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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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 ...
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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{...
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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. ...
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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.
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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 ...
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How to find the characteristic equation of a third-order system?
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 ...
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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 "...
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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 ...
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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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KVL and KCL laws to develop the state model
I am developing a state space model for the given circuit. I am confused about the series capacitors C7 and C8 and that connected parallel to C6 but in between C7 and C8 there is ground connected.
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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:-
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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 ...
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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 ...
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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 ...
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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:...
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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 ...
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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 ...
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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. ...
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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 ...
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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 ...
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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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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 $$V_{R_1}=V_{C_2}$$ ...
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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?
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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,...
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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 $$ m\frac{d^2H}{dt^2} = mg-k\frac{I^2}{H^2} $$...
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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 ...
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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....
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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 ...
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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 ...
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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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"state" in state space analysis?
What is meant by "state"in state space analysis?
Is it something related to initial conditions such as in RLC circuit in attached snap,we have two states
1)Current through inductor
2) ...
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Why are state variables sufficient to describe the exact future temporal dynamics of a system
I'm confused about state-space state variables. How come knowing the initial conditions with the input 'determine completely the future behavior of the system'? From such knowledge, I can only ...
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Balancing a stick using two different designs and comparing both
I want to understand which feedback systems are in general preferred over another model (that I'm going to show in image),so first we take a example of a particular system (here stick at 90degree from ...
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