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Questions tagged [state-space]

State-space representation is a mathematical model of a physical system as a set of input, output and state variables related by first-order differential equations. "State space" refers to the space whose axes are the state variables. The state of the system can be represented as a vector within that space.

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How to linearize the system below(Controller and observer design) and what are the desired poles for it?

I'm trying to linearize the system below(Controller and observer design) and find the desired poles for it?. Could anyone help me in this method, please?.
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Determining Number of states in State Space Modeling

I want to use state space modeling for representing the following circuit system. However, I am unable to decide the number of states. I am able to describe the system with a set of three equations. ...
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46 views

How to plot response of a non-linear state space model in Simulink?

I am trying to plot a non-linear model in order to compare it with it's linearized counterpart. I am following this paper Nonlinear Model & Controller Design for Magnetic Levitation System and ...
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Automatic control - linearization with two states

I don't understand a part of the solution to c) of this problem, namely linearization at a stationary point using Taylor series and partial derivatives. I am used to linearization of \$ f(x,u) \$ (...
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165 views

State Space model for three-loop circuit

How do I choose the least number of state variables for the following circuit? I started out by assuming currents $$i_{1}, i_{2}, i_{3}$$ in each of the loops and applied KVL, which fetched me three ...
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112 views

state-space model for bidirectional buck-boost with input capacitors

I'm having some trouble simulating the behaviour of a bidirectional buck-boost converter for battery charging purposes. The circuit looks as follows: I would like to create an averaged state-space ...
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Relationship between eigen values and state feedback

so lets suppose we have a state space model x[k+1] = Ax[k] + Bu[k] y[k] = Cx[k] + Bu[k] and we want to design a state feedback, assuming that the system is ...
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How to I go from generalized Transfer Function to generalized State Space, and back?

Question: How can I transform a generalized Transfer Function a generalized state space form (preferable with the First Companion Form), and back? For the sake of presenting an example, let us say ...
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How do I write the equations for three inductors connected together in state space form?

The system is basically three inductors connected to each other in one end and the other end connected to three independent voltage sources. I want to get the equations in state space form. For this ...
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Pole-placement problem

I was following this example of implementing a pole-placement with an Integral controller. Matrices A_star=[-5 -3 0;1 0 0;0 -1 0] B_star=[1;0;0] desired poles -100,-8+i*11,-8-i*11 I know the ...
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1answer
73 views

Frequency domain representation

I'm studying the space-state representation and I'm not understanding a simple situation that I created. I created the following system, on the frequency domain: By writing the time domain ...
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71 views

Control Systems - State equations

I'm starting to learn about the state-space representation and i'm facing some difficulties. Suppose we have a system with connected blocks, like the one below: where Sometimes we want to choose ...
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Obtaining the analytical expression using the state transformation matrix

I am trying to derive the analytical expression in the box below. T is the state transformation matrix. x_dot=A*x(t) is a second order linear system. A has 2 distinct eigenvalues s1 and s2 and ...
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224 views

State Model Representation of RLC network

I am confused with the above problem. Should I take a new state variable for rightmost capacitor or 3 variables are sufficient? Please help me in writing the state space equations.
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tracking error state space, linear control example

I am trying to understand a detail from an example, from the control textbook Slotine and Li (1991) "Applied Nonlinear Control", Prentice-Hall, Example 6.4, pag. 220. A linear system is given: $$\...
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231 views

Finding asymptotic stability of RLC circuits

Given the state model for an RLC circuit, how can I show that it is asymptotically stable? So my state assignment is as follows: x1 = Vc x2 = iL And using the KVL and KCL equations I can get a ...
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Why is it necessary to know a state of a system?

In a system why is necessary ? why cant we use a simple transfer funtion in an S or Z domain ,to get an input output relation , or as we already know our input and measure our outputs through sensors ?...
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State Space Model Basics

I have added the problem with its solution. I tried applying Mason's Gain Formula which led me to the same result and it should have as Transfer Function is unique. Is there a shorter way to get ...
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378 views

How RF Choke doubles Vcc at collector in BJT Power Amplifier

I'm trying to analyze a class A RF power amplifier as represented in the picture. The main thing I'm trying to understand is how the collector voltage can go to 2x Vcc as according to this page. ...
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245 views

Averaging matrix is not invertible in state space averaging

I am having a problem with state averaging method. The circuit is a SIDO converter as in the figure below. This circuit is just an example to show the problem. So please don't care much about the ...
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matrix transformation for state space matrices

Can we use matrix transformation for the A,B,C,D matrices involved in the state space analysis? e.g. In the above figure the state variables are not numbered, like which one is X1 and which one is X2 ...
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126 views

state-space averaging with matrices not same dimension

Below are procedures for state-space averaging: Question: For some circuits, each matrix pair (A1 and A2) or (B1 and B2) doesn't have the same dimension. To be specific, A1 is not same dimension as ...
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55 views

Is the system's pole movable?

Here is the state space representation of the system. $$\dot x=\begin{bmatrix}\dot x_1\\\dot x_2\end{bmatrix}=\begin{bmatrix}0&0\\1&0\end{bmatrix}\begin{bmatrix} x_1\\ x_2\end{bmatrix}+\begin{...
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177 views

Find output given state space representation

This is usually easy but there are things I haven't encountered in this one. This is the problem. $$\dot x=\begin{bmatrix}0&1\\-2&-3\end{bmatrix}x+\begin{bmatrix}0\\2\end{bmatrix}u=Ax+Bu\\y=\...
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Question about the transfer function found from state space model

I'll make up a problem to explain what I'm having trouble with. $$\dot x=\begin{bmatrix}0&1\\-5&-6\end{bmatrix}x+\begin{bmatrix}0\\1\end{bmatrix}u=Ax+Bu\\\\y=\begin{bmatrix}0&1\end{bmatrix}...
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Compensator for a specific damping ratio ζ

Okay, so I've been given a system to linearize and it gave me this result $$δ\ddot x+δx=δu$$ I tried state-space modeling this and this is what I got: $${\dot x}=Ax+Bu=\begin{bmatrix}0&1\\-1&...
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What is the current component at the input of dc-dc converters?

The table below describles state space analysis in the field of power electronics. It is from a paper entitled "Signal Flow Graph in Loop Gain Analysis of DC–DC PWM CCM Switching Converters by Wing-...
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Confusion on State Space Equation of Buck Converter

I'm trying to represent a buck converter in terms of state space equations. I'm assuming CCM operation and I had derived the state space equations for two modes of operations: Mode 1: Switch is ON (...
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Find transfer function from state space representation

The following system is given : $$\dot{\bar x}=\begin{bmatrix}0&1&0&0\\-1&-2&0&0\\0&0&0&1\\0&0&0&-3 \end{bmatrix}\bar x+\begin{bmatrix}0&0\\-1&0\...
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Get transfer function from state space

The following system is given and I'm asked to find the transfer function $$\frac{Y(s)}{U(s)}=G(s)$$ $$\bar {\dot x}=\begin{bmatrix} 0 & 1 & 0 & 0 &0 \\0 & 0 & 1 & 0 & ...
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338 views

PID controller - How is plant equation derived?

During our control systems course we often work on control techniques where the plant equation/state space model is given .However , how are these derived? For example, if I wanted to build a ...
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182 views

State Space model for a MIMO, coupled system

I came across a non-linear MIMO system with coupled inputs which is to be modelled in state space form. The kinematics are as follows: $$ \ddot{x} = F_Ecos(\psi)sin(\theta) + F_Esin(\psi)cos(\theta) +...
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identifying overshoots in given state space system with step inputs

Suppose I have the following state space system: $$ \dot{x}(t) = Ax(t) + Bu, \quad y(t) = Lx(t), \quad x(0) = x_0\neq 0 $$ where \$A\$, \$B\$ and \$L\$ are real matrices, \$u\$ is a constant real ...
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Determine whether the system can be stabilized by the control law

I have a controls homework question I am having trouble figuring out where to start. The questions is Determine whether the system can be stabilized by the control law \$u = - {G_1}{x_1} - {G_2}{x_2} ...
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266 views

Analysis of Closed Loop Transfer Function

I am trying to understand how to solve a homework problem I have. It states: Analytically show that closed-loop system is stable for all values of K. By looking at the block diagram, I know that this ...
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Find state space representation with 2 inputs and 2 outputs

I have no problem finding the transfer function with systems of 1 input and 1 output and then I can easily obtain the space state representation, but this exercise requires me to "Find the space state ...
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control systems - state space representation using transfer functions

I am trying to manually get the state space representation of an RLC network. I often end up with a bunch of differential equations that I can't relate to each other. I think it would be easier to ...
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2k views

Jordan Canonical Form matrix

I apologize in advance if I didn't give enough information. I don't really have the mathematical background to this type of problem. Given the following equation: $$G(s) = \frac{2s+3}{s^4 + 3s^2 + ...
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Problem: \$\frac{4s + 2}{s(s-1)(s+2)} \$ Expectation of Root Locus Asymptote. (Control Systems)

My transfer function is \$\frac{4s + 2}{s(s-1)(s+2)} \$ Given that there are 3 poles and 1 zeroes, the amount of loci going to infinity is 3-1 = 2 loci = r. I calculated where the centroid of the ...
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Identifying the parameters of a linear state-space-model using Kalman Filter

I have a linear state space model (SSM) that looks like this \begin{align} {\dot {x}} & = {\rm \textbf{A}}{x} + {\rm \textbf{B}}{u} \\ {y} & = {\...
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State Space Model for Variable Mutual Inductance

This is a hell of a request, but today I have recently introduced myself to the concept of the 'State Space' model. I've understood, to a basic level, how state space models work and I am convinced ...