# 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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### Is there any formula to get the IRR from the slope of the Cumulative Cash Flow?

I've simulated a monthly regular cash flow with Excel, and the Internal Rate of Return (IRR) calculated from the first date to the current row. The curve of the IRR is very similar to the Transfer ...
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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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### 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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### 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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With a given linear drive system ...
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### 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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### 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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### 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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### 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 ...
208 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 ...
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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 ...
194 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 ...
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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 ...
181 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 ...
686 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 ...
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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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### 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 ...