Buildings.Controls.OBC.Utilities

Package with utility functions

Information

This package contains utility blocks, base classes and validation models for the OpenBuildingControl (OBC) library.

Package Content

Name	Description
OptimalStart	Block that outputs the optimal start time for an HVAC system before occupancy
PIDWithInputGains	P, PI, PD, and PID controller with output reset and input gains
SetPoints	Package with blocks for setpoint resets
Validation	Collection of validation models
BaseClasses	Package with base classes

Buildings.Controls.OBC.Utilities.OptimalStart

Block that outputs the optimal start time for an HVAC system before occupancy

Information

This block predicts the shortest time for an HVAC system to meet the occupied setpoint prior to the scheduled occupancy. The block requires inputs of zone temperature, occupied zone setpoint(s) and next occupancy. The two outputs are the optimal start duration tOpt and the optimal start on signal optOn for the HVAC system.

The block estimates the thermal mass of a zone using its measured air temperature gradient with respect to time. Once the temperature slope of a zone is known, the optimal start time can be calculated by the difference between the zone temperature and the occupied setpoint divided by the temperature slope, assuming the zone responds as if all thermal mass were concentrated in the room air.

The temperature slope is self-tuned based on past data. The moving average of the temperature slope of the past nDay days is calculated and used for the prediction of the optimal start time in the current day.

Parameters

The parameter nDay is used to compute the moving average of the temperature slope; the first n days of simulation is therefore used to initialize the block.

The parameter tOptMax is the maximum allowed optimal start time.

The block includes two hysteresis parameters uLow and uHigh. The parameter uLow is used to determine if the zone temperature reaches the setpoint. The algorithm assumes that the zone temperature has reached the setpoint if TSetZonHea-TZon ≤ uLow for a heating system, or TZon-TSetZonCoo ≤ uLow for a cooling system, where TSetZonHea denotes the zone heating setpoint during occupancy, TSetZonCoo denotes the zone cooling setpoint during occupancy, and TZon denotes the zone temperature. The parameter uHigh is used by the algorithm to determine if there is a need to start the HVAC system prior to occupancy. If TSetZonHea-TZon ≤ uHigh for heating case or TZon-TSetZonCoo ≤ uHigh for cooling case, then there is no need for the system to start before the occupancy.

The optimal start is only active (i.e., the optimal start on signal optOn becomes true) if the optimal start time is larger than the parameter thrOptOn.

Configuration for HVAC systems

The block can be used for heating system only or cooling system only or for both heating and cooling system. The two parameters computeHeating and computeCooling are used to configure the block for these three scenarios.

The block calculates the optimal start time separately for heating and cooling systems. The base class Buildings.Controls.OBC.Utilities.BaseClasses.OptimalStartCalculation is used for the calculation.

Algorithm

The algorithm is as follows:

Step 1: Calculate temeperature slope TSlo

Once the HVAC system is started, a timer records the time duration Δt for the zone temperature to reach the setpoint. At the time when the timer starts, the zone temperature TSam1 is sampled. The temperature slope is approximated using the equation TSlo = |TSetZonOcc-TSam1|/Δt, where TSetZonOcc is the occupied zone setpoint. Note that if Δt is greater than the maximum optimal start time tOptMax, then tOptMax is used instead of Δt. This is to avoid corner cases where the setpoint is never reached, e.g., the HVAC system is undersized, or there is a steady-state error associated with the HVAC control.

Step 2: Calculate temperature slope moving average TSloMa

After computing the temperature slope of each day, the moving average of the temperature slope TSloMa during the previous nDay days is calculated. Please refer to Buildings.Controls.OBC.CDL.Discrete.TriggeredMovingMean for details about the moving average algorithm.

Step 3: Calculate optimal start time tOpt

Each day at a certain time before the occupancy, the algorithm takes another sample of the zone temperature, denoted as TSam2. The sample takes place tOptMax prior to occupancy start time.

The optimal start time is then calculated as tOpt = |TSetZonOcc-TSam2|/TSloMa.

Validation

Validation models can be found in the package Buildings.Controls.OBC.Utilities.Validation.

Parameters

Connectors

Modelica definition

Buildings.Controls.OBC.Utilities.PIDWithInputGains

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

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, 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.

This block is identical to Buildings.Controls.OBC.CDL.Reals.PIDWithReset, except that the controller gains k, T_i and T_d are inputs rather than parameters.

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