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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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 ...
642 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 ...
123 views

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 ...
56 views

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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56 views

OutputResponse numerical error?

It shoud approach to 1 and remains at 1, but when time over 20s it deteriorates. Mathematica 12.1 ...
73 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 ...
69 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 ...
102 views

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 ...
122 views

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 ...
395 views

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 ...
33 views

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 $0$,...
44 views

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 \...
67 views

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 ...
155 views

State Space Model in Controllable Canonical Form

Mathematica by default puts state space model realizations in controllable companion form, as seen here: ...
75 views

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 ...
117 views

With a given linear drive system ...
943 views

Can we use Mathematica to design an electronic active filter?

How can we use Mathematica to design an electronic implementation of an active filter?
97 views

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 ...
142 views

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: ...
409 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,...
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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 ...