Buildings.Controls.OBC.CDL.Reals

Package with blocks for continuous variables

Information

Package with blocks for elementary mathematical functions for continuous variables.

Package Content

Name	Description
Abs	Output the absolute value of the input
Acos	Output the arc cosine of the input
Add	Output the sum of the two inputs
AddParameter	Output the sum of an input plus a parameter
Asin	Output the arc sine of the input
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
Cos	Output the cosine of the input
Derivative	Block that approximates the derivative of the input
Divide	Output first input divided by second input
Exp	Output the exponential (base e) of the input
Greater	Output y is true, if input u1 is greater than input u2 with hysteresis
GreaterThreshold	Output y is true, if input u is greater than threshold with hysteresis
Hysteresis	Transform Real to Boolean signal with Hysteresis
IntegratorWithReset	Output the integral of the input signal
Less	Output y is true, if input u1 is less than input u2
LessThreshold	Output y is true, if input u is less than threshold with hysteresis
LimitSlewRate	Limit the increase or decrease rate of input
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)
MatrixGain	Output the product of a gain matrix with the input signal vector
MatrixMax	Output vector of row- or column-wise maximum of the input matrix
MatrixMin	Output vector of row- or column-wise minimum values
Max	Pass through the largest signal
Min	Pass through the smallest signal
Modulo	Output the remainder of first input divided by second input (~=0)
MovingAverage	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]
Multiply	Output product of the two inputs
MultiplyByParameter	Output the product of a gain value with the input signal
PID	P, PI, PD, and PID controller
PIDWithReset	P, PI, PD, and PID controller with output reset
Ramp	Limit the changing rate of the input
Round	Round real number to given digits
Sin	Output the sine of the input
Sort	Sort elements of input vector in ascending or descending order
Sqrt	Output the square root of the input (input >= 0 required)
Subtract	Output the difference of the two inputs
Switch	Switch between two Real signals
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.Reals.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.Reals.Acos

Output the arc cosine of the input

Information

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

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Reals.Add

Output the sum of the two inputs

Information

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

    y = u1 + u2.

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Reals.AddParameter

Output the sum of an input plus a parameter

Information

Block that outputs y = u + p, where p is parameter and u is an input.

Parameters

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Reals.Asin

Output the arc sine of the input

Information

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

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Reals.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.Reals.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.Reals.Atan gives a solution in the range -π/2 ≤ y ≤ π/2.

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Reals.Average

Output the average of its two inputs

Information

Block that outputs y = (u1 + u2) / 2, where u1 and u2 are inputs.

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Reals.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.Reals.Derivative

Block that approximates the derivative of the input

Information

This blocks defines the transfer function between the input u and the output y as approximated derivative:

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

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

Parameters

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Reals.Divide

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.Reals.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.Reals.Greater

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

Information

Block that outputs true if the Real input u1 is greater than the Real input u2, optionally within a hysteresis h.

The parameter h ≥ 0 is used to specify a hysteresis. For any h ≥ 0, the output switches to true if u₁ > u₂, and it switches to false if u₁ ≤ u₂ - h. Note that in the special case of h = 0, this produces the output y=u₁ > u₂.

To disable hysteresis, set h=0.

Usage

Enabling hysteresis can avoid frequent switching.
In simulation, adding hysteresis is recommended to guard against numerical noise. Otherwise, numerical noise from a nonlinear solver or from an implicit time integration algorithm may cause the simulation to stall. Numerical noise can be present if an input depends on a state variable or a quantity that requires an iterative solution, such as a temperature or a mass flow rate of an HVAC system.
In real controllers, adding hysteresis is recommended to guard against measurement noise. Otherwise, measurement noise may cause the output to change frequently.

Parameters

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Reals.GreaterThreshold

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

Information

Block that outputs true if the Real input u is greater than a threshold t, optionally within a hysteresis h.

The parameter h ≥ 0 is used to specify a hysteresis. For any h ≥ 0, the output switches to true if u > t, where t is the threshold, and it switches to false if u ≤ t - h. Note that in the special case of h = 0, this produces the output y=u > t.

To disable hysteresis, set h=0.

Usage

Enabling hysteresis can avoid frequent switching.
In simulation, adding hysteresis is recommended to guard against numerical noise. Otherwise, numerical noise from a nonlinear solver or from an implicit time integration algorithm may cause the simulation to stall. Numerical noise can be present if an input depends on a state variable or a quantity that requires an iterative solution, such as a temperature or a mass flow rate of an HVAC system.
In real controllers, adding hysteresis is recommended to guard against measurement noise. Otherwise, measurement noise may cause the output to change frequently.

Parameters

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Reals.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.Reals.IntegratorWithReset

Output the integral of the input signal

Information

Block that outputs

y(t) = y_start + ∫_t0^t u(s) ds.

Whenever the input signal trigger changes from false to true, the integrator is reset by setting y_start to the value of the input signal y_reset_in.

Parameters

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Reals.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, optionally within a hysteresis h.

The parameter h ≥ 0 is used to specify a hysteresis. For any h ≥ 0, the output switches to true if u₁ < u₂, and it switches to false if u₁ ≥ u₂ + h. Note that in the special case of h = 0, this produces the output y=u₁ < u₂.

To disable hysteresis, set h=0.

Usage

Enabling hysteresis can avoid frequent switching.
In simulation, adding hysteresis is recommended to guard against numerical noise. Otherwise, numerical noise from a nonlinear solver or from an implicit time integration algorithm may cause the simulation to stall. Numerical noise can be present if an input depends on a state variable or a quantity that requires an iterative solution, such as a temperature or a mass flow rate of an HVAC system.
In real controllers, adding hysteresis is recommended to guard against measurement noise. Otherwise, measurement noise may cause the output to change frequently.

Parameters

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Reals.LessThreshold

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

Information

Block that outputs true if the Real input u is less than a threshold t, optionally within a hysteresis h.

The parameter h ≥ 0 is used to specify a hysteresis. For any h ≥ 0, the output switches to true if u < t, where t is the threshold, and it switches to false if u ≥ t + h. Note that in the special case of h = 0, this produces the output y=u < t.

Usage

Enabling hysteresis can avoid frequent switching. Adding hysteresis is recommended in real controllers to guard against sensor noise, and in simulation to guard against numerical noise. Numerical noise can be present if an input depends on a state variable or a quantity that requires an iterative solution, such as a temperature or a mass flow rate of an HVAC system. To disable hysteresis, set h=0.

Parameters

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Reals.LimitSlewRate

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 of the 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 differentiable 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.Reals.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.

Parameters

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Reals.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.

If the limits are used, then this block requires x1 < x2.

Parameters

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Reals.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.Reals.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.Reals.MatrixGain

Output the product of a gain matrix with the input signal vector

Information

This blocks computes output vector y as the product of the gain matrix K with the input signal vector u as y = K u. For example,

   parameter Real K[:,:] = [0.12, 2; 3, 1.5];

results in

     | y[1] |     | 0.12,  2.00 |   | u[1] |
     |      |  =  |            | * |      |
     | y[2] |     | 3.00,  1.50 |   | u[2] |

Parameters

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Reals.MatrixMax

Output vector of row- or column-wise maximum of the input matrix

Information

If rowMax = true, this block outputs the row-wise maximum of the input matrix u, otherwise it outputs the column-wise maximum of the input matrix u.

Parameters

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Reals.MatrixMin

Output vector of row- or column-wise minimum values

Information

If rowMin = true, this block outputs the row-wise minimum of the input matrix u, otherwise it outputs the column-wise minimum of the input matrix u.

Parameters

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Reals.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.Reals.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.Reals.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.Reals.MovingAverage

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.Reals.Validation.MovingAverage and Buildings.Controls.OBC.CDL.Reals.Validation.MovingAverage_nonZeroStart for example.

Parameters

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Reals.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.Reals.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.Reals.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.Reals.Validation.MultiSum for an example.

Parameters

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Reals.Multiply

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.Reals.MultiplyByParameter

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.Reals.PID

P, PI, PD, and PID controller

Information

PID controller in the standard form

y_u = k/r   (e(t) + 1 ⁄ T_i   ∫ e(τ) dτ + T_d d⁄dt e(t)),

where y_u is the control signal before output limitation, e(t) = u_s(t) - u_m(t) 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, T_d is the time constant of the derivative term, and r is a scaling factor, with default r=1. The scaling factor should be set to the typical order of magnitude of the range of the error e. For example, you may set r=100 to r=1000 if the control input is a pressure of a heating water circulation pump in units of Pascal, or leave r=1 if the control input is a room temperature.

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.

The actual control output is

y = min( y_max, max( y_min, y)),

where y_min and y_max are limits for the control signal.

P, PI, PD, or PID action

Through the parameter controllerType, the controller can be configured as P, PI, PD or PID controller. The default configuration is PI.

Reverse or direct action

Through the parameter reverseActing, the controller can be configured to be reverse or direct acting. The above standard form is reverse acting, which is the default configuration. For a reverse acting controller, for a constant set point, an increase in measurement signal u_m decreases the control output signal y (Montgomery and McDowall, 2008). Thus,

• for a heating coil with a two-way valve, leave reverseActing = true, but
• for a cooling coil with a two-way valve, set reverseActing = false.

If reverseAction=false, then the error e above is multiplied by -1.

Anti-windup compensation

The controller anti-windup compensation is as follows: Instead of the above basic control law, the implementation is

y_u = k   (e(t) ⁄ r + 1 ⁄ T_i   ∫ (-Δy + e(τ) ⁄ r) dτ + T_d ⁄ r d⁄dt e(t)),

where the anti-windup compensation Δy is

Δy = (y_u - y) ⁄ (k N_i),

where N_i > 0 is the time constant for the anti-windup compensation. To accelerate the anti-windup, decrease N_i.

Note that the anti-windup term (-Δy + e(τ) ⁄ r) shows that the range of the typical control error r should be set to a reasonable value so that

e(τ) ⁄ r = (u_s(τ) - u_m(τ)) ⁄ r

has order of magnitude one, and hence the anti-windup compensation should work well.

Reset of the controller output

Note that this controller implements an integrator anti-windup. Therefore, for most applications, the controller output does not need to be reset. However, if the controller is used in conjuction with equipment that is being switched on, better control performance may be achieved by resetting the controller output when the equipment is switched on. This is in particular the case in situations where the equipment control input should continuously increase as the equipment is switched on, such as a light dimmer that may slowly increase the luminance, or a variable speed drive of a motor that should continuously increase the speed. In this case, the controller Buildings.Controls.OBC.CDL.Reals.PIDWithReset that can reset the output should be used.

Approximation of the derivative term

The derivative of the control error d ⁄ dt e(t) is approximated using

d⁄dt x(t) = (e(t)-x(t)) N_d ⁄ T_d,

and

d⁄dt e(t) ≈ N_d (e(t)-x(t)),

where x(t) is an internal state.

Guidance for tuning the control gains

The parameters of the controller can be manually adjusted by performing closed loop tests (= controller + plant connected together) and using the following strategy:

1. Set very large limits, e.g., set y_max = 1000.
2. Select a P-controller and manually enlarge the parameter k (the total gain of the controller) until the closed-loop response cannot be improved any more.
3. Select a PI-controller and manually adjust the parameters k and Ti (the time constant of the integrator). The first value of Ti can be selected such that it is in the order of the time constant of the oscillations occurring with the P-controller. If, e.g., oscillations in the order of 100 seconds occur in the previous step, start with Ti=1/100 seconds.
4. If you want to make the reaction of the control loop faster (but probably less robust against disturbances and measurement noise) select a PID-controller and manually adjust parameters k, Ti, Td (time constant of derivative block).
5. Set the limits yMax and yMin according to your specification.
6. Perform simulations such that the output of the PID controller goes in its limits. Tune Ni (N_i T_i is the time constant of the anti-windup compensation) such that the input to the limiter block (= lim.u) goes quickly enough back to its limits. If Ni is decreased, this happens faster. If Ni is very large, the anti-windup compensation is not effective and the controller works bad.

References

R. Montgomery and R. McDowall (2008). "Fundamentals of HVAC Control Systems." American Society of Heating Refrigerating and Air-Conditioning Engineers Inc. Atlanta, GA.

Parameters

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Reals.PIDWithReset

P, PI, PD, and PID controller with output reset

Information

PID controller in the standard form

y_u = k/r   (e(t) + 1 ⁄ T_i   ∫ e(τ) dτ + T_d d⁄dt e(t)),

with output reset, where y_u is the control signal before output limitation, e(t) = u_s(t) - u_m(t) 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, T_d is the time constant of the derivative term, and r is a scaling factor, with default r=1. The scaling factor should be set to the typical order of magnitude of the range of the error e. For example, you may set r=100 to r=1000 if the control input is a pressure of a heating water circulation pump in units of Pascal, or leave r=1 if the control input is a room temperature.

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.

The actual control output is

y = min( y_max, max( y_min, y)),

where y_min and y_max are limits for the control signal.

P, PI, PD, or PID action

Through the parameter controllerType, the controller can be configured as P, PI, PD or PID controller. The default configuration is PI.

Reverse or direct action

Through the parameter reverseActing, the controller can be configured to be reverse or direct acting. The above standard form is reverse acting, which is the default configuration. For a reverse acting controller, for a constant set point, an increase in measurement signal u_m decreases the control output signal y (Montgomery and McDowall, 2008). Thus,

• for a heating coil with a two-way valve, leave reverseActing = true, but
• for a cooling coil with a two-way valve, set reverseActing = false.

If reverseAction=false, then the error e above is multiplied by -1.

Anti-windup compensation

The controller anti-windup compensation is as follows: Instead of the above basic control law, the implementation is

y_u = k   (e(t) ⁄ r + 1 ⁄ T_i   ∫ (-Δy + e(τ) ⁄ r) dτ + T_d ⁄ r d⁄dt e(t)),

where the anti-windup compensation Δy is

Δy = (y_u - y) ⁄ (k N_i),

where N_i > 0 is the time constant for the anti-windup compensation. To accelerate the anti-windup, decrease N_i.

Note that the anti-windup term (-Δy + e(τ) ⁄ r) shows that the range of the typical control error r should be set to a reasonable value so that

e(τ) ⁄ r = (u_s(τ) - u_m(τ)) ⁄ r

has order of magnitude one, and hence the anti-windup compensation should work well.

Reset of the controller output

Whenever the value of boolean input signal trigger changes from false to true, the controller output is reset by setting y to the value of the parameter y_reset.

Approximation of the derivative term

The derivative of the control error d ⁄ dt e(t) is approximated using

d⁄dt x(t) = (e(t)-x(t)) N_d ⁄ T_d,

and

d⁄dt e(t) ≈ N_d (e(t)-x(t)),

where x(t) is an internal state.

Guidance for tuning the control gains

The parameters of the controller can be manually adjusted by performing closed loop tests (= controller + plant connected together) and using the following strategy:

1. Set very large limits, e.g., set y_max = 1000.
2. Select a P-controller and manually enlarge the parameter k (the total gain of the controller) until the closed-loop response cannot be improved any more.
3. Select a PI-controller and manually adjust the parameters k and Ti (the time constant of the integrator). The first value of Ti can be selected such that it is in the order of the time constant of the oscillations occurring with the P-controller. If, e.g., oscillations in the order of 100 seconds occur in the previous step, start with Ti=1/100 seconds.
4. If you want to make the reaction of the control loop faster (but probably less robust against disturbances and measurement noise) select a PID-controller and manually adjust parameters k, Ti, Td (time constant of derivative block).
5. Set the limits yMax and yMin according to your specification.
6. Perform simulations such that the output of the PID controller goes in its limits. Tune Ni (N_i T_i is the time constant of the anti-windup compensation) such that the input to the limiter block (= lim.u) goes quickly enough back to its limits. If Ni is decreased, this happens faster. If Ni is very large, the anti-windup compensation is not effective and the controller works bad.

References

R. Montgomery and R. McDowall (2008). "Fundamentals of HVAC Control Systems." American Society of Heating Refrigerating and Air-Conditioning Engineers Inc. Atlanta, GA.

Parameters

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Reals.Ramp

Limit the changing rate of the input

Information

Block that limits the rate of change of the input u by a ramp if the boolean input active is true, otherwise the block outputs y = u.

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 a 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.

A smaller time constant Td > 0 means a higher accuracy for the derivative approximation.

Note that when the input activate switches to false, the output y can have a discontinuity.

Implementation

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

Parameters

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Reals.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.Reals.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.Reals.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 y 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}. The output signal yIdx contains the indices of the sorted elements, with respect to the input vector u.

Usage

Note that this block shall only be used for input signals u that are time sampled.
Otherwise, in simulation, numerical noise from a nonlinear solver or from an implicit time integration algorithm may cause the simulation to stall. Numerical noise can be present if an input depends on a state variable or a quantity that requires an iterative solution, such as a temperature or a mass flow rate of an HVAC system.
In real controllers, measurement noise may cause the output to change frequently.

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.Reals.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. The input u must be non-negative.

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Reals.Subtract

Output the difference of the two inputs

Information

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

    y = u1 - u2

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Reals.Switch

Switch between two Real signals

Information

Block that outputs one of two real input signals based on a boolean input signal.

If the input signal u2 is true, the block outputs y = u1. Otherwise, it outputs y = u3.

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Reals.Tan

Output the tangent of the input

Information

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

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Reals.Greater.GreaterWithHysteresis

Greater block without hysteresis

Parameters

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Reals.Greater.GreaterNoHysteresis

Greater block without hysteresis

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Reals.GreaterThreshold.GreaterWithHysteresis

Greater block without hysteresis

Parameters

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Reals.GreaterThreshold.GreaterNoHysteresis

Greater block without hysteresis

Parameters

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Reals.Less.LessWithHysteresis

Less block without hysteresis

Parameters

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Reals.Less.LessNoHysteresis

Less block without hysteresis

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Reals.LessThreshold.LessWithHysteresis

Less block without hysteresis

Parameters

Connectors

Modelica definition

Buildings.Controls.OBC.CDL.Reals.LessThreshold.LessNoHysteresis

Less block without hysteresis

Parameters

Connectors

Modelica definition