views

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 ...
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3 votes
1 answer
211 views

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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1 vote
0 answers
87 views

Problem with the analytical study of transient processes in nonlinear systems with linear dynamic links

I ask for advice and help. 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 ...
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22 votes
2 answers
968 views

Can we use Mathematica to design an electronic active filter?

How can we use Mathematica to design an electronic implementation of an active filter?
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2 votes
1 answer
121 views

Linear Quadratic Integrator

With a given linear drive system ...
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0 votes
1 answer
55 views

Compiling RiccatiSolve LQRegulator gains

Given some specific matricies, numA, numB, numP, q and r to calculate LQR gains, one can use simply LQRegulatorGains or solve the same via ...
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3 votes
2 answers
109 views

Limiting transfer function of PID to upper and lower bounds

I have a question about Limiting the output of a transfer function in my system model. (Im fairly new to control theory and control systems) I have a model where a PID controller is directly ...
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0 votes
0 answers
182 views

How to solve Partial differential equation (PDE) with delay!

I just have one question please, I searched on Mathematica documents concerning partial differential equations with delay, all I had found is ordinary differential equations(EDO), that's means ...
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6 votes
1 answer
474 views

Estimation of parameters of limit cycles for systems of high-order differential equations (n> = 3)

There is a system of differential equations: Then, call the limit cycle the projection of the phase trajectory onto the plane in a pairwise combination of state variables ($x-y,y-z,x-z$). where $x,y,...
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3 votes
1 answer
89 views

TransferFunctionModel produces large coefficients

First, I define the following transfer functions using TransferFunctionModel: ...
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4 votes
1 answer
112 views

Finding group delay of transfer function

I'm having trouble finding the group delay of a transfer function. I've seen a solved question on here about finding the group delay, but I want to understand why my method doesn't work. Here is some ...
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6 votes
1 answer
121 views

How to use RiccatiSolve with symbolic matrix

According to the RiccatiSolve documentation the Eigensystem method can apply to symbolic matrices. However, I can not get it to ...
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