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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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KVL and KCL for an RLC circuit

I have a circuit for a resistor \$ R \$, inductor \$ L \$, capacitor \$ C \$. I also have two sources of power, \$ u_1(t) \$ and \$ u_2 \$. My task is to set up a state equation for the circuit, and I ...
ganesh1102's user avatar
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State-Space Equation of 2 Capacitor and Resistor [closed]

Good Day Everyone, I'm trying to solve for the state-space model of the circuit shown below: simulate this circuit – Schematic created using CircuitLab Below are my state Variables: X1=Vc1 ; X2=...
Denavit-Hartenburg's user avatar
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Confusion on correct state space differential equations for LR circuit

For the circuit shown below, I have been deriving state space equation considering inductor current I1 and I2 as states, Vi, Ri and R as inputs (input supply and load resistance are variable inputs). ...
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State Space Formulation When the Equations Require Derivative of Input

Please see my related question here: Solution of electrical network where arbitrary initial conditions cannot be assigned Please consider that circuit. I now understand that derivatives of the input ...
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State space model of third order circuit

I'm trying to derive a state space model for this circuit: - simulate this circuit – Schematic created using CircuitLab The circuit contains four energy storing elements, but is only of third ...
Carl's user avatar
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Order of Complexity

Generally, number of independent state variables (order of complexity of a system) is equal to the number of reactive elements in RLC network. But, if capacitor and voltage source loops are present ...
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Derive state space from initial value problem

I am given the following initial value problem \$ y^{(4)} - y = u \$ with \$ y^{(3)}(0)=0, \ddot{y}(0)=1, \dot{y}=1, y(0)=10 \$ and am supposed to calculate the state space in the usual form \begin{...
insertRandomName's user avatar
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2 answers
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Derive a State-Space Model for an Electric Circuit with three Energy Storage Components

I want to model the shown circuit diagram with a state-space model. However, I cant solve it since I obtain four unknown variables while only three of the derived equations are linear independent. ...
Chris's user avatar
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State space representation of RLC circuit [closed]

Express the circuit in state space equations, the output is V2. I have tried defining the state variables but got stuck with the differential equations.
Menzi Ntshangase's user avatar
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Dynamic model of three dof to state space?

I´m trying to convert a 3 dof robot manipulator from dynamic model to state space. I saw a video where explains how to convert a 2 dof robot manipulator, but I don´t know how to apply it to a 3 dof ...
Rodrigo Barbosa's user avatar
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How to find the characteristic equation of a third-order system? [closed]

I am currently solving a question on pole placement method and in it we develop a required characteristic equation for the system using % overshoot and settling time. I know that in a 2nd-order system,...
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What is Byrnes-Isidori form and why is it usefu?

I was reading a paper about analysis of "Zero Dynamics" of a system but they initially converted the state-space model of the system into a "Byrnes-Isidori normal" form. What is ...
aakarsh's user avatar
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In state-space control systems, what is the correct convention for the symbol for the unit step function?

I don't wanna use the conventional "\$u(t)\$" because that is the input signal to a system represented in the state-space model. And I don't wanna use "\$H(t)\$" (for "...
robert bristow-johnson's user avatar
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What is meant by the shifting property of the companion form?

I am going through the book "Linear System Theory and Design" by Chi-Tsong Chen, where they talk about the controllable canonical form and how it is a realization of a transfer matrix. In ...
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Obtaining the State Space representation of a microgrid by combining the state space models of the subsystems

I am trying to obtain the state space model of the DC microgrid shown in the figure. It is made of three converters connected in parallel. Each one is modeled with a voltage source that outputs the ...
FernandoPT's user avatar
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Developing the state space model of an electrical circuit with 4 loops

I am trying to get the state space model for the given electrical circuit, but I am confused about selecting the state variable. How do I write the equation for the state space model?
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Confusion regarding transfer function and state space conversion in MATLAB

I have values of my state space MATRICES(A,B,C,D). I implemented them in MATLAB. My code is below, but I got confused when I tried to convert my state space representation to transfer function, ...
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Confusion regarding state space?

I am trying to understand state space and I have came across a circuit as shown in attached snapshot. According to my understanding number of states will be equal to number of effective energy storage ...
cxv4's user avatar
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Question regarding state-space modeling of a simple electrical circuit

Consider the circuit in the picture, where we have a voltage source (input) \$V(t)\$ and a capacitor \$C\$. The goal is to derive a state-space model of this circuit. The circuit satisfies the ...
Shi James's user avatar
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Superposition in state space equation with multiple harmonics in the inputs

I have a question related to the superposition in state space equation. Suppose I have a state space equation below \begin{equation} \frac{d}{dt}X = AX + B\begin{bmatrix} u_1(t)\\ u_2(t) \\ \end{...
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State-Space Model of Resonant Circuit

I am trying to determine the state-space model of the circuit shown below. Also shown are the KH equations. Those equations I put in a Solver (Mathcad), however the result does not seem correct. For ...
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State Space Representation for Initial Conditions

I am trying to design a system in which a capacitor's current discharge into an inductor is controlled by a MOSFET. I am trying to use a closed-loop control system to control the MOSFET's Vgs, and ...
TurboChad's user avatar
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State space model of a PWM driven circuit

I am trying to write down the state space model of the circuit given below: As it can be seen above, a P channel mosfet transistor is driven by a PWM signal. I am trying to model the circuit ...
FriendlyNeighborhoodEngineer's user avatar
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Cannot obtain a generalized state space averaged model for simple wireless power transfer system

this is the first time I ask a question. I am currently working on finding a state space model of the following system : where \$U_i\$ is a square wave of amplitude \$U_{in}\$. This circuit ...
Nicolas's user avatar
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Quick state feedback controller question

If two estimators where used in a state feedback system, one with error dynamics poles at -10 and -9 and another one at -80 and -90. Which system will give you a better overall performance?
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Implementing quadratic linear regulator (lqr) in simulink

I am working with a non-linear model of a hot-air balloon. I have linearized the system, found the operating point, the state space matrices and I know these are correct:- ...
Carl's user avatar
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Differential Equation to state spaces representation

I have to find the transfer function and state-space representation of the following first-order differential equation that represents a dynamic system: $$5\, \dot{x}(t) +x(t) = u(t) \\$$ The first ...
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State space model in the form of dx/dt=AX+BU

V=IZg V=IaZ IaZ=IZg LdIc/dt+RIc=(L+Lg)di/dt+(R+Rg)i simulate this circuit – Schematic created using CircuitLab Hi , how can I get state space model in the ...
safi2016's user avatar
5 votes
1 answer
362 views

How to transform the state space model of the induction motor?

First of all I would like to apologize if I have chosen wrong forum. My question is related to the electrical engineering but basically it is a mathematical problem. I have the state space model of ...
Steve's user avatar
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finding state space equation in x=Ax+Bu form

Can anyone please help me to find the state space equation of this circuit diagram in the form of x=Ax+Bu? The equation I am getting is not giving me square matrix. Can anyone help please? These are ...
safi2016's user avatar
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Space State on SEP/Ex DC-Motor

I'm currently studying DC motors and I do have some doubts about the dynamics of it. As per explained on [Guru, B.S. and Hiziroglu, H.R., 2001. Electric machinery and transformers (Vol. 726). New York:...
Michel Rodrigues's user avatar
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Going from transfer function to state space model

This is section from Linear Systems Control by Hendricks, and it is about going from a transfer function to a state space: - In eq. 2.40 they have a transfer function \$\frac{Y(s)}{U(s)} \$, where \$...
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What are the transfer functions of \$G(s)+G(s)^*\$ and \$G(s)-G(s)^*\$?

Consider the following system: \begin{align} &\dot{x}(t)=Ax(t)+Bu(t),\\ &y(t)=Cx(t), \end{align} where \$x\in\mathbb{C}^n\$ is the state and \$y\in\mathbb{C}^m\$ is the output, \$A,B,C\$ are ...
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Independent and dependent initial conditions

Consider the RLC circuit below. In fact, it is a normalized filter with Butterworth approximation of 3rd order. Now suppose that for some reason I am interested in the time domain formulation. Using ...
struct's user avatar
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error in dimension for adder in negative feedback loop

im a universiity student i was trying to model this state space with simulink i tried to use the state block but got the same error i think i need to use mux i already checked the dimensions for A B C ...
lolls222's user avatar
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How to estimate derivative of state in state-space model?

I would like to know what would be the best way to estimate a derivative of state of state-space model. I one would like to estimate one of the state, then the Kalman filter should work just fine. ...
Chanwoo Ahn's user avatar
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How to get second derivative of state as a output of state-space model?

Let's say modeling the free-falling object on state-space. Obviously, the equation of motion is a second order differential equation of the vertical position of the object. And one would normally set ...
Chanwoo Ahn's user avatar
2 votes
2 answers
426 views

Supernodes and KCL

Lets talk about Colpitts oscillator again (or the very basic circuit theory if you want). Suppose I modeled circuit as on the schematics below I am interested in systematic ways of obtaining circuit ...
struct's user avatar
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Small signal modelling of buck converter, varying frequency

It seems that the most popular method of voltage mode control of buck converters is by varying the duty cycle. Is this because it is easier to do so because we can set the duty cycle using PWM ICs? ...
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3 answers
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Space state circuit modeling question

i have a question about this circuit and its space-state modeling. I have the node A, modeled by $$I_{C_1}= I_{C_2}+ I_{R_1}$$ But i don't know what can I do. I already know that $$V_{R_1}=V_{C_2}$$ ...
Daniel Vargas's user avatar
3 votes
1 answer
140 views

State Space Clock Model & Control

I was hoping to get some help understanding a state space model that I have found in time and frequency literature. The literature pertains to a discrete-time model of a steered clock. A phase ...
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Is there software with CAS to solve drawn electrical circuit in form of differential equations which describes that electrical circuit?

Is there any software with Computer Algebra System to solve drawn electrical circuit in the form of differential equations which describe that electrical circuit? Or to write symbolic solution (...
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State Vector vs State-Space

I wonder if there is anything common in the concept of 'State vector' and 'State-Space'? Are they anyway related to each other or they are completely different ideas?
buttontech's user avatar
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Setting the initial output value for state space block in MATLAB

I've got the following control loop in Simulink: What I'm trying to do is to set the initial value for the output to be 23, right now it starts from 0 and I can't find any explanation how that's done,...
BigRedMachine's user avatar
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Simulate and compare the responses of a linear and non linear system

A metalic object is held up in air under an electromagnet. The vertical displacement of the object can be described by the following differential equation $$ m\frac{d^2H}{dt^2} = mg-k\frac{I^2}{H^2} $$...
Muhammed Roshan's user avatar
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Show A Non-Min Phase System Cannot be Controlled via Controllability Matrix?

I've been reading about how a non-minimum phase system with a Right-Half Plane Zero and Right-Half Plane Pole can become impossible to control IF the RHP Pole becomes faster than the RHP Zero. I was ...
EthanT's user avatar
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State equations of Colpitts oscillator

I am struggling with the simple oscillator on the picture below. My aim is to obtain system of ODEs or DAE at most for numerical simulation in Matlab. But few issues occured with basic circuit theory....
struct's user avatar
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State Space Averaging combined with Static Analysis

In class we learned about State Space Averaging Mathod to analize DC-DC converter topologies. Therefore we defined a stete vector x containing variables proportinal to the stored energy in a circuit ...
Matthias Waelti's user avatar
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Help to construct a State space model of a unipolar stepper motor with shorted phases

I hope to get some help on an interesting task - I cannot seem to get my model to work which is my I ask for help here. I am trying to construct a model of the unipolar stepper (seen below in the ...
superbrusen's user avatar
1 vote
1 answer
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Linearization of Non Linear State Space Model

Im designing a PI controller for a Maglev experiement but im a little stuck on how to linearize the non linear state space model. I have developed the state equations (seen below) and i know the ...
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