6 votes

Linearization of Non Linear State Space Model

The typical steps followed to linearise the system \$\dot{x} = f(x, u)\$ is to split the state variable into two parts; a steady part (operating point) and a small-signal part. This can be done with ...
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  • 3,646
4 votes
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What is the current component at the input of dc-dc converters?

Generally in DC-DC circuit models, the converter load is modeled as a current source (i2) with a resistance in parallel. This is to generalize the model as much as possible and to take into account ...
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  • 1,074
3 votes
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Why is it necessary to know a state of a system?

If the system has memory, you need to know what state the memory is in. For example: a system with a low pass filter of a resistor and a capacitor will respond differently if the capacitor is fully ...
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  • 63.7k
3 votes

State Space Clock Model & Control

This is more of an extended comment than an answer. The system may be inherently discrete-time. It may not make sense to find the continuous time plant model, as it may not exist. I am not familiar ...
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  • 3,646
2 votes
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Relationship between eigen values and state feedback

My question is that even if we have control over eigen values of this new vector how does that help us control the system i.e. to bring our system to our desired state? If you consider your system as ...
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2 votes
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state space representation of system with a disturbance

It is basic block diagram algebra. First, you write out the algebraic equations and solve for the unknowns \$x1\$ and \$x2\$. $$\text{x1}=\frac{0.05 (\text{Ua}-0.1 \text{x2})}{0.01 s+1}$$ $$\text{x2}...
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  • 1,234
2 votes
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Find state space representation with 2 inputs and 2 outputs

A possible solution: Choosing state variables as current in the inductor and the voltage in the capacitor: $$ x_1 = i_L = i_1 $$ $$x_2 = v_C $$ Applying KVL and KCL to the left mesh and top node, ...
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2 votes

Why is it necessary to know a state of a system?

Sometimes we have systems where a transfer function representation, called an external description, is insufficient to completely characterize it. As an example consider the circuit below, taken for ...
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  • 1,025
2 votes
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Is transformation from one state representation to other state representation changes the transfer function of the system

The similarity transformation is only a change of basis (co-ordinates) and doesn't change the input to output relations, viz, the transfer function (TF). The similarity transformation preserves the ...
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  • 3,646
2 votes
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Why are state variables sufficient to describe the exact future temporal dynamics of a system

How come knowing the initial conditions with the input 'determine completely the future behaviour of the system'? From such knowledge, I can only approximate the 'next' state at 0+dt... If you have \$...
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  • 3,646
2 votes

"state" in state space analysis?

At a given time this circuit has several solutions. Of course, once all voltages and currents are stabilised, there is only one solution ( current through L1 and R1 = 0.01A, C2 voltage = 1 volt). But ...
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  • 996
2 votes

Space state circuit modeling question

You know that \$V_{R_1} = V_{C_2}\$ So replacing \$V_{R_1}\$ by \$V_{C_2}\$ in your equation \$V_{C_1} + V_{R_1} - V_1 = 0\$ leads to \$V_{C_1} + V_{C_2} = V_1\$ Differentiating results in \$d(V_{C_1})...
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  • 186
2 votes
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Independent and dependent initial conditions

I think the problem might be that your cap currents don't follow your +/- convention. Here I've drawn all of the +/- indicators and current arrows: simulate this circuit – Schematic created ...
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  • 4,256
2 votes
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Space State on SEP/Ex DC-Motor

At this moment, on the second bullet, is there a reason not to consider if time-varying (shouldn't it be \$i_f(t)\$ or was it just a typo)? I would consider it a typo. I've tried to put together the ...
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  • 36.3k
2 votes
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Differential Equation to state spaces representation

There is no one correct answer for the state-space representation. If you choose the state as \$x_1=x\$, then the equations are $$ x_1'=-0.2x_1+0.2u\\y=x_1$$ If the state is chosen as \$x_1=2.5 x\$, ...
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  • 1,234
1 vote

State variable equations for a RLC circuit

The inductor equation: $$L i_3'=v_1-v_C$$ The capacitor equation: $$c v_c'=i_3\ \ \ (1)$$ Kirchoff's current law: $$\frac{u-v_1}{R_1}=i_3+\frac{v_1}{R_2}$$ which can be solved for \$v_1\$ to get $$...
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  • 1,234
1 vote

control systems - state space representation using transfer functions

There are several ways to convert a transfer function into a state space representation. They lead to apparently different results, but retain the same essential information. Possible representations:...
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1 vote

Problem: \$\frac{4s + 2}{s(s-1)(s+2)} \$ Expectation of Root Locus Asymptote. (Control Systems)

The angle the asymptotes make with the real-axes is \$\frac{(2 k+1)\pi}{2} \$. The denominator is the number of finite poles minus the number of finite zeros (\$3-1\$). This turns out as \$\frac{\pi}{...
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  • 1,234
1 vote

What is wrong with my inverted pendulum?

There are many nonlinearities that can be impacting your system. The most likely factor is a dead-zone -- a PWM duty cycle too small to make the motor move at all.
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1 vote

What is wrong with my inverted pendulum?

I knew of a group of students that were building an inverted pendulum, they analyzed the system found the transfer function and programmed it. It refused to work until they put a negative sign on the ...
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  • 63.7k
1 vote

Determining Number of states in State Space Modeling

The answer to the question is already provided by other users in the comments, but I think that solved questions should not be marked as unanswered (https://meta.stackoverflow.com/q/251597). I didn't ...
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1 vote

Automatic control - linearization with two states

I believe you are aware of the concept of the Jacobian matrix. This is a case of Linearization of Multistate Models. See, for example, pages 6-7 of Linearization of Nonlinear Models. Yes, that ...
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1 vote

state-space model for bidirectional buck-boost with input capacitors

Consider the output \$y(t)\$, as typically represented in state-space models: \$y(t) = Cx(t)+Du(t)\$. If you were to equate one element of \$x(t)\$ to \$u(t)\$, then this means the original ...
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1 vote

How to I go from generalized Transfer Function to generalized State Space, and back?

The transformation back, from a state-space model to a transfer function can be done with \$C(sI-A)^{-1}B\$, irrespective of the number of inputs and outputs. In general, you might not end up with a ...
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1 vote

Frequency domain representation

Your notation is confusing. Let \$ \small y(t)\rightarrow Y(s)\$ be the system output signal from the integrator, and let the system input signal be \$\small u(t) \rightarrow U(s)\$. The CLTF is then:...
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  • 7,274
1 vote
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State Model Representation of RLC network

You will need 4 variables and there are 4 equations $$V_{\text{C1}}-V_{\text{C2}}=L_4 i_1'$$ $$i_1=\frac{V_i-V_{\text{C1}}}{R_2}-C_3 V_{\text{C1}}'$$ $$i_1=C_4 \left(V_0'-V_{\text{C2}}'\right)+\frac{...
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  • 1,234
1 vote

Finding asymptotic stability of RLC circuits

Well, according to 'Faraday's law' in a series RLC-circuit: $$\text{V}_{\space\text{C}}\left(t\right)+0+\text{V}_{\space\text{R}}\left(t\right)-\text{V}_{\space\text{in}}\left(t\right)=-\text{V}_{\...
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  • 5,061
1 vote

Why is it necessary to know a state of a system?

1) when you consider a state feedback controller 2) when linear system theory can not be applied ( nonlinear systems) 3)when you don‘t have a sensor for the state you are interested in (estimators) ...
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  • 172
1 vote

Averaging matrix is not invertible in state space averaging

I am going to just assume that this is a "mathematical problem" rather than an engineering problem. As @Sparky256 and @Dorian have mentioned, the circuit topology is questionable and not practical. I ...
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  • 1,074

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