# 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 ...
1 vote
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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=...
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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 ...
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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? [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 ...
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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 ...
1 vote
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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 ...
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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 \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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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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### 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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