# 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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95 views

### BodePlot with wrong phase [closed]

I'am trying to plot the function: BodePlot[1/(1 + 0.1 s), s] The phase plot is wrong (I'm using Mathematica 11.2): Why does this happens and how can I get the ...
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### 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 ...
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### 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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### 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 ...
696 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 ...
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### 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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### 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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### 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. 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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### 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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### 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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### 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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### FeedBack linearization and stabilization error

Consider nonlinear system: \begin{cases} \dot{x_1}=x_4+u \\ \dot{x_2}=-x_2+\frac{(\tanh(k \cdot x_5)+1)}{2}+U(t)+u \\ \dot{x_3}=-x_3+\dot{f} \\ \dot{x_4}=-x_4+x_3 \cdot s(t) \\ \dot{x_5}=-x_5+x_3 \...
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### 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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### 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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### 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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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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### 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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### 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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### 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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With a given linear drive system ...
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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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### 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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### TransferFunctionModel produces large coefficients

First, I define the following transfer functions using TransferFunctionModel: ...
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### 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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### TransferFunctionModel and BodePlot shows different result between Mathematica and MATLAB

I was doing the TransferFunctionModel and BodePlot. But the result from Mathematica and MATLAB are different. The function is ...