Limiter & Switching Blocks

Blocks that bound a signal or select between signals. Several carry discrete state and so introduce discrete transitions into the model.

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lim

Limiter with constant bounds.

Syntax

& lim
x_i
x_j
{x_min}
{x_max}

x_i is the input, x_j is the (limited) output. x_min and x_max are constant bounds (data names, parameter names, or math expressions).

Internal states: none

Discrete variable: $z \in \{-1, 0, 1\}$

Equations

$$0 = \begin{cases} x_j - x_i & \text{if } z = 0 \\ x_j - x_{max} & \text{if } z = 1 \\ x_j - x_{min} & \text{if } z = -1 \end{cases}$$

Discrete transitions

if z = 0:
    if x_i > x_max:
        z ← 1
    else if x_i < x_min:
        z ← -1
else if z = 1:
    if x_i < x_max:
        z ← 0
else:  # z = -1
    if x_i > x_min:
        z ← 0

Initialization

if x_j > x_max:
    z ← 1
else if x_j < x_min:
    z ← -1
else:
    z ← 0

---

limvb

Limiter with variable bounds.

Syntax

& limvb
x_i
x_min
x_max
x_j

x_i is the input; x_min and x_max are variable (state) lower and upper bounds; x_j is the (limited) output.

Internal states: none

Discrete variable: $z \in \{-1, 0, 1\}$

Equations

$$0 = \begin{cases} x_j - x_i & \text{if } z = 0 \\ x_j - x_{max} & \text{if } z = 1 \\ x_j - x_{min} & \text{if } z = -1 \end{cases}$$

Discrete transitions

if z = 0:
    if x_i > x_max:
        z ← 1
    else if x_i < x_min:
        z ← -1
else if z = 1:
    if x_i < x_max:
        z ← 0
else:  # z = -1
    if x_i > x_min:
        z ← 0

Initialization

if x_i > x_max:
    z ← 1
else if x_i < x_min:
    z ← -1
else:
    z ← 0

Notes

Unlike lim, the bounds $x_{min}$ and $x_{max}$ are model states (variables) rather than fixed parameters, allowing dynamic limit variation during simulation.

---

db

Deadband.

Syntax

& db
x_i
x_j
{delta_1}
{s_1}
{a_1}
{delta_2}
{s_2}
{a_2}

x_i is the input, x_j is the output. Parameters $\delta_1$, $s_1$, $a_1$, $\delta_2$, $s_2$, $a_2$ are data names, parameter names, or math expressions.

Internal states: none

Discrete variable: $z \in \{0, 1, -1\}$

Equations

$$0 = \begin{cases} x_j & \text{if } z = 0 \\ x_j - s_2 - a_2(x_i - \delta_2) & \text{if } z = 1 \\ x_j - s_1 - a_1(x_i - \delta_1) & \text{if } z = -1 \end{cases}$$

Discrete transitions

if z ∈ {0, 1}:
    if x_i < delta_1:
        z ← -1
else if z ∈ {-1, 0}:
    if x_i > delta_2:
        z ← 1
else if z ∈ {-1, 1}:
    if delta_1 < x_i < delta_2:
        z ← 0

Initialization

if x_i > delta_2:
    z ← 1
else if x_i < delta_1:
    z ← -1
else:
    z ← 0

Notes

• The data must satisfy $\delta_1 < \delta_2$, $a_1 \ge 0$, and $a_2 \ge 0$.
• A common special case is $s_1 = s_2 = 0$ and $a_1 = a_2 = 1$, although all values are permitted.
• The pwlin4, pwlin5, or pwlin6 blocks can be used as alternatives.

---

hyst

Hysteresis.

Syntax

& hyst
x_i
x_j
{x_I}
{y_IB}
{y_IA}
{x_D}
{y_DB}
{y_DA}
{z0}

x_i is the input, x_j is the output. The parameters $x_I$, $y_{IB}$, $y_{IA}$, $x_D$, $y_{DB}$, $y_{DA}$ define the hysteresis shape. z0 specifies the initial discrete state when the input starts in the indeterminate region.

Internal states: none

Discrete variable: $z \in \{-1, 1\}$

Equations

$$0 = \begin{cases} \displaystyle x_j - y_{IA} - \frac{y_{IA} - y_{DB}}{x_I - x_D}(x_i - x_I) & \text{if } z = 1 \\[8pt] \displaystyle x_j - y_{DA} - \frac{y_{IB} - y_{DA}}{x_I - x_D}(x_i - x_D) & \text{if } z = -1 \end{cases}$$

Discrete transitions

if z = -1:
    if x_i > x_I:
        z ← 1
else:  # z = 1
    if x_i < x_D:
        z ← -1

Initialization

if x_i > x_I:
    z ← 1
else if x_i < x_D:
    z ← -1
else:
    if z0 >= 0:
        z ← 1
    else:
        z ← 0

Notes

At $t = 0$, if $x_D < x_i(0) < x_I$ the initial operating branch is indeterminate. The system could operate on either the $(y_{IA}, y_{DB})$ line ($z = 1$) or the $(y_{DA}, y_{IB})$ line ($z = -1$). The user must therefore supply z0 to resolve the ambiguity.

If $x_i(0) < x_D$ then $z$ is initialised to $-1$; if $x_i(0) > x_I$ then $z$ is initialised to $1$, and z0 is ignored in both cases.

The data must satisfy $x_D < x_I$. The degenerate case $x_D = x_I$ is not allowed by this block but can be handled with the pwlin4 block.

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switch

Set the output state to one among $n$ input states, based on the value of a controlling state. Separate blocks exist for $n = 2, 3, 4$ and $5$.

Syntax

& switch2
name of variable x_i(1)
name of variable x_i(2)
name of variable x_k        (selector)
name of variable x_j        (output)

For switch3–switch5, prepend additional input variables $x_i(3)$ through $x_i(n)$ before $x_k$.

Internal States

None.

Discrete Variables

$z \in \{1, 2, \ldots, n\}$

Equations

$0 = x_j - x_i(z)$

Discrete Transitions

$z \leftarrow \max\!\left(1,\, \min\!\left(n,\, \text{nint}(x_k)\right)\right)$

where $\text{nint}$ returns the nearest integer.

Initialization

Same as discrete transitions.

---

swsign

Switch between two input states, based on the sign of a third input state.

Syntax

& swsign
name of variable x_i   (selected when x_k >= 0)
name of variable x_j   (selected when x_k < 0)
name of variable x_k   (sign selector)
name of variable x_l   (output)

Internal States

None.

Discrete Variables

$z \in \{1, 2\}$

Equations

$$0 = \begin{cases} x_l - x_i & \text{if } z = 1 \\ x_l - x_j & \text{if } z = 2 \end{cases}$$

Discrete Transitions

if z = 1:
  if x_k < 0:  z ← 2
else if z = 2:
  if x_k >= 0:  z ← 1

Initialization

if x_k < 0:  z ← 2
else:  z ← 1

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See Also

• Block Index, all CODEGEN blocks by category
• CODEGEN Model Examples, complete models built from these blocks
• User-Defined Models, the DSL file format