Multivariable controllers balance competing objectives

Multivariable controllers differ from traditional single-variable controllers in that they can regulate more than one process variable by using more than one actuator at once. Doing so can be difficult if each actuator effects more than one process variable, but if those interactions can be quantified, the controller can determine the control efforts required to drive all of the process variab...

09/01/2008


Multivariable controllers differ from traditional single-variable controllers in that they can regulate more than one process variable by using more than one actuator at once. Doing so can be difficult if each actuator effects more than one process variable, but if those interactions can be quantified, the controller can determine the control efforts required to drive all of the process variables towards their respective setpoints simultaneously.

For example, an HVAC system responsible for maintaining the temperature and humidity in a conditioned space will find that the process variables are coupled. That is, they rise and fall together since condensing excess moisture out of the air requires cooling it, and adding moisture to the air requires an injection of hot steam. The trick is to chill the air and inject the steam in just the right combination.

Simultaneous control of a spacecraft
Simultaneous control of a spacecraft's yaw, pitch and roll was one of the earliest applications of multivariable control theory. Source: Control Engineering

Unfortunately, computing that ideal combination requires mathematical models and computational methods considerably more sophisticated than basic PID loops. The temperature and humidity can not be adequately controlled by two independent controllers operating in parallel. Each has to know what the other is doing or else any attempt to correct the temperature will disturb the humidity, which will in turn initiate humidity corrections that will disturb the temperature. Absent a coordinated effort, the two controllers would continue to fight each other in a never-ending cycle.

NASA engineers encountered a similar problem with the attitude control systems for their earliest spacecraft. They tried to control pitch, yaw and roll with three independent control loops. But since pitch causes yaw and yaw causes roll, the efforts of each controller affected the other two. The competing controllers ended up expending inordinate amounts of precious fuel during every maneuver.

The solution was found in the mathematical discipline of linear algebra, which can be used to quantify and compensate for the interactions between multiple actuators and process variables. Scores of multivariable control techniques based on the principles of linear algebra have ensued over the last 40 years, though very few have been applied outside of the aerospace, petrochemical and energy industries. They tend to be mathematically complex, but well worth the effort when coupled process variables are a problem.

Other benefits

Not only can multivariable controllers coordinate the efforts of multiple actuators simultaneously, they can optimize and constrain the overall control problem. That is, if the desired results can be achieved by more than one combination of control efforts, an optimizing controller can select the combination that minimizes a user-defined cost such as the discomfort of a room's occupants or the total volume of rocket fuel expended.

On the other hand, if it happens that the optimal control effort would require an impossible actuator position or an excessively high or low value for any of the process variables, a constraining controller can select the best combination of control efforts that comes closest to achieving the desired results without violating any of those constraints. Constraint management makes linear-algebra-based multivariable controllers especially valuable in the petrochemical industry where the greatest profit is realized when processes are run with all of their operating conditions at their maximum allowable values.

A linear-algebra-based multivariable controller can also determine if a particular selection of setpoints is even possible. In the HVAC example, high humidity and low temperatures can not generally be achieved simultaneously. A multivariable controller equipped with a thermodynamic model of the conditioned space would be able to deduce the controllability of the process and flag an unachievable combination of process variables.


Author Information
Vance VanDoren is consulting editor to Control Engineering. Reach him at controleng@msn.com .




The Engineers' Choice Awards highlight some of the best new control, instrumentation and automation products as chosen by...
The System Integrator Giants program lists the top 100 system integrators among companies listed in CFE Media's Global System Integrator Database.
Each year, a panel of Control Engineering and Plant Engineering editors and industry expert judges select the System Integrator of the Year Award winners in three categories.
This eGuide illustrates solutions, applications and benefits of machine vision systems.
Learn how to increase device reliability in harsh environments and decrease unplanned system downtime.
This eGuide contains a series of articles and videos that considers theoretical and practical; immediate needs and a look into the future.
Women in engineering; Engineering Leaders Under 40; PID benefits and drawbacks; Ladder logic; Cloud computing
Robotic integration and cloud connections; SCADA and cybersecurity; Motor efficiency standards; Open- and closed-loop control; Augmented reality
Controller programming; Safety networks; Enclosure design; Power quality; Safety integrity levels; Increasing process efficiency
This article collection contains several articles on how advancements in vision system designs, computing power, algorithms, optics, and communications are making machine vision more cost effective than ever before.
Featured articles highlight technologies that enable the Industrial Internet of Things, IIoT-related products and strategies to get data more easily to the user.
This digital report will explore several aspects of how IIoT will transform manufacturing in the coming years.

Find and connect with the most suitable service provider for your unique application. Start searching the Global System Integrator Database Now!

Cloud, mobility, and remote operations; SCADA and contextual mobility; Custom UPS empowering a secure pipeline
Infrastructure for natural gas expansion; Artificial lift methods; Disruptive technology and fugitive gas emissions
Mobility as the means to offshore innovation; Preventing another Deepwater Horizon; ROVs as subsea robots; SCADA and the radio spectrum
Automation Engineer; Wood Group
System Integrator; Cross Integrated Systems Group
Jose S. Vasquez, Jr.
Fire & Life Safety Engineer; Technip USA Inc.
This course focuses on climate analysis, appropriateness of cooling system selection, and combining cooling systems.
This course will help identify and reveal electrical hazards and identify the solutions to implementing and maintaining a safe work environment.
This course explains how maintaining power and communication systems through emergency power-generation systems is critical.
The Engineers' Choice Awards highlight some of the best new control, instrumentation and automation products as chosen by...
The System Integrator Giants program lists the top 100 system integrators among companies listed in CFE Media's Global System Integrator Database.
Each year, a panel of Control Engineering and Plant Engineering editors and industry expert judges select the System Integrator of the Year Award winners in three categories.
This eGuide illustrates solutions, applications and benefits of machine vision systems.
Learn how to increase device reliability in harsh environments and decrease unplanned system downtime.
This eGuide contains a series of articles and videos that considers theoretical and practical; immediate needs and a look into the future.
Women in engineering; Engineering Leaders Under 40; PID benefits and drawbacks; Ladder logic; Cloud computing
Robotic integration and cloud connections; SCADA and cybersecurity; Motor efficiency standards; Open- and closed-loop control; Augmented reality
Controller programming; Safety networks; Enclosure design; Power quality; Safety integrity levels; Increasing process efficiency
This article collection contains several articles on how advancements in vision system designs, computing power, algorithms, optics, and communications are making machine vision more cost effective than ever before.
Featured articles highlight technologies that enable the Industrial Internet of Things, IIoT-related products and strategies to get data more easily to the user.
This digital report will explore several aspects of how IIoT will transform manufacturing in the coming years.

Find and connect with the most suitable service provider for your unique application. Start searching the Global System Integrator Database Now!

Cloud, mobility, and remote operations; SCADA and contextual mobility; Custom UPS empowering a secure pipeline
Infrastructure for natural gas expansion; Artificial lift methods; Disruptive technology and fugitive gas emissions
Mobility as the means to offshore innovation; Preventing another Deepwater Horizon; ROVs as subsea robots; SCADA and the radio spectrum
Automation Engineer; Wood Group
System Integrator; Cross Integrated Systems Group
Jose S. Vasquez, Jr.
Fire & Life Safety Engineer; Technip USA Inc.
This course focuses on climate analysis, appropriateness of cooling system selection, and combining cooling systems.
This course will help identify and reveal electrical hazards and identify the solutions to implementing and maintaining a safe work environment.
This course explains how maintaining power and communication systems through emergency power-generation systems is critical.
The Engineers' Choice Awards highlight some of the best new control, instrumentation and automation products as chosen by...
The System Integrator Giants program lists the top 100 system integrators among companies listed in CFE Media's Global System Integrator Database.
Each year, a panel of Control Engineering and Plant Engineering editors and industry expert judges select the System Integrator of the Year Award winners in three categories.
This eGuide illustrates solutions, applications and benefits of machine vision systems.
Learn how to increase device reliability in harsh environments and decrease unplanned system downtime.
This eGuide contains a series of articles and videos that considers theoretical and practical; immediate needs and a look into the future.
Women in engineering; Engineering Leaders Under 40; PID benefits and drawbacks; Ladder logic; Cloud computing
Robotic integration and cloud connections; SCADA and cybersecurity; Motor efficiency standards; Open- and closed-loop control; Augmented reality
Controller programming; Safety networks; Enclosure design; Power quality; Safety integrity levels; Increasing process efficiency
This article collection contains several articles on how advancements in vision system designs, computing power, algorithms, optics, and communications are making machine vision more cost effective than ever before.
Featured articles highlight technologies that enable the Industrial Internet of Things, IIoT-related products and strategies to get data more easily to the user.
This digital report will explore several aspects of how IIoT will transform manufacturing in the coming years.

Find and connect with the most suitable service provider for your unique application. Start searching the Global System Integrator Database Now!

Cloud, mobility, and remote operations; SCADA and contextual mobility; Custom UPS empowering a secure pipeline
Infrastructure for natural gas expansion; Artificial lift methods; Disruptive technology and fugitive gas emissions
Mobility as the means to offshore innovation; Preventing another Deepwater Horizon; ROVs as subsea robots; SCADA and the radio spectrum
Automation Engineer; Wood Group
System Integrator; Cross Integrated Systems Group
Jose S. Vasquez, Jr.
Fire & Life Safety Engineer; Technip USA Inc.
This course focuses on climate analysis, appropriateness of cooling system selection, and combining cooling systems.
This course will help identify and reveal electrical hazards and identify the solutions to implementing and maintaining a safe work environment.
This course explains how maintaining power and communication systems through emergency power-generation systems is critical.
click me