# 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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### What is the correct way of defining an affine transform with NonlinearStateSpaceModel?

I am trying to construct an affine transform (y=g(x-a)) to be applied to the output of a discrete time model using SystemsModelSeriesConnect. The documentation gives a working example in the ...
• 4,604
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I am trying to use MicroControllerEmbedCode to download a program to an Arduino NANO 33 IoT using MMA 14, Win 10. I have successfully done this with an Arduino Uno R3. When the Uno is plugged in to ...
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1 vote
68 views

I have been learning the control system tools in Mathematica, and recently exploring the Microcontroller Kit. I have run into a use of NonlinearStateSpaceModel which I don't understand. The use occurs ...
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### What's the reverse operation of TransferFunctionExpand?

Given a transfer funtion TransferFunctionModel[1/(s + I) + 1/(s - I) + 1/(s + 1) + 1/(s - 2)^2,s] we can obtain the polinomial form by using TransferFunctionExpand ...
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1 vote
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### How to change the sampling period of discrete time model?

Mathematica Version 14.0 on Win 10. This is a problem I am having with a much more complicated notebook. I crafted the simple example below for this question. If I begin with an expression in the s-...
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1 vote
61 views

### Adapt Code to Solve Fractional-Order System Delay Differential Equations- Chen System

Dynamics of fractional-ordered Chen system with delay I have tried to modify this code ...
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### Transfer function for Rayleigh-Plesset equation

I want to calculate the transfer function for the following second order nonlinear differential equation: ...
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### Finding a way to skip an iteration in a table

I am creating a project in Wolfram that models oil slicking using Cellular Automata. In my project I have a function called vonNeumann Neighborhood that takes in a radius and a length of a size of a ...
1 vote
55 views

### Limiting State-space Controller

I have a state-space representation of a system with a few inputs and outputs. Further, I've used LQRegulatorGains to (surprise, surprise) construct an LQ regulator controller. This is all well and ...
58 views

### 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. ...
100 views

### How to Paste Complex Transfer Function Equation to Excel [closed]

I am trying to paste this transfer function to Excel, is it possible?
81 views

### 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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### 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. ...
83 views

### 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 ...
156 views

### Possible Lagrangian: ODE and System of ODE's

For the Lagrangian: ...
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1 vote
153 views

### 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 ...
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1 vote
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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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1 vote
292 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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274 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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1 vote
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### 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
97 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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70 views

### OutputResponse numerical error?

It shoud approach to 1 and remains at 1, but when time over 20s it deteriorates. Mathematica 12.1 ...
• 337
1 vote
74 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
83 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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### 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
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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: $y=e^{-x_1^2}$ ...
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187 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
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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