# 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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### 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 ...
205 views

### Finite Poles and Zeros Approximation of a Transfer Function Having Cylindrical Functions

I have the following expression containing cylindrical functions: c = HankelH2[1, s]/(HankelH2[1, s] + I HankelH2[0, s]); I wish to find the approximate transfer ...
43 views

### Affine state-space: Nonlinear output

I am using a system of equations to experiment: $\begin{cases} x_1'=x_2 \\ x_2'=x_1^2-x_2+u \end{cases}$ As an output, I want to use the following non-linear output: $y=e^{-x_1^2}$ ...
80 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 ...
108 views

### Constraining the independent variable in a control system

For an analog closed loop feedback control, I can do the following to model the response of a second-order physical system with an order 1 zeros polynomial to a step disturbance. I have a proportional ...
57 views

### FullInformationOutputRegulator -how does it work?

How does this function work? I don't understand how the regulator equation is synthesized when the model is nonlinear. Does it make use of a power series approach? Can someone suggest something to ...
77 views

### How to model discontinuities in a NonlinearStateSpaceModel

I know that it is possible to model discontinuities like bouncing and other collisions by using WhenEvent with NDSolve. However, I am using the tools for Non linear systems and I'd like to know if ...
75 views

### 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 ...
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 ...
41 views

### 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{...
37 views

### Which way of solving from nonlinear control to choose?

I have a nonlinear system: \begin{cases} x'=f(x)+u \\ y=f(x) \end{cases} where $f(x)$ - gradient of some one-extremal function (for example $f=e^{-(x)^2}$), i.e. $\frac{df}{dx}$. I want to construct a ...
84 views

### Do Loop contained in a function defined within a custom package doesn’t work as expected but works fine when function is defined directly in a script

Below is my code and I am having problems running the StdMPC function that I am trying to define. Running my code gives me the error that the matrix A and Xopt[[i]] are not of compatible shapes for ...
73 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 ...
51 views

### Finding the mathematical function is plotted by using the bodeplot command

I've the following code: ...
91 views

### Wrong answers while trying to analyze stability

I want to analyze the stability of a closed-loop system (with feedback). The idea is to choose a proper gain kc for the controller. The code is the following: ...
90 views

### Plotting a switching function

I'm trying to use a switch-function. I'm using $d(t)=d_o+\Delta d_1*UnitStep(t-0.01)+\Delta d_2*UnitStep(t-0.04)$ and a sawtooth function with period 0.002 and amplitude 1. To generate the sawtooth ...
54 views

### Root finder vs. feedback loop

I have a simulation that applies a force to a particle in a simple constant gravitational acceleration environment, and uses FindRoot in conjunction with ...
505 views

### No response from DSolve

Using optimal control theory, I am trying to find the optimal paths of d and k such that they will maximize profit as given by lc: ...
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 \...
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 \...
86 views

### NDSolve Error - There are fewer dependent variables, than equations, so the system is overdetermined

I have a program in which I am simulating the motion of two-wheel vehicle. I have four global parameters xo (position x of rear wheel), yo (position y of rear wheel), teta (the angle of inclination of ...
I want to find a numerical solution of $\omega(t,q)$, where $t\in[0,T]$ and $q\in[0,N]$. $q_t$ is a determinstic w.r.t $t$, other unmentioned parameters can be fullfilled or given by the user. I met ...