Linear control theory is the sub-branch of control theory dealing with linear or linearized systems.
Questions tagged [linear-control]
549 questions
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Causality of linear singular systems
According to Dai(1989, p. 234), the following system:
$Ex(k+1)=Ax(k)+Bu(k)$
$y(k)=Cx(k), $ $k=0, 1, ..., L$
where $ x(k) \in \mathbb{R}^n$, $ u(k) \in \mathbb{R}^m$, $y(k) \in \mathbb{R}^r$ and $E, A \in \mathbb{R}^{n\times n}$, $B \in…
RGB
- 21
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the system controllability and observability
If a linear system is controllable, does it mean we can find the control standard form in state space, but it doesn't mean all the forms of state space representations is controllable?
孙志鹏
- 11
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Product of Observability and Controllability matrices
I noticed in Linear Control Theory, we may multiply matrices for controllability $\mathcal{C} \in \mathbb{R}^{n \times np}$ and observability $\mathcal{O} \in \mathbb{R}^{nq \times n}$ as follows $\mathcal{O} \mathcal{C} \in \mathbb{R}^{np \times…
User 42
- 325
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Equivalent Statements for a Discrete-Time System
I have a discrete-time system x_(k+1) = A*x_k, x(0) = x_0 where A is in n x n dimensional space and is a real constant matrix. How do I show that the following statements are equivalent?
All eigenvalues of A are located on the open unit disc
For…
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Block Diagram Reduction Error?
I am reducing a block diagram manually and am not sure whether the following step is a valid step? I am using the rule of moving a summing ahead of a block in reverse.
Reduction Step in Question
I've checked the resulting transfer function before…
Jord
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1 answer
Update state-space representation by hand
Suppose we have the following state-space representation:
$x(k + 1) = Ax(k) + Bu(k)$
$y(k) = Cx(k) + Du(k)$
When calculating the state space by hand, should I use the following procedure?
Set k = 0
Calculate $x(1)$ using $u(0)$ and…
nekoneko
- 3
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2 answers
stability of linear system
I have a discrete system of the form
$x(k+k_o) = Ax(k+k_o-1) + Bx(k)$
where $A$ and $B$ are $n\times n$ matrices ($k_o>0$). I want to know about the stability of the system when
both A and B have eigen values inside the unit circle
Eigen values of…
faisal
- 37
0
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1 answer
CCF of Transfer Function
Given this
transfer function
I have two questions:
1) What is the state space model in controllable canonical form?
2) How can you that the system is always controllable; i.e. show that the controllability matrix: $$ \mathscr C =…
Matt
- 45
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1 answer
AC motor Mathematical Modelling
paper
I want to model an AC Servomotor where I assume that a dynamic load is attached to the shaft of AC Servomotor. The link of the paper that i have attached at the beginning of this post has ac servomotor model running without load that's why in…
Abdul Wali
- 11
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1 answer
Difference between input and output disturbance
I have been reading several manuscripts, primarily involving modified Smith Predictors to improve disturbance rejection for time-delayed systems. The overwhelming majority of these manuscripts discuss in rejecting input disturbances to the process.…
0
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2 answers
Linearize $\tau -mgl cos(\theta)$ for $\tau = \tau_0 + \delta \tau, \theta = \theta_0 + \delta \theta$
I'm trying to solve a control problem involving a pendulum, in which the equation of motion is:
$ml^2\frac{d^2 \theta}{d\theta^2} = \tau -mgl cos(\theta)$
I need to linearize $\tau -mgl cos(\theta)$ for $\tau = \tau_0 + \delta \tau, \theta =…
Luc Evertzen
- 53
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1 answer
Feedback Group in Linear Control System
The state model of linear control system is $\Sigma:\dot{x}=Ax+Bu$, where $x$ is the state and $u$ is the input. A state feedback $F:u=Fx+v$ can be treated as a transformation which maps $\Sigma$ to $\Sigma_F:\dot{x}=(A+BF)x+Bv$. Prove the…
gaoxinge
- 4,434