Hello,
I have a numerical time series of voltage V(t) and aim to derive the analytical equation for the charge q(t)q(t)q(t) in an RLC circuit. The relationship between V(t), q(t), and the circuit parameters R, L, and C is governed by the following equation:
V(t) = R * dq/dt + L * d2q/dt2 + (1/C) * q(t)
I have attempted the following steps to estimate the parameters R, L, and C:
q(t); I calculated the charge q(t)as the cumulative integral of V(t), assuming a constant time step (delta_t):
q(t) = sum(V(t) * delta_t)
Computing Derivatives: I computed the first and second derivatives of q(t) numerically using finite differences:
The first derivative (dq/dt): dq/dt = (q(t+delta_t) – q(t)) / delta_t
The second derivative (d2q/dt2): d2q/dt2 = (dq/dt at t+delta_t – dq/dt at t) / delta_t
Creating the Matrix A:I created a matrix A and a vector V to represent the system of equations:
Matrix A has three columns:
The first column contains q(t),
The second column contains dq/dt,
The third column contains d2q/dt2.
Vector V contains the voltage values V(t).
Estimating Parameters:I solved for the parameters R, L, and C using the least-squares method: X = inv(A’ * A) * A’ * V.
Here, X contains the values [1/C, R, L].
Extracting Parameters:I extracted the parameter values from X as follows: C = 1 / X(1), R = X(2), L = X(3)
While I successfully estimated the parameters R, L, and C, I have not been able to derive the analytical equation for q(t). My goal is to find the closed-form expression for q(t) using these parameters and the RLC circuit equation.
How can I derive an analytical expression for q(t)q(t)q(t) from the RLC circuit equation?
Since V(t)V(t)V(t) is provided as numerical data, is there a way to approximate q(t)q(t)q(t) in a closed form?
Are there any MATLAB tools or functions that can handle this type of numerical differential equation?Hello,
I have a numerical time series of voltage V(t) and aim to derive the analytical equation for the charge q(t)q(t)q(t) in an RLC circuit. The relationship between V(t), q(t), and the circuit parameters R, L, and C is governed by the following equation:
V(t) = R * dq/dt + L * d2q/dt2 + (1/C) * q(t)
I have attempted the following steps to estimate the parameters R, L, and C:
q(t); I calculated the charge q(t)as the cumulative integral of V(t), assuming a constant time step (delta_t):
q(t) = sum(V(t) * delta_t)
Computing Derivatives: I computed the first and second derivatives of q(t) numerically using finite differences:
The first derivative (dq/dt): dq/dt = (q(t+delta_t) – q(t)) / delta_t
The second derivative (d2q/dt2): d2q/dt2 = (dq/dt at t+delta_t – dq/dt at t) / delta_t
Creating the Matrix A:I created a matrix A and a vector V to represent the system of equations:
Matrix A has three columns:
The first column contains q(t),
The second column contains dq/dt,
The third column contains d2q/dt2.
Vector V contains the voltage values V(t).
Estimating Parameters:I solved for the parameters R, L, and C using the least-squares method: X = inv(A’ * A) * A’ * V.
Here, X contains the values [1/C, R, L].
Extracting Parameters:I extracted the parameter values from X as follows: C = 1 / X(1), R = X(2), L = X(3)
While I successfully estimated the parameters R, L, and C, I have not been able to derive the analytical equation for q(t). My goal is to find the closed-form expression for q(t) using these parameters and the RLC circuit equation.
How can I derive an analytical expression for q(t)q(t)q(t) from the RLC circuit equation?
Since V(t)V(t)V(t) is provided as numerical data, is there a way to approximate q(t)q(t)q(t) in a closed form?
Are there any MATLAB tools or functions that can handle this type of numerical differential equation? Hello,
I have a numerical time series of voltage V(t) and aim to derive the analytical equation for the charge q(t)q(t)q(t) in an RLC circuit. The relationship between V(t), q(t), and the circuit parameters R, L, and C is governed by the following equation:
V(t) = R * dq/dt + L * d2q/dt2 + (1/C) * q(t)
I have attempted the following steps to estimate the parameters R, L, and C:
q(t); I calculated the charge q(t)as the cumulative integral of V(t), assuming a constant time step (delta_t):
q(t) = sum(V(t) * delta_t)
Computing Derivatives: I computed the first and second derivatives of q(t) numerically using finite differences:
The first derivative (dq/dt): dq/dt = (q(t+delta_t) – q(t)) / delta_t
The second derivative (d2q/dt2): d2q/dt2 = (dq/dt at t+delta_t – dq/dt at t) / delta_t
Creating the Matrix A:I created a matrix A and a vector V to represent the system of equations:
Matrix A has three columns:
The first column contains q(t),
The second column contains dq/dt,
The third column contains d2q/dt2.
Vector V contains the voltage values V(t).
Estimating Parameters:I solved for the parameters R, L, and C using the least-squares method: X = inv(A’ * A) * A’ * V.
Here, X contains the values [1/C, R, L].
Extracting Parameters:I extracted the parameter values from X as follows: C = 1 / X(1), R = X(2), L = X(3)
While I successfully estimated the parameters R, L, and C, I have not been able to derive the analytical equation for q(t). My goal is to find the closed-form expression for q(t) using these parameters and the RLC circuit equation.
How can I derive an analytical expression for q(t)q(t)q(t) from the RLC circuit equation?
Since V(t)V(t)V(t) is provided as numerical data, is there a way to approximate q(t)q(t)q(t) in a closed form?
Are there any MATLAB tools or functions that can handle this type of numerical differential equation? curve fitting, model MATLAB Answers — New Questions

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