Linearizing PID Loop Control

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This post is a brief recap of an article written by Eric Utterson, President of 8760 Engineering, that was published in March 2003 publication of the ASHRAE Journal.

This article addresses a method for achieving predictable linear response for supply duct pressure control, economizer damper control and steam heat exchanger leaving water temperature control using PID control loops.

Some background of PID loops may help understand why PID control loops are important to energy efficiency.  At a high level, feedback controllers attempt to minimize the error between a setpoint, say discharge air temperature setpoint, and a measured process variable, such as actual discharge air temperature.  The controller will compare the actual temperature versus the desired temperature and adjust some process control input, such as the chilled water control valve, to minimize the error.  PID controllers allow systems more closely track their setpoints and achieve the efficiencies an engineer has specified.  If an engineer sets the discharge air temperature at 60° F in the middle of winter, a properly tuned PID loop controller will achieve this setpoint instead of operating at the 55° F summer setpoint (thus saving energy back at the chiller plant and at the reheat box).

A proportional-integral-derivative controller (PID controller) uses three separate constant parameters in the algorithm that can be interpreted with respect to time: P (proportional) depends on the present error, I (integral) depend on the accumulation of past errors, and D (derivative) is a prediction of future errors, based on current rate of change.  In the simplest form, the output of a PID loop is described as:

PIDOutput = Pgain × (Error+  1/Itime  × ∫ 〖Error ×dt〗+Dtime ×  dError/dt)

where:

Error = PID Input – PID Setpoint (for direct acting control scenarios)

Pgain = Proportional Gain Term

Itime = Integral Time

Dtime = Derivative Time

Supply Duct Pressure Control

The goal of the linearization process is to create PID input and setpoint equations that describe the controlled process and compensate for all known varying inputs.  For supply duct pressure control, the final linearized equation must apply for any given supply airflow rate, supply duct pressure loss coefficient and supply fan speed (equations are shown in the paper).  Thus, we can establish the following equations for PIDsetpoing and PIDinput:

 PIDsetpoint = FanSpeed_sp = FanSpeed × √((∆P_sp)/∆P)

PIDinput = FanSpeed

Economizer Damper Control

Similar to the supply duct pressure control linearization method described above, the goal of the economizer damper linearization process is to calculate a PID input equation and PID setpoint equation so that each compensates for the known nonlinearities.  For economizer damper control, the following equations can be used:

PIDsetpoint =  %OA_sp ≈ 100% × ((RAT - DAT_sp) / (RAT - OAT))

PIDinput =  %OA  ≈ 100% × ((RAT - DAT) / (RAT - OAT))

Steam Heat Exchanger Leaving Water Temperature

Linearization of the steam heat exchanger system requires measurement of either water flow rate or entering water temperature.  Because obtaining the water temperature is less expensive and more reliable, the following linearization method addresses the case where the entering water temperature is known.  The fundamental equations for water flow are detailed in the paper; this post showcases resulting PID equations:

PIDsetpoint =  %Q_sp = %Q × ((LWT_sp - EWT) / (LWT - EWT))

PIDinput = %Q ≈ SteamValvePosition

All of these equations can be used to the benefit of energy savings by allowing the engineer to specify energy saving setpoints.

As usual, we end with a typical energy conservation measure that is all too often over looked, having parking garage exhaust fans tied into a CO monitor.  This system runs the fan only when the CO levels reach certain levels and greatly reduces the run time of exhaust fans.

ECM:  Parking Garage CO Ventilation
Average kWh Saved per Sq. Ft.:  2.25

Article Author:  Eric Utterson
eutterson@8760engineering.com
Blog Post Author:  Ryan Corrigan

rcorrigan@8760engineering.com

Marketing and Rebranding: Selling Green to a Gray Generation

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At the 35^th Association of Energy Engineers annual World Energy Engineering Congress in Chicago, I presented a paper that discussed some of the difficulties the sustainability movement is facing and some of the opportunities for this movement.  The fundamental theme of the paper is that the “green” industry can now be thought of as more a brand and less of a movement.  Realizing the power or marketing and branding, the green industry needs to take control of its image and understand the current marketplace in order to advance the cause of sustainability.  The paper presented three ways the “green” industry can control its image and advance sustainability; the first is through an accurate assessment of the current marketplace, the second is a better understanding of who our customers are and how they consume energy, and the third is the continuous improvement of past goals and restructuring of future goals.

This post will not go into too much detail of each item presented in the paper but I do want to touch on each of these subjects.  The first being an accurate assessment of the current building landscape and the affect this landscape has on the image / brand of “green” building.  As our economy slowly climbs out of the recession we are going to face an overcapacity of building occupancy and an even greater attention to price (sometimes known as the bottom line effect which manifests itself in the most ironic activity called “value engineering”).  The question then is pretty simple, does the “green” industry position itself as a high cost option that helps the environment, or rather as a solution to lower future operating cost?

The second topic centered on who are the people in charge of energy consumption and how does anything “green” create value for them?  The first part of that equation, who are the people in charge of energy consumption, is not as intuitive as one might think.  They are usually a little older and more advanced in their career and the people with the most influence over energy consumption probably reside in the facilities or maintenance department as opposed to the executive suites.  Their main concern is keeping buildings running and satisfying the building occupants, not reducing their energy burden.  This leads to the second part of the equation, how does anything “green” help them?  The answer to this question will force us to address the main drivers of energy consumption in any building, the large motors that operate chillers, compressors, fans, and pumps.  Why install solar panels when the chilled water plant is not automated, what benefit are lighting occupancy sensors if the air handling units are not scheduled to turn off?  We can create tremendous value for facility managers while simultaneously reducing their energy burden by addressing the major sources of energy consumption within a building.

The final topic dealt with building upon past achievements and recognizing future opportunities.  This is a much more open ending topic and one that this engineer is not best suited to answer.  What should our industry do going forward?  How do we best create value for our customers?  All questions that I addressed in the paper but found much more utility by engaging the fellow attendees in what they thought the future of the “green” industry would be.  Let me know what your thoughts are.

As always this blog post will end with kWh counter, this time it comes from one single ECM (energy conservation measure) that automated the chilled water plant of one of our customers (was part of a larger retrofit).

ECM:  Chilled Water Optimization

Payback:  1.46 years

kWh Saved:  338,937

Author:  Ryan Corrigan

rcorrigan@8760engineering.com

Welcome to the 8760 Engineering Blog!

For starters, 8760 Engineering is an engineering firm that is committed to reducing our customers energy burden and making the business case for sustainability. Our motto...Engineered Efficiency Every Hour... may help explain our name:

   365 Days in one year
x   24 Hours in one day
 8760 Hours in a year

The goal of this blog is to spread ideas and information within the mechanical engineering / architecture / energy engineering / environmental / math and science community.  We appreciate you taking the time to skim through our post and encourage you to participate in the discussion.

Come back every other week to peek into the minds of some the best engineers I have ever met.  And if you don't see anything interesting then reach out to us, we are always looking for new ideas!

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Since our goal here is to save customers money by reducing their energy burden and becoming more sustainability, we will end each blog post with a kWh counter that tallies the kWh's we have saved our customers.  This weeks number comes from a job that was done in coordination with Ameren Illinois' ActOnEnergy Program.

Type:  Hospital
Job:  RetroCommissioning
kWh Saved:  2,140,069

Author: Ryan Corrigan
rcorrigan@8760engineering.com