# Dynamical

## Integral

This block implements an integrator. The output is the integral of the input signal.

## ContTransFunc

This block implements a continuous-time linear system that is defined by its rational transfer function (Numerator/Denominator). The transfer function must be proper meaning that the degree of numerator must not exceed that of the denominator. In the MIMO case, the numerator and denominator must be defined as cells (see OML tf2ssc function for details).

## ContPoleZero

This block implements, when activated at a fixed rate, a SISO linear system represented by its rational transfer function. The transfer function must be proper, meaning that the degree of the numerator must not exceed that of the denominator.

## ContStateSpace

This block implements a continuous-time linear state-space system defined by the A,B,C,D matrices and the initial state vector.

## Derivative

This block applies a numerical approximation method to provide the derivative of its input.

## DiscreteDelay

This block, when activated, outputs its state then stores its input in its state. When activated at a fixed rate, the block realizes a single-step delay represented by z-inverse in the Z transform domain.

## DiscrTransFunc

This block implements, when activated at a fixed rate, a linear system represented by its rational transfer function. The transfer function must be proper, meaning that the degree of the numerator must not exceed that of the denominator. In the MIMO case, the numerator and denominator must be defined as cells (see OML tf2ssc function for details).

## DiscrPoleZero

This block implements, when activated at a fixed rate, a SISO linear system represented by its rational transfer function. The transfer function must be proper, meaning that the degree of the numerator must not exceed that of the denominator.

## DiscrStateSpace

This block implements a discrete-time linear state-space system when activated at a fixed rate. The system is defined by the A,B,C,D matrices and the initial state x0.

## SampleHold

When activated, this block copies its input to its output. If activated at a regular rate, the block realizes a periodic sample and hold operation.

## DiscreteDerivative

This block computes the discrete derivative of the input signal. The derivative is obtained by dividing the difference between the current value of the input and the previous value of the input divided by the difference of their respective times.

## DiscreteIntegral

This block implements a discrete integrator. The output is the integral of the input signal.

## Accumulator

This block implements an accumulator with the option to reset the state.

## FixedDelay

This block delays the input signal by a specified amount of time.

## VariableDelay

This block delays the signal on the first input port. The amount of delay varies in time and is either given directly by the signal on the second input (regular delay), or its integral (transport delay).

## JumpStateSpace

This block implements a continuous-time linear state-space system with the possibility of jumps in the state. The first input is the regular input signal of the linear system, the second carries the new value of the state which is copied into the state when an event activates the block through its unique activation input port.

## ShiftRegister

This block implements a FIFO shift register. A shift is performed with every activation of the block. The Register Initial Condition parameter is a matrix that contains in its columns the values originally present in the shift register.

## Memory

This block keeps the input value and delays it by an integration time step.

## SampledData

This block implements a sampled data system. The system is defined by the block parameters, which are the A,B,C,D matrices of the underlying continuous-time linear system and the associated initial state vector. The resulting discrete-time linear system is computed using the values of the parameters and the activation period of the block. The block must be activated by a periodic activation signal.

## ImplDerivative

This block outputs the derivative of its input signal. The solver uses a multi-order, multi-step BDF, Backward Differentiation Formula to estimate the derivative. The accuracy of this method is higher than the "du/dt" block which uses an order 1 method. The accuracy can be improved by reducing the solver error tolerances.

## PID

This block is a PID (Proportional-Integral-Derivative) controller.

## RunTimePID

This block implements a tunable PID. During the simulation, the coefficients of the PID can be manually tuned.
The current value of the gain is equal to the Value multiplied by the Factor

## ContDescriptorStateSpace

This block implements a continuous-time, linear, implicit state-space system specified by the A, B, C, D, E matrices, the initial state vector, and the equation, E*der(x)=A*x+B*u.

## ContStateSpace_SS

This block implements a continuous-time, linear, state-space system specified by the A, B, C, D matrices. The initial state of the system is automatically computed in such a way that the state derivative, der(x)=Ax+Bu=0, is zero at the initial time.

## ContStateSpace_Y

This block implements a continuous-time, linear, state-space system specified by the A, B, C, D matrices. The state vector is computed in such a way that the requested initial output is obtained at the initial time.

## ContTransFunc_SS

This block implements a SIMO (continuous-time, single-input, multi-output) linear system that is defined by the linear system's transfer function. The transfer function, specified by the coefficients of the function's numerator and denominator, must be proper, meaning that the degree of the numerator must not exceed that of the denominator. The initial state is computed such that the system is initially in steady-state.

## ContTransFunc_Y

This block implements a SIMO (continuous-time, single-input, multi-output) linear system that is defined by the linear system's transfer function. The transfer function, specified by the coefficients of the function's numerator and denominator, must be proper, meaning that the degree of the numerator must not exceed that of the denominator. The internal state of the block is initialized so that the initial output corresponds to the specified value.

## ContTransFunc_X

This block implements a SIMO (continuous-time, single-input, multi-output) linear system that is defined by the linear system's transfer function. The transfer function, specified by the coefficients of the function's numerator and denominator, must be proper, meaning that the degree of the numerator must not exceed that of the denominator. The transfer function is converted to a state-space form with tf2ss and the initial state is applied.

## LoopBreaker

This block requires that its output be equal to its input, but the block does not have a direct feedthrough dependency and therefore can be used to break algebraic loops.