Buildings.Controls.OBC.CDL.Continuous

Package with elementary mathematical functions for continuous variables

Information

Package with blocks for elementary mathematical functions for continuous variables.

Extends from Modelica.Icons.Package (Icon for standard packages).

Package Content

Name	Description
Abs	Output the absolute value of the input
Add	Output the sum of the two inputs
AddParameter	Output the sum of an input plus a parameter
Atan	Output the arc tangent of the input
Atan2	Output atan(u1/u2) of the inputs u1 and u2
Average	Output the average of its two inputs
ChangeSign	Change sign of the input
Cos	Output the cosine of the input
Derivative	Block that approximates the derivative of the input
Division	Output first input divided by second input
Exp	Output the exponential (base e) of the input
Feedback	Output difference between commanded and feedback input
Gain	Output the product of a gain value with the input signal
Greater	Output y is true, if input u1 is greater than input u2
GreaterEqual	Output y is true, if input u1 is greater or equal than input u2
GreaterEqualThreshold	Output y is true, if input u is greater or equal than threshold
GreaterThreshold	Output y is true, if input u is greater than threshold
Hysteresis	Transform Real to Boolean signal with Hysteresis
HysteresisWithHold	Hysteresis block that optionally allows to specify a hold time
IntegratorWithReset	Output the integral of the input signal
Less	Output y is true, if input u1 is less than input u2
LessEqual	Output y is true, if input u1 is less or equal than input u2
LessEqualThreshold	Output y is true, if input u is less or equal than threshold
LessThreshold	Output y is true, if input u is less than threshold
LimPID	P, PI, PD, and PID controller with limited output, anti-windup compensation and setpoint weighting
Limiter	Limit the range of a signal
Line	Output the value of the input x along a line specified by two points
Log	Output the natural (base e) logarithm of the input (input > 0 required)
Log10	Output the base 10 logarithm of the input (input > 0 required)
Max	Pass through the largest signal
Min	Pass through the smallest signal
Modulo	Output the remainder of first input divided by second input (~=0)
MovingMean	Block to output moving average
MultiMax	Output the maximum element of the input vector
MultiMin	Output the minimum element of the input vector
MultiSum	Sum of Reals, y = k[1]*u[1] + k[2]*u[2] + ... + k[n]*u[n]
NumberOfRequests	Outputs the number of signals that are above/below a certain threshold
Product	Output product of the two inputs
Round	Round real number to given digits
Sin	Output the sine of the input
SlewRateLimiter	Limit the increase or decrease rate of input
Sort	Sort elements of input vector in ascending or descending order
Sqrt	Output the square root of the input (input >= 0 required)
Tan	Output the tangent of the input
Sources	Package with blocks that generate source signals
Validation	Collection of models that validate the continuous blocks of the CDL

Buildings.Controls.OBC.CDL.Continuous.Abs

Output the absolute value of the input

Information

Block that outputs y = abs(u), where u is an input.

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Continuous.Add

Output the sum of the two inputs

Information

Block that outputs y as the weighted sum of the two input signals u1 and u2,

    y = k1*u1 + k2*u2;

where k1 and k2 are parameters.

Parameters

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Continuous.AddParameter

Output the sum of an input plus a parameter

Information

Block that outputs y = k u + p, where k and p are parameters and u is an input.

Parameters

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Continuous.Atan

Output the arc tangent of the input

Information

Block that outputs y = atan(u), where u is an input.

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Continuous.Atan2

Output atan(u1/u2) of the inputs u1 and u2

Information

Block that outputs the tangent-inverse y = atan2(u1, u2) of the input u1 divided by the input u2.

u1 and u2 shall not be zero at the same time instant. Atan2 uses the sign of u1 and u2 in order to construct the solution in the range -π ≤ y ≤ π, whereas Buildings.Controls.OBC.CDL.Continuous.Atan gives a solution in the range -π/2 ≤ y ≤ π/2.

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Continuous.Average

Output the average of its two inputs

Information

Block that outputs y = avg(u1,u2), where u1 and u2 are inputs.

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Continuous.ChangeSign

Change sign of the input

Information

Block that outputs y = -u, where u is an input.

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Continuous.Cos

Output the cosine of the input

Information

Block that outputs y = cos(u), where u is an input.

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Continuous.Derivative

Block that approximates the derivative of the input

Information

This blocks defines the transfer function between the input u and the output y (element-wise) as approximated derivative:

             k * s
     y = ------------ * u
            T * s + 1

If k=0, the block reduces to y=0.

Parameters

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Continuous.Division

Output first input divided by second input

Information

Block that outputs y = u1 / u2, where u1 and u2 are inputs.

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Continuous.Exp

Output the exponential (base e) of the input

Information

Block that outputs y = exp(u), where u is an input and exp() is the base-e exponential function.

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Continuous.Feedback

Output difference between commanded and feedback input

Information

Block that outputs y = u1 - u2, where u1 and u2 are inputs.

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Continuous.Gain

Output the product of a gain value with the input signal

Information

Block that outputs y = k * u, where k is a parameter and u is an input.

Parameters

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Continuous.Greater

Output y is true, if input u1 is greater than input u2

Information

Block that outputs true if the Real input u1 is greater than the Real input u2. Otherwise the output is false.

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Continuous.GreaterEqual

Output y is true, if input u1 is greater or equal than input u2

Information

Block that outputs true if Real the input u1 is greater than or equal to the Real input u2. Otherwise the output is false.

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Continuous.GreaterEqualThreshold

Output y is true, if input u is greater or equal than threshold

Information

Block that outputs true if the Real input is greater than or equal to the parameter threshold. Otherwise the output is false.

Parameters

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Continuous.GreaterThreshold

Output y is true, if input u is greater than threshold

Information

Block that outputs true if the Real input is greater than the parameter threshold. Otherwise the output is false.

Parameters

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Continuous.Hysteresis

Transform Real to Boolean signal with Hysteresis

Information

Block that transforms a Real input signal into a Boolean output signal:

• When the output was false and the input becomes greater than the parameter uHigh, the output switches to true.
• When the output was true and the input becomes less than the parameter uLow, the output switches to false.

The start value of the output is defined via parameter pre_y_start (= value of pre(y) at initial time). The default value of this parameter is false.

Parameters

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Continuous.HysteresisWithHold

Hysteresis block that optionally allows to specify a hold time

Information

Model for a hysteresis block that optionally allows to specify a hold time. During the hold time, the output is not allowed to switch.

When the input u becomes greater than uHigh, the output y becomes true and remains true for at least trueHoldDuration seconds, after which time it is allowed to switch immediately.

When the input u becomes less than uLow, the output y becomes false and remains false for at least falseHoldDuration seconds, after which time it is allowed to switch immediately.

This model for example could be used to disable an economizer, and not re-enable it for 10 minutes, and vice versa. Using hysteresis can avoid the distraction from the input noise.

Parameters

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Continuous.IntegratorWithReset

Output the integral of the input signal

Information

This model is similar to Modelica.Blocks.Continuous.Integrator except that it optionally allows to reset the output y of the integrator.

The output of the integrator can be reset as follows:

• If reset = Types.Reset.Disabled, which is the default, then the integrator is never reset.
• If reset = Types.Reset.Parameter, then a boolean input signal trigger is enabled. Whenever the value of this input changes from false to true, the integrator is reset by setting y to the value of the parameter y_reset.
• If reset = Types.Reset.Input, then a boolean input signal trigger is enabled. Whenever the value of this input changes from false to true, the integrator is reset by setting y to the value of the input signal y_reset_in.

Implementation

To adjust the icon layer, the code of Modelica.Blocks.Continuous.Integrator has been copied into this model rather than extended.

Parameters

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Continuous.Less

Output y is true, if input u1 is less than input u2

Information

Block that outputs true if the Real input u1 is less than the Real input u2. Otherwise the output is false.

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Continuous.LessEqual

Output y is true, if input u1 is less or equal than input u2

Information

Block that outputs true if the Real input u1 is less than or equal to the Real input u2. Otherwise the output is false.

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Continuous.LessEqualThreshold

Output y is true, if input u is less or equal than threshold

Information

Block that outputs true if the Real input is less than or equal to the parameter threshold. Otherwise the output is false.

Parameters

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Continuous.LessThreshold

Output y is true, if input u is less than threshold

Information

Block that outputs true if the Real input is less than the parameter threshold. Otherwise the output is false.

Parameters

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Continuous.LimPID

P, PI, PD, and PID controller with limited output, anti-windup compensation and setpoint weighting

Information

PID controller in the standard form

y = k   ( e(t) + 1 ⁄ T_i   ∫ e(s) ds + T_d de(t)⁄dt ),

where y is the control signal, e(t) = u_s - u_m is the control error, with u_s being the set point and u_m being the measured quantity, k is the gain, T_i is the time constant of the integral term and T_d is the time constant of the derivative term.

Note that the units of k are the inverse of the units of the control error, while the units of T_i and T_d are seconds.

For detailed treatment of integrator anti-windup, set-point weights and output limitation, see Modelica.Blocks.Continuous.LimPID. The model is similar to Modelica.Blocks.Continuous.LimPID, except for the following changes:

1. It can be configured to have a reverse action.

   If the parameter reverseAction=false (the default), then u_m < u_s increases the controller output, otherwise the controller output is decreased. Thus,

   • for a heating coil with a two-way valve, set reverseAction = false,
   • for a cooling coils with a two-way valve, set reverseAction = true.

2. It can be configured to enable an input port that allows resetting the controller output. The controller output can be reset as follows:

   • If reset = CDL.Types.Reset.Disabled, which is the default, then the controller output is never reset.
   • If reset = CDL.Types.Reset.Parameter, then a boolean input signal trigger is enabled. Whenever the value of this input changes from false to true, the controller output is reset by setting y to the value of the parameter y_reset.
   • If reset = CDL.Types.Reset.Input, then a boolean input signal trigger is enabled. Whenever the value of this input changes from false to true, the controller output is reset by setting y to the value of the input signal y_reset_in.

   Note that this controller implements an integrator anti-windup. Therefore, for most applications, keeping the default setting of reset = CDL.Types.Reset.Disabled is sufficient. Examples where it may be beneficial to reset the controller output are situations where the equipment control input should continuously increase as the equipment is switched on, such as as a light dimmer that may slowly increase the luminance, or a variable speed drive of a motor that should continuously increase the speed.

3. The parameter limitsAtInit has been removed.
4. Some parameters assignments in the instances have been made final.

For recommendations regarding tuning of closed loop control, see Modelica.Blocks.Continuous.LimPID or the control literature.

Parameters

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Continuous.Limiter

Limit the range of a signal

Information

Block that outputs y = min(uMax, max(uMin, u)), where u is an input and uMax and uMin are parameters.

If uMax < uMin, an error occurs and no output is produced.

Parameters

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Continuous.Line

Output the value of the input x along a line specified by two points

Information

Block that outputs y = a + b u, where u is an input and the coefficients a and b are determined so that the line intercepts the two input points specified by the two points x1 and f1, and x2 and f2.

The parameters limitBelow and limitAbove determine whether x1 and x2 are also used to limit the input u.

Parameters

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Continuous.Log

Output the natural (base e) logarithm of the input (input > 0 required)

Information

Block that outputs y = log(u), where u is an input and log() is the natural logarithm (base-e) function.

An error occurs if the input u is zero or negative.

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Continuous.Log10

Output the base 10 logarithm of the input (input > 0 required)

Information

Block that outputs y = log10(u), where u is an input and log10() is the logarithm (base-10) function.

An error occurs if the input u is zero or negative.

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Continuous.Max

Pass through the largest signal

Information

Block that outputs y = max(u1, u2), where u1 and u2 are inputs.

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Continuous.Min

Pass through the smallest signal

Information

Block that outputs y = min(u1, u2), where u1 and u2 are inputs.

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Continuous.Modulo

Output the remainder of first input divided by second input (~=0)

Information

Block that outputs y = mod(u1/u2), where u1 and u2 are inputs.

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Continuous.MovingMean

Block to output moving average

Information

This block outputs the mean value of its input signal as

      1  t
y =   -  ∫   u(s) ds
      δ  t-δ

where δ is a parameter that determines the time window over which the input is averaged. For t < δ seconds, it outputs

           1      t
y =   --------    ∫   u(s) ds
      t-t0+10-10   t0

where t₀ is the initial time.

This block can for example be used to output the moving average of a noisy measurement signal.

See Buildings.Controls.OBC.CDL.Continuous.Validation.MovingMean and Buildings.Controls.OBC.CDL.Continuous.Validation.MovingMean_nonZeroStart for example.

Parameters

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Continuous.MultiMax

Output the maximum element of the input vector

Information

Outputs the maximum element of the input vector.

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Continuous.MultiMin

Output the minimum element of the input vector

Information

Outputs the minimum element of the input vector.

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Continuous.MultiSum

Sum of Reals, y = k[1]*u[1] + k[2]*u[2] + ... + k[n]*u[n]

Information

Block that outputs

y = ∑_i=1ⁿ k_i   u_i,

where k is a parameter with n elements and u is an input of the same length. The dimension of u can be enlarged by drawing an additional connection line. The connection is automatically connected to this new free index.

If no connection to the input connector u is present, the output is y=0.

See Buildings.Controls.OBC.CDL.Continuous.Validation.MultiSum for an example.

Parameters

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Continuous.NumberOfRequests

Outputs the number of signals that are above/below a certain threshold

Information

Block that outputs the number of inputs that exceed a threshold. The parameter kind is used to determine the kind of the inequality. The table below shows the allowed settings.

This model may be used to check how many rooms exceed a temperature threshold.

Parameters

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Continuous.Product

Output product of the two inputs

Information

Block that outputs y = u1 * u2, where u1 and u2 are inputs.

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Continuous.Round

Round real number to given digits

Information

Block that outputs the input after rounding it to n digits.

For example,

• set n = 0 to round to the nearest integer,
• set n = 1 to round to the next decimal point, and
• set n = -1 to round to the next multiple of ten.

Hence, the block outputs

    y = floor(u*(10^n) + 0.5)/(10^n)  for  u > 0,
    y = ceil(u*(10^n) - 0.5)/(10^n)   for  u < 0.

Parameters

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Continuous.Sin

Output the sine of the input

Information

Block that outputs y = sin(u), where u is an input.

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Continuous.SlewRateLimiter

Limit the increase or decrease rate of input

Information

The block limits the rate of change of the input by a ramp. This block computes a threshold for the rate of change between input u and output y as thr = (u-y)/Td, where Td > 0 is parameter. The output y is computed as follows:
If thr < fallingSlewRate, then dy/dt = fallingSlewRate,
if thr > raisingSlewRate, then dy/dt = raisingSlewRate,
otherwise, dy/dt = thr.

Implementation

For the block to work with arbitrary inputs and in order to produce a differential output, the input is numerically differentiated with derivative time constant Td. Smaller time constant Td means nearer ideal derivative.

Parameters

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Continuous.Sort

Sort elements of input vector in ascending or descending order

Information

Block that sorts the elements of the input signal u. If the parameter ascending = true, then the output signal satisfies y_i <= y_i+1 for all i ∈ {1, ..., n-1}. Otherwise, it satisfies y_i >= y_i+1 for all i ∈ {1, ..., n-1}.

This block may for example be used in a variable air volume flow controller to access the position of the dampers that are most open.

Parameters

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Continuous.Sqrt

Output the square root of the input (input >= 0 required)

Information

Block that outputs square root of the input y = sqrt(u), where u is an input. All elements of the input vector shall be non-negative.

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Continuous.Tan

Output the tangent of the input

Information

Block that outputs y = tan(u), where u is an input.

Connectors

Modelica definition