# Tagged Questions

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

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### Numerical optimal control

I was hoping to tackle optimal control using Mathematica in order to learn how I can use Mathematica's built in numerical integration and optimization functions together in order to solve an optimal ...
788 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 ...
943 views

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

Lets assume we have a system model: ...
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### Working Precision in nonlinear control systems

When simulating a nonlinear control system using StateResponse , do the options WorkingPrecision, ...
546 views

### Adding noise to nonlinear control system using NDSolve

I have a nonlinear control system ...
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### 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: ...
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 ...
330 views

### How do you use SystemsModelFeedbackConnect?

I'm trying to grasp the new control system functions in Mathematica 8. I'd like to connect a controller model to a model of a plant to simulate the behavior of the system. I define a simple servo ...
898 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 ...
846 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 ...
659 views

### How to convert a transfer function model to a zero-pole-gain model?

Mathematica has a function to convert TransferFunctionModels to StateSpaceModels: mytf=TransferFunctionModel[(2 s + 3)/(s^3 + 4 s^2 + 5), s] StateSpaceModel[mytf] ...
730 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 ...
355 views

### Strange behaviour of OutputResponse

I am having some trouble when using OutputResponse. For instance consider the following command ...
132 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: <...
316 views

### Problems with RootLocusPlot

I am having some trouble to understand how the RootLocusPlot works (options, drawing and etc.) Here is an example ...
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### 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 ...
286 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 "command-...
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### 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 ...
4k 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 ...
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### How does RootLocusPlot handle TransferFunctionModel

I'd like to analyze the poles (denominator-roots) of a TransferFunctionModel, that was generated from a NonLinearStateSpaceModel....
938 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: ...
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### 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. ...
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### Mathematica for dynamics and controls [closed]

I am new to Mathematica and want it to use for dynamic and control systems. To begin with, I would want to be limited to symbolic computation for linear and nonlinear control systems - including ...
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### 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 ...
867 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: ...
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### 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 ...
170 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 ...
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### StateSpaceModel- damped oscillator

I'm new in Control system and in Mathematica too. res1 is the state space as follows ...
268 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 ...
751 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 ScalingFunctions->{{...
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### 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 ...
103 views

### How to see controllers response?

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