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 .




No comments
The Top Plant program honors outstanding manufacturing facilities in North America. View the 2015 Top Plant.
The Product of the Year program recognizes products newly released in the manufacturing industries.
The Engineering Leaders Under 40 program identifies and gives recognition to young engineers who...
2016 Product of the Year; Diagnose bearing failures; Asset performance management; Testing dust collector performance measures
Safety for 18 years, warehouse maintenance tips, Ethernet and the IIoT, GAMS 2016 recap
2016 Engineering Leaders Under 40; Future vision: Where is manufacturing headed?; Electrical distribution, redefined
SCADA at the junction, Managing risk through maintenance, Moving at the speed of data
Safety at every angle, Big Data's impact on operations, bridging the skills gap
The digital oilfield: Utilizing Big Data can yield big savings; Virtualization a real solution; Tracking SIS performance
Applying network redundancy; Overcoming loop tuning challenges; PID control and networks
Driving motor efficiency; Preventing arc flash in mission critical facilities; Integrating alternative power and existing electrical systems
Package boilers; Natural gas infrared heating; Thermal treasure; Standby generation; Natural gas supports green efforts

Annual Salary Survey

Before the calendar turned, 2016 already had the makings of a pivotal year for manufacturing, and for the world.

There were the big events for the year, including the United States as Partner Country at Hannover Messe in April and the 2016 International Manufacturing Technology Show in Chicago in September. There's also the matter of the U.S. presidential elections in November, which promise to shape policy in manufacturing for years to come.

But the year started with global economic turmoil, as a slowdown in Chinese manufacturing triggered a worldwide stock hiccup that sent values plummeting. The continued plunge in world oil prices has resulted in a slowdown in exploration and, by extension, the manufacture of exploration equipment.

Read more: 2015 Salary Survey

Maintenance and reliability tips and best practices from the maintenance and reliability coaches at Allied Reliability Group.
The One Voice for Manufacturing blog reports on federal public policy issues impacting the manufacturing sector. One Voice is a joint effort by the National Tooling and Machining...
The Society for Maintenance and Reliability Professionals an organization devoted...
Join this ongoing discussion of machine guarding topics, including solutions assessments, regulatory compliance, gap analysis...
IMS Research, recently acquired by IHS Inc., is a leading independent supplier of market research and consultancy to the global electronics industry.
Maintenance is not optional in manufacturing. It’s a profit center, driving productivity and uptime while reducing overall repair costs.
The Lachance on CMMS blog is about current maintenance topics. Blogger Paul Lachance is president and chief technology officer for Smartware Group.
This article collection contains several articles on the vital role of plant safety and offers advice on best practices.
This article collection contains several articles on the Industrial Internet of Things (IIoT) and how it is transforming manufacturing.
This article collection contains several articles on strategic maintenance and understanding all the parts of your plant.
click me