Second-Order Integrator
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Second-order integrator.
Description
The Integrator, Second-Order block performs second-order integration. The behaviour of the block is described by the following equations:
,
,
where is the input signal. Thus, the block represents a dynamic system with two continuous states: and .
| These two states have a mathematical relationship, is the derivative of . To fulfil this relationship during simulation, Engee imposes various constraints on the parameters and behaviour of the block. |
These equations describe the exact dependence of output on input in continuous time. Numerical approximation methods are used to estimate them with finite accuracy. In Engee there are several types of solvers that implement different numerical integration methods to compute the output of a block. Each solver has its own advantages depending on the specific problem.
The selected solver calculates the output of the Integrator, Second-Order block at the current time step using the current input value and the state value at the previous time step.
The initial values and can be set in the block parameters dialogue box.
Ports
Input
#
u
—
input signal
scalar | vector | matrix
Details
The input signal u to the integrator as a scalar, vector or matrix.
| Data types |
|
| Complex numbers support |
No |
Output
#
x
—
output signal
scalar | vector | matrix
Details
The output of the x state signal as a scalar, vector or matrix.
| Data types |
|
| Complex numbers support |
No |
#
dx
—
output signal
scalar | vector | matrix
Details
The output of the dx state signal as a scalar, vector or matrix.
| Data types |
|
| Complex numbers support |
No |
Parameters
Parameters
#
Initial condition x —
initial value of state x
Scalar / array of real numbers
Details
Initial value of state x of the block.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
#
Limit x —
state limit values x
Logical
Details
Limit the block output to a value between the Lower limit x and Upper limit x parameters. By default, this checkbox is unchecked.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
No |
#
Wrap x —
transfer switch x
Logical
Details
Enable carry states x between the Wrapped upper value x and Wrapped Lower value x parameters. Enabling carry states eliminates the need for zero crossing detection, reduces the number of solver resets, improves solver performance and accuracy, and increases simulation time when modelling rotational and cyclic state trajectories.
If you specify Wrapped upper value x as inf and Wrapped Lower value x as -inf, no carryover will occur.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
No |
Parameters
#
Initial condition dx/dt —
initial value of the state dx/dt
Scalar / array of real numbers
Details
Initial value of the state dx/dt.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |
#
Limit dx/dt —
state limit values dx/dt
Logical
Details
Limit the block output to a value between the Lower limit dx/dt and Upper limit dx/dt parameters. By default, this checkbox is unchecked.
If x state limits are set, the interval defined by the Lower limit dx/dt and Upper limit dx/dt parameters must contain zero.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
No |