Questions on the use of Mathematica to analyze, design, and simulate continuous- and discrete-time control systems.

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30 views

Problem with solving an optimal control system with Shooting Method

I try to solve a system of differential equation by shooting method. I looked at questions asked on the site but I could not find that could help me. My functions are ; ...
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1answer
29 views

NonlinearStateSpaceModel/OutputResponse gives doubled outputs

I want to simulate a pendulum or rather the controlled system. But NonlinearStateSpaceModel or the OutputResponse gives weird ...
8
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1answer
63 views

Working Precision in nonlinear control systems

When simulating a nonlinear control system using StateResponse , do the options WorkingPrecision, ...
0
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1answer
29 views

Compute StateResponse for list of inputs

How do I find the state response of a system for a list of inputs? Simply writing an array in the place where the input enters as an argument of StateResponse ...
2
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0answers
37 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 ...
1
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1answer
55 views

From non-linear homogeneous DAE to linear state-space form

I have a non-linear homogeneous DAE $x' = F(y)$, $G(y) = 0$ where $x$, $y$ are vectors, $F$ is linear with constant coefficients, and $G$ is a polynomial with parametric coefficients. How can I ...
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1answer
90 views

How to see controllers response?

How can I get/plot the controller's effort of a controlled system (state space model)? Example system: ...
2
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1answer
52 views

How does RootLocusPlot handle TransferFunctionModel

I'd like to analyze the poles (denominator-roots) of a TransferFunctionModel, that was generated from a ...
0
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1answer
148 views

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 as follows: ...
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2answers
118 views

Convert DE to first order?

I have the following set of second-order differential equations: ...
0
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0answers
65 views

solving dynamic system by a finite difference equation approximation

I have a four dimensional dynamical system from optimal control model. I have 2 states and 2 control variables. I have already found the corresponding initial conditions for two control variables for ...
8
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1answer
148 views

Problems with StateSpaceModel in v10.2

Bug introduced in 10.0.2 and fixed in 10.3 I don't know if this is a bug, or if just something changed I can't figure out. Take the following examples: ...
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1answer
84 views
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3answers
143 views

How do I make a definition/function/method as I would in Java/MATLAB/Python

I've been trying to figure this out for a few hours now and it's driving me nuts. I am trying to confirm that, after transforming a Schrodinger equation, that the new wavefunctions satisfy the new ...
4
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2answers
261 views

Evaluation problems with NDSolve using the fixed step ExplicitEuler-Method

Motivation I am using Mathematica to implement System Dynamics (SD) models, e.g. differential equation models as applied to management/economic problems following the "methodology" of Jay W. ...
3
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0answers
120 views

System Identification from test data

I've been looking for a way to model a simple SISO system from test data using Mathematica. Something similar to MATLAB's System Identification Toolkit, that estimates a transfer function from the ...
4
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1answer
161 views

OutputResponse in V9 vs V10

Bug introduced in 10.0.1 and persisting through 10.2 or later I have same code that works in version 9.0.1, but not in version 10.0.1.0 (according to @Sektor, it works in 10.0.0.0, too). ...
0
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0answers
97 views

Selecting values over lists for discrete inputs in NDSolve [duplicate]

I'm currently trying to simulate a step response in a simple tank system with NDSolve. I would like it to start at say time 2 (the precise time is not important). ...
1
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1answer
105 views

StateSpaceModel- damped oscillator

I'm new in Control system and in Mathematica too. res1 is the state space as follows ...
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2answers
189 views

Operations on transfer function model

Suppose I have a transfer function defined via TransferFunctionModel, e.g. tf == TransferFunctionModel[{{1/s}}, s]. How can I ...
2
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2answers
66 views

Is StateSpaceModel command ignoring the StateSpaceRealization option?

fixed in 10.0.2 This is version 10.01 on windows. It seems that StateSpaceModel is completely ignoring the StateSpaceRealization option when create a state space object. ...
1
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1answer
152 views

Why does LyapunovSolve solve non-standard form?

LyapunovSolve[A,Q] solves the equation $A P + P A^T = Q$ for $P$ whereas the standard form (wikipedia,lecture notes, p.25, linear control systems) of the Lyapunov ...
5
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1answer
84 views

StateSpaceRealization “ControllableCompanion” does not generate ControllableCompanion form from DE

Fixed in 10.1 I must be doing something wrong, but do not see it. There is an option in Mathematica control system function StateSpaceModel where one asks it to ...
5
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0answers
241 views

How to draw block diagrams as Graph objects?

In the documentation ClosedLoopResponsesWithAPIDController, There is a very nice block diagram. I want to create my own block diagrams similar to this. I clicked on the diagram and pressed ...
1
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1answer
78 views

NonlinearStateSpaceModel: Trying to parse the documentation

I am trying to follow the documentation on NonlinearStateSpaceModel here, and the first basic example throws me for a loop. It says it's defining the nonlinear ...
5
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2answers
128 views

ToDiscreteTimeModel fails following video

Following the systems-modeling video here at about 15 min, 20 seconds in, the presenter (Bob Sanhedrick, I think) shows a model for an "Asteroids-game"-like 2D spacecraft. The model is trivial: ...
8
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1answer
155 views

On using DiracDelta[t] in OutputResposne in version 10. Different result from version 9

I am baffled by this. I was trying to run same example I had working in version 9.01 and found now I get empty plots. The example is here . Here is a simplified version of the above. The same exact ...
6
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3answers
766 views

Laplace: from differential equation to transfer function

First at all, this is trictly related to my own question: How to transform transfer functions into differential equations? How can I transfer my differential equation into a transfer function? For ...
0
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1answer
95 views

A problem with “RiccatiSolve::ncsol: Cannot compute a stabilizing solution to the matrix equation ”

I have a SSM ( State Space Model ) and I want to calculate its optimum gains unisng LQOutputRegulatorGains[] command. When I run the code, it solves the equations ...
4
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1answer
162 views

Why do NDSolve and OutputResponse not evaluate non-analytic functions numerically?

test = OutputResponse[TransferFunctionModel[1/(1 + s), s], Exp[-(1/t)], {t, 0, 10}] does not evaluate. If Exp[-(1/t)] is ...
4
votes
2answers
586 views

How to transform transfer functions into differential equations?

is there a way with Mathematica to transform transferfunctions (Laplace) into differential equations? Let's say I have the transfer function $\frac{Y(s)}{U(s)}=\text{Kp} \left(\frac{1}{s ...
4
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1answer
108 views

How to apply RootLocusPlot correctly

I have to analyze the complex regions of variable c which is define obtained with InverseLaplace help in the form ...
6
votes
1answer
665 views

Estimate parameters of the state space model

I'm using Mathematica 9 and its Control Systems functionality. I've searched the references extensively but seem not to be able to find any examples of state space model parameters estimation. All ...
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1answer
635 views

Unit of the frequency axis in BodePlot

I have a simple question: What is the unit of the frequency axis in the BodePlot? I searched the documentation, but only found this: The scaling functions can be specified as ...
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0answers
287 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: ...
0
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1answer
166 views

How to use NyquistPlot without having a transfer function model?

Could anyone tell me how to use NyquistPlot with a first argument that is not a transfer function model? The expression I'd like to pass to ...
9
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1answer
786 views

How to calculate the $H_2$ and $H_\infty$ norms of TransferFunctionModels or StateSpaceModels?

Lets assume we have a system model: ...
3
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1answer
743 views

How to increase Maximum number of steps in any other functions except NDSolve?

I want to plot an output response from a state space model. I use StateResponse[] to calculate it and then plot it. When I run my code, I face this message: ...
5
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2answers
476 views

Adding noise to nonlinear control system using NDSolve

I have a nonlinear control system ...
2
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1answer
3k views

How can I draw an asymptotic bode plot?

When I use Mathematica to draw a bode plot, it always gives the precise version, like this: BodePlot[(10 (s + 3))/(s (s + 2) (s^2 + s + 2))] How can I draw the ...
1
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1answer
757 views

How to simulate the response of a linear parametric varying system in Mathematica?

Consider the following system \begin{align} \dot{x}(t)&=\sum_{i=1}^{2}\rho_{i}(x(t))\left[A_{i}x(t)+B_{i}u(t)\right]\\ y(t)&=Cx(t) \end{align} with: ...
5
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1answer
287 views

Problems with RootLocusPlot

I am having some trouble to understand how the RootLocusPlot works (options, drawing and etc.) Here is an example ...
14
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1answer
732 views

Simulating discrete time stochastic dynamic systems

What is the canonical way of simulating discrete time stochastic dynamical systems in Mathematica using the new functionality of Random processes? To take a concrete example, lets consider the ...
5
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0answers
604 views

Kalman filter by hand

I am now learning the Kalman filter and wants to implement it by hand to understand it better. To be specific I want to first simulate a sequence of data by $$ \dot x=Ax+Bw\\ y=Cx+Dv,\\ ...
2
votes
2answers
836 views

Using transfer function model to generate state space model

I am trying to generate the state space model for the following system: However, the following code does not generate the state space model I expect: ...
6
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1answer
846 views

Does Mathematica solve transfer functions differently to Matlab?

Please note this is an edit to the same question posed a few weeks back: I'm using Mathematica to derive the transfer functions for a three phase AC/DC inverter. Given below is the code for the ...
4
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1answer
266 views

Using the LQGRegulator to build a human operator model

I'm trying to build a human operator model using an optimal control model in Mathematica: The vehicle dynamics are given by ...
4
votes
3answers
345 views

Strange behaviour of OutputResponse

I am having some trouble when using OutputResponse. For instance consider the following command ...
3
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1answer
327 views

How to adjust the parameters on a Nyquist Plot?

In order to see some details on a Nyquist Diagram I have used the function NyquistPlot that comes with Mathematica v8 and v9. ...
4
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3answers
2k views

How to fix BodePlot that comes with Mathematica?

I am using Mathematica to go through the examples and exercises on the book Modern Control Systems, 6th edition by Dorf. On page 605, there is a table (Table 8.5) with the Bode plot for several ...