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

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20
votes
2answers
391 views

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 ...
14
votes
1answer
774 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 ...
9
votes
1answer
895 views

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

Lets assume we have a system model: ...
8
votes
1answer
156 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: ...
8
votes
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 ...
8
votes
1answer
69 views

Working Precision in nonlinear control systems

When simulating a nonlinear control system using StateResponse , do the options WorkingPrecision, ...
7
votes
1answer
320 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 ...
7
votes
2answers
519 views

Adding noise to nonlinear control system using NDSolve

I have a nonlinear control system ...
6
votes
3answers
839 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 ...
6
votes
1answer
634 views

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

Mathematica has a function to convert TransferFunctionModels to StateSpaceModels: ...
6
votes
1answer
887 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 ...
6
votes
1answer
715 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 ...
5
votes
3answers
352 views

Strange behaviour of OutputResponse

I am having some trouble when using OutputResponse. For instance consider the following command ...
5
votes
2answers
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: ...
5
votes
1answer
310 views

Problems with RootLocusPlot

I am having some trouble to understand how the RootLocusPlot works (options, drawing and etc.) Here is an example ...
5
votes
1answer
88 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
votes
0answers
275 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 ...
5
votes
0answers
640 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,\\ ...
4
votes
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 ...
4
votes
2answers
327 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. ...
4
votes
1answer
73 views

Issues with modeling pulses in a very simple system of DAEs

Some time ago I had asked this question about evaluation difficulties using Euler Integration to solve a system of ODE where discrete pulses occur. While I have now abandoned Euler integration and ...
4
votes
2answers
677 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
votes
1answer
111 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 ...
4
votes
1answer
274 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
1answer
165 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). ...
4
votes
1answer
177 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 ...
3
votes
1answer
345 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. ...
3
votes
1answer
795 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: ...
3
votes
2answers
86 views

Solve transfer function with non-zero initial conditions

Hand computation I have a transfer function defined as $\frac{0.6p+1}{0.6p^2+2.2p+8}$ which was derived from a circuit. Solving this by hand gives the equation, $$i(t)=Ce^{-1.83t}\cos(3.16t + \phi)$$ ...
3
votes
1answer
42 views

Basic computations in frequncy domain

I have been trying to find documentation on performing basic operation with transfer function models but have been unable to do so. By basic operation I mean, e.g. Multiply controller transfer ...
3
votes
0answers
136 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 ...
2
votes
1answer
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 ...
2
votes
1answer
57 views

How does RootLocusPlot handle TransferFunctionModel

I'd like to analyze the poles (denominator-roots) of a TransferFunctionModel, that was generated from a ...
2
votes
2answers
908 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: ...
2
votes
2answers
69 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. ...
2
votes
0answers
45 views

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 ...
2
votes
0answers
42 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
vote
2answers
842 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: ...
1
vote
3answers
148 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 ...
1
vote
1answer
164 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 ...
1
vote
1answer
110 views

StateSpaceModel- damped oscillator

I'm new in Control system and in Mathematica too. res1 is the state space as follows ...
1
vote
3answers
240 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 ...
1
vote
1answer
715 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 ...
1
vote
1answer
71 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 ...
1
vote
1answer
100 views

How to see controllers response?

How can I get/plot the controller's effort of a controlled system (state space model)? Example system: ...
1
vote
1answer
83 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 ...
1
vote
1answer
32 views

NonlinearStateSpaceModel/OutputResponse gives doubled outputs

I want to simulate a pendulum or rather the controlled system. But NonlinearStateSpaceModel or the OutputResponse gives weird ...
1
vote
0answers
341 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
votes
2answers
138 views

Convert DE to first order?

I have the following set of second-order differential equations: ...
0
votes
1answer
96 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 ; ...