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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4
votes
1answer
136 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,...
3
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1answer
67 views

TransferFunctionModel produces large coefficients

First, I define the following transfer functions using TransferFunctionModel: ...
4
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1answer
62 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 ...
6
votes
1answer
78 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 ...
3
votes
1answer
30 views

Get the greatest time contant of a system's output given its expression

Let $y(t)$ be a function that consists of a sum of terms, each of which is in general a product of an exponential function $e^{\sigma t}$, and a sine function $\sin{\omega t}$ or cosine function $\cos{...
3
votes
0answers
52 views

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 ...
6
votes
1answer
88 views

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 ...
8
votes
2answers
182 views

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 ...
5
votes
1answer
200 views

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 ...
6
votes
1answer
255 views

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 ...
3
votes
2answers
191 views

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 ...
2
votes
1answer
63 views

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. ...
0
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1answer
55 views

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: ...
3
votes
1answer
94 views

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:...
5
votes
3answers
746 views

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 ...
3
votes
1answer
97 views

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: ...
1
vote
1answer
80 views

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 ...
1
vote
1answer
79 views

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-...
1
vote
1answer
48 views

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 ...
7
votes
1answer
170 views

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 ...
1
vote
1answer
78 views

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 ...
2
votes
1answer
48 views

Does NonlinearStateSpaceModel work with symbolic constants?

I'm trying to put a nonlinear system of two 2nd order ODEs given by: ...
1
vote
1answer
114 views

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 ...
6
votes
1answer
169 views

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 ...
1
vote
1answer
55 views

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: ...
2
votes
3answers
133 views

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 ...
5
votes
1answer
164 views

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 ...
30
votes
2answers
602 views

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 ...
1
vote
1answer
74 views

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 ...
1
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1answer
75 views

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 $...
1
vote
1answer
291 views

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 ...
1
vote
1answer
65 views

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 ...
2
votes
1answer
77 views

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 ...
2
votes
2answers
353 views

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. ...
3
votes
1answer
462 views

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 ...
3
votes
2answers
125 views

Inconsistencies when using BodePlot with `StateSpaceModel` and `TransferFunctionModel`

Consider a linear system . ...
2
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0answers
71 views

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 ...
2
votes
1answer
233 views

Simulating a combination of PDEs and ODEs

I am trying to simulate a combination of PDEs and ODEs, given below. $$ \begin{matrix} -L\dfrac{\partial}{\partial t}I(t,z)&=&\dfrac{\partial}{\partial z}V(t,z)+RI(t,z)\\ C\dfrac{\...
3
votes
1answer
99 views

BodePlot of Warburg impedance - Errors

I'm trying to plot the Bode diagrams of the Warburg impedance (A=1, s=jw): $$Z=\frac{A}{\sqrt{\omega}}+\frac{A}{j\sqrt{\omega}}$$ $$Z=A \sqrt{\frac{j}{s}}+\frac{A}{j}\sqrt{\frac{j}{s}}$$ ...
2
votes
1answer
92 views

Event Trigger Ode's

I am trying to simulate a Hybrid system using the WhenEvent function in Mathematica. I have asked this question earlier. It was not an MWE. Now I tried to make an ...
1
vote
1answer
109 views

AxesLabel in a phase plot in the BodePlot command

I've the following code: ...
1
vote
0answers
47 views

Finding the mathematical function is plotted by using the bodeplot command

I've the following code: ...
2
votes
1answer
42 views

bodeplot phase in normal scale

I've the following fuction: ...
5
votes
1answer
351 views

Solving optimal control problem when input is constrained

Given a linear time-invariant system: $$x'(t)=Ax(t)+Bu(t)$$ with initial state $x(0)=x0$ and final state $x(T)=xT$. The performance measure to be minimized is: $$∫_0^Tu(t)^2dt$$ The most important ...
3
votes
2answers
418 views

Is it possible to find the transfer function of these three differential equations using Mathematica

Imagine you are attempting to obtain a model of a device with two inputs [u1, u2] and three outputs [O1, O2, x] from the Lagrangian. After some of Lagrangian work, you find the following three ...
9
votes
2answers
559 views

Why does NonlinearStateSpaceModel linearise?

The documentation for NonlinearStateSpaceModel says: In NonlinearStateSpaceModel[eqns, ...] the Taylor linearization is with ...
2
votes
1answer
83 views

Searching for poles of a transfer function on the edge of stability

I just started using Mathematica and I am a bit stuck. I want to compute poles of transfer function that are on edge of stability i.e. Re[s] = 0 and I want to find ...
10
votes
1answer
662 views

Solving an optimal control problem (LQR)

Given a linear time-invariant system: $$ \dot{x}(t)=Ax(t)+Bu(t) $$ with initial state $ x(0)=x_0 $ and final state $ x(T)=x_T $. The performance measure to be minimized is: $$ \int_{0}^{T} ((x_T-...
0
votes
1answer
129 views

Solve for input with given TransferFunctionModel

I obtained the transfer function for an electrical system from experimental data (left plot). Thereby, I can calculate the output voltage response for a given voltage input, using ...
1
vote
3answers
88 views

Can't find solutions to an equation involving a variable in eigenvalues

In control sytems we know that a system is of order 2 if there are two different eigenvalues such that they ratio is 10. In this case I want to find the controller gain that makes the above possible. ...