# 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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### Transfer Matrix Approach to the Triangular Decoupling of General Neutral Multi-Delay Systems

I want to simplify a multi-delay system from 4 delays in 2 delays rational independent but the problem is that my delays are irrational numbers so the lcm does not work ,do you have any idea in this ?
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### Simple neural network with feedbacks in state-space form

Having studied more or less in detail the mechanisms of working with the state-space that Mathematica provides us with, I asked myself: can these tools be applied to neural networks? This article ...
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### Implicit Riccati Equation Solver (to find the anti-stabilizing solution)

I've found that the latest MATLAB icare() solver includes the possibility to find also the anti-stabilizing solution of the Riccati equation. I haven't found a ...
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### Converting a backward/forward sweep code for optimal control to _Mathematica_

I'm trying to convert to Mathematica a simple backward/forward sweep (with RK4 integrator) code to solve an optimal control problem in epidemiology, but I'm getting some error messages and I cannot ...
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### Solution to the inverted pendulum problem (system of non-linear ODE)

A classic control systems problem is that of the translational inverted pendulum, as shown below. By applying a force $f(t)$ to the car (e.g. through a DC motor attached to the car), the goal is to ...
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### Understanding code generated by MicrocontrollerEmbedCode

I've been using MicrocontrollerKit for a while now to generate code for little projects, inverse pendulums, filters, etc. Generally it works well. I am now currently trying to design a LQI (Linear ...
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### Lagrangian of three-mass system with Mathematica

Before proceeding to calculations in Mathematica, I would like to clarify with knowledgeable people. There is an ordinary linear three-mass system. If we write its Lagrangian, we get the following ...
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### Representation in state-space of a system with ideal and real differentiating links in feedback

There are two systems in the state space with an ideal and a real differentiator. For the first system, the code in Mathematica is as follows. ...
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### Closed-Loop Systems and System Response Modeling [closed]

I'm testing out code from a textbook for possible bugs. This chapter demonstrates a plot of a motor's angular position response in accordance to it's transfer function model: ...
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### Output response for state-space with piecewise nonlinear elements

In addition to the previous topic: System model merge with multiple input and one output For example, I am trying to reproduce a system from simulink, a diagram of which is shown in the figure below:...
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### Mathematica and MatLab giving different results from inverse Laplace transform [closed]

The questionis is as this Given the transfer function gs = (5*s + 4)/(s^4 + 4*s^3 + 2*s^2 + 3*s); and the input signal ...
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### System model merge with multiple input and one output

I was curious, and I used the built-in functions of Mathematica to analyze the following scheme: I used SystemModelMerge as: ...
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### Problem when solving Kalman filter in Mathematica: How to define a spectral density matrix and calculate the covariance matrix?

I am reading the classic book on state-space control theory by Bernard Friedland. In order to strengthen my understanding of Kalman filter, I want to reproduce Example 11A (Inverted pendulum on page ...
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### Why doesn’t x’ = a.x + b.u, y = c . x + d.u hold in this state-space model?

I have noted that sometimes state variables may change (thanks Thomas’s help :)), due to the Mathematica’s internal automatic transformation from a descriptor state-space model to a standard state-...
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### Confusing behavior of LQR control that strongly depends on system output (with odes solved by NDSolve)

I am implementing a LQR control of a 3-floors structure. Firstly, I obtained a reasonable result with my first code (Code 1 as shown below). In this code, the ...
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### How to implement a Kalman or LQG regulator in the control of classical pendulum problem

My final purpose is to realize an LQG control of inverted pendulum. To this end, my first step I think is to build a Kalman regulator in Mathematica. The original Matlab version of Kalman filter is ...
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### Strange output of a simple statespace model

The output of statespace model seems strange. In the follwing code, the odes are governing equations of a three floors structure, and the output are three accelerations of floors. If I ...
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### Does NonlinearStateSpaceModel work with symbolic constants?

I'm trying to put a nonlinear system of two 2nd order ODEs given by: ...
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### Experiments with Feedback Linearization and StateTransformLinearization in Mathematica

I have some nonlinear system, and i have three big question: Non-linear ODE from closed-loop system and Response 1. how correctly use such terms, like "Feedback Linearization and StateTransform ...
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### Non-linear ODE from closed-loop system and Response

I started using Mathematica 12 and ran into difficulties. Namely, I want to compare the results of the calculation of a closed system from Simulink and in Mathematica. I rummaged around a bit on the ...
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### Error with StateSpaceTransform: the rule based transformation must be of length 2

I would like to perform a change of variables on the following dynamics system: ...
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### PIDTune and characteristic equation of zero

I have a BLDC electric motor, I'm currently trying to control via a PIDTune. This is mostly an attempt to reduce (remove) a small run away drift that ends up ...
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### Extended Kalman Filter by hand

While trying to learn a bit about control theory, observers and most importantly, to use Microcontroller Kit in version 12 of MMA, I've stumbled upon the KalmanEstimator. After reading a bit (and ...
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### Can we use Mathematica for electronics design?

A spoiler alert: I intend to answer my own question. I am posting this because I would like to share my excitement regarding the control theory tools in Mathematica, and also to promote further ...
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### Speeding up the calculations by Reduce and NSolve

I have a non-linear system of equations with numeric parameter values as shown below. I first tried FindRoot with given initial values and it did not converge. Then ...
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### StateTransformationLinearize - references?

I am impressed by StateTransformationLinearize, and I feel terribly bad for not having noticed this function before. How does it work? Does it attempt to find a \$...
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### Solving Differential Equation System for HIV Treatment Model

I was working on a project about optimal strategies for HIV treatment, models used from [Butler, Kirschner, and Lenhart] 1997. This model explains the spread of HIV viruses in the human body, where ...
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### Manual control plots differ from StateResponse and OutputResponse

So In my quest to try to learn some control theory inspired by the following link, I have been modeling an inverse pendulum regulated with a flywheel. The system model is pretty ok I think, and when ...
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### OutputResponse and contradictory control models

So I'm trying to learn some control theory for a little project I'm working on and decided I'd try the examples of pendulum and cart one can find all over the internets, and I'm following this post ...
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### BodePlot with magnitude in db or log scale

I have to plot a BodePlot with magnitude in db or log, but i could not find the option for setting the magnitude scale. ...
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### Analyze stability of equilibria using Routh-Hurwitz conditions

For an assignment, I need to analyze the stability of a system very close to equilibrium, using "Routh-Hurwitz conditions". I have already obtained the characteristic equation of my system, but I do ...
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### Inconsistencies when using BodePlot with StateSpaceModel and TransferFunctionModel

Consider a linear system . ...
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### Accuracy problem with BodePlot

Hoping to find a quick answer to a question of frequency response of multiple band-pass filters in closed loop, I opened up Mathematica,and entered the first set of ...