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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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state space representation of system with a disturbance

my question is how you can convert the bloc diagram which have a disturbance input to a state space representation and how you can calculate the controllability matrix then if you can give me any ...
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Observability matrix different forms

The observability matrix formula is present in two forms in textbooks. My question is about which one to use. the first one: the second one: Now when applying both on the same system, I get ...
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What will be minimum number of states / state variables for these control systems in state-space model?

Consider the systems as LTI and SISO with transfer functions given below: I have read that minimum number of states for an LTI SISO system required to represent in state space analysis for any ...
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What is wrong with my inverted pendulum?

I have been making an inverted pendulum using LQR. Here's a list of my hardware: Microcontroller: Microchip WiFIRE (PIC 32) Motor Control: L298N Encoders (2x): US Digital shaft encoders (4095 ...
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Minimal State-Space-Realization using SVD

A similarity transformation with U produces so following state space model \begin{equation} (A, B, C, D) \stackrel{\tilde{x}=U^{\prime} \cdot x}{\longrightarrow}\left(U^{\prime} \cdot A \cdot U, U^{\...
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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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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 ...
54 views

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 $f(x,u)$ (...
249 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 ...
130 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 ...
83 views

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 ...
104 views

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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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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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 ...
286 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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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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