# Questions tagged [system-identification]

is related to control theory, dynamic optimization and statistical methods to build mathematical models based on some measured data.

56 questions
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### Derive transfer function of an unstable plant [duplicate]

Is there a method to mathematically estimate/model the transfer function of a plant around an unstable equilibrium point? A constant step input causes the plant output to increase exponentially with ...
1answer
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### System Identification in a Closed-loop feedback system

I have an unstable system that doesn't have a useable output when open-loop excitation is applied. Subsequently I've used a controller to control its output. I want to use the system identification ...
3answers
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### Suppose $\dot{x}=Ax$, where $A \in \mathbb{R}^{2\times2}$. Determine $A$ from the initial and final states

Two experiments were done: $x(0)= [1,1]^T$ and $x(1)=[4, -2]^T$ $x(0)= [1, 2]^T$ and $x(1)=[5, -2]^T$ How can I find the $A$ matrix? I know how to find $e^{At}$, for $t=1$, using these $2$ ...
1answer
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### How can I find the initial state vector from state space model?

Assume that we have input $u(k)\in \Re$ and output $y(k) \in \Re$ and we estimate the black box model by using subspace identification method. $$x (k+1) = Ax (k) + Bu(k)$$ $$y (k) = Cx (k)$$ If ...
1answer
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### Model reduction of estimated state space models - System identification

Assume that we have a dynamical model in form of this simple transfer function $$G(s) = \frac{1}{2s^2 + 5s + 4}$$ G = tf(1, [2 5 4]) We do a step response with ...
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### How can I reduce noise from measurement without a Kalman Filter?

I'm going to create an adaptive Model Predictive Controller (MPC). The model is a state space model. Due to noise, it's very difficult to determine the model order. I'm using subspace identification ...
0answers
50 views

### How can I compute recursive QR-factorization?

I wonder if it's possible to find the $Q$ and $R$ matrices from this QR-equation with only compute QR at one time only: $$A = QR$$ if, the first column of $A$ got removed and then a new column got ...
0answers
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### Recursive QR-factorisation for N4SID - What does this equation mean?

I was reading a paper about recursive subspace identification, where they are using N4SID-algorithm with some extantion for the recursive method. http://www.iaescore.com/journals/index.php/IJEECS/...
2answers
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### Is there any rule of thumb when it comes to selecting control/predict horizon for MPC?

I have a simple question: Is there any rule of thumb when it comes to selecting control/predict horizon for MPC? Normaly I set control and predict horizon equals, but I have heard that's not good ...
1answer
47 views

### sample covariance matrix

Suppose two covariance function estimators, with the same formula except for a coefficient. Then make two sample covariance matrix(SCM) from each of the functions. Why should these matrices differ in ...
0answers
40 views

### Recommended book on “Dynamic Model Learning” related to “System Identification”?

I need to take a course on so-called "Dynamic Model Learning" related to "System Identification" + "Machine Learning stuff". But my backrgound is more on Computer Science and Electrical Engineering ...
1answer
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### Getting differential equation from Boyle's law

I'm trying to simulate pipe installation with known amount of air in Simulink and design a PI controller for it. I was able to construct equations which reflects well my real installation. My pressure ...
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### Nonlinear system identification with known model

I would like to ask for suggestions regarding system identification with known model structure, but without known parameters. The model is a model of a physical system, it can be assumed that it is ...
0answers
93 views

### What's the point of having a reference model in Model Reference Adaptive Control?

The MRAC(or called MRAS where S = 'System') controller is called a adaptive controller. I don't know why, because it have no system identification process loop. But what's the point to having a ...
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1answer
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### I can't get my Recursive Least Square algorithm work - What have I miss?

I'm want to do a recursive least square algorithm but I can't get it to work. If you don't know what recursive least square algorithm is. Well, it just ordinary least square, but it's an algorithm ...
1answer
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### How should I interprent the Recursive Least Square algorithm?

This is the recursive least square algorithm. $$\hat{\theta}(t) = \hat{\theta}(t-1) + K(t)(y(t) - \phi^T(t)\hat{\theta}(t-1)) \\ K(t) = P(t)\phi(t) \\ P(t) = (I-K(t)\phi^T(t))P(t-1)$$ As I know, I ...
1answer
429 views

### MIT rule VS Lyapunov design - Adaptive Control

I wonder what's the difference between MIT rule and Lyapunov design when it comes to adaptive control law? As I get it, MIT rule is more like "transfer function"-based control system and Lyapunov ...
1answer
150 views

### Structured transfer function estimation in MATLAB?

I have some input-output data for a dynamical system (input = stimulus, output = observation). Assuming that this system is linear time-invariant, I am trying to estimate a transfer function $H(s)$ of ...
1answer
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### How do I get the amplitude of a variable sine function?

Let's assume that we have a dynamical system $$G(s) = \frac{Y(s)}{U(s)}$$ And we have measure the input $u(t)$ And we have measure the output $y(t)$. Here we can see that if we increase the ...
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### Can I use least square method to estimate a Box-Jenkins model?

I have the known measurement: Noise $e(t)$, output $y(k)$, input $u(k)$. I need to find the Box-Jenkins model: $$y[k] = \frac{B(q)}{F(q)}u[k] + \frac{C(q)}{D(q)}e[k]$$ Where $B, F, C, D$ are ...
1answer
36 views

### Estimate a transfer function from an arbitrary response?

Assume that we have a step answer which look like this: This step answer is from a difference equation. Called a discrete ODE: $$y[k] + a_1y[k - 1] + a_2y[k - 2] = b_1u[k]$$ Which can be a ...
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### Identify a transfer function from frequency data?

Assume that I want to identify a transfer function from frequency data. Assume that I have a transfer function step response which look like this: By experience, I would say that this step response ...
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### Identify a state space model from measured inputs and outputs

I'm using subspace identification to identify a black-box state space model. To identify I follow these steps: We have measured a vector of inputs $u_k \in \Re^{m}$ and outputs $y_k \in \Re^{l}$. For ...
2answers
38 views