July/August 2010

Using modeling, simulation to optimize
plant control systems

By Tony Lennon

Increased emphasis on more environmentally friendly, efficient, and safe processes has led companies to focus optimization efforts across plants, including refining, chemical, and pulp and paper. Plant control systems, which rely on a concert of supervisory and loop-level controls to hold set points and reject disturbances, present notorious optimization challenges. Multiphase flows, entrained solids, hybrid continuous-batch operations, and other highly nonlinear behaviors contribute to this complexity. Even plants with the same process for producing the same product often have different capacities and layouts, and require separate optimizations to maximize production and minimize operational costs.

Trial-and-error approaches to improve performance can adversely affect plant operations and safety. Setting less aggressive controller gains as a quick fix to control system instability problems often leads to suboptimal performance. As an alternative to these approaches, engineers can perform dynamic simulations of the control system (controllers and process) to gain insight into the system dynamics, understand what is causing instabilities, tune controllers, design and validate a better control architecture, and achieve better plant performance.

During plant design, simulation enables engineers to optimize processes, formulate the plant control system architecture, and study steady-state capacity. Once in operation, plant simulations let engineers identify the root cause of inefficiencies and fine-tune the process. Often, problems can be resolved by tuning isolated control loops with a single controller. Loop tuning uses an empirical model based on process data during a predefined set point change, helping calculate new gain coefficients such as in PID controllers.

When plant conditions change and no longer match those used in the original design simulations, the problems can become more complex. Multiple control loops may interact with each other, and systems may have unforeseen coupled dynamics that cause oscillatory behavior or uncontrollable instabilities. Multivariate control techniques are often used to address this class of problem.

Modeling plant processes must be done before running control system simulations. Modeling approaches such as data-based and first-principles each have advantages and drawbacks, so engineers should understand model types and have insight into the level of model fidelity needed to solve their problem. Process models can either be linear, representing a small operating region of interest and limited input range, or nonlinear, representing the dynamics of a much larger range of operating conditions and input amplitudes. It can be difficult to develop an accurate model that provides enough confidence to reconfigure a control system. Engineers must recognize not only the principles behind the models they develop but also the capabilities and limitations of their simulation software.

Starting point

The starting point to using simulation to investigate a control system problem is to show simulation reproduces the process problems identified in the real world. This activity proves the process models correctly represent real conditions in the plant. It also shows the simulated control system is reacting to the dynamics of the processes in the same way as the actual control system. This is an important proof point that demonstrates that the simulation is based on a realistic control system model of the actual plant operation. The verified simulation provides the foundation for a formal analysis of the problems and the corrective actions.

Modeling with dynamic data

System identification is essential to modeling with dynamic data. It involves using dynamic input-output data captured from plant operation. To obtain the data, engineers place control loops into manual mode and introduce a defined disturbance to set points of the loops of interest. Choosing the size of the disturbance is critical. Changes too large can introduce plant instability, while changes too small may not reveal the system dynamics.

Often, data-based models are first-, second-, or third-order linear ordinary differential equation representations of the process about the point of the disturbance. They should be accurate for the operating range of the data; however, their applicability may not extend beyond the conditions under which the data was collected. In some cases, this resolves the problem.

If linear models do not describe the problem well, then nonlinear dynamic models can be explored. A nonlinear model, such as a nonlinear autoregressive model or a neural network, is more flexible than a linear model and is thus able to emulate the system behavior over a broader range of operation. Typically, nonlinear models require much more data and computational effort to train than linear models. Alternately, combining piecewise linear models with overlapping operating regions can capture a broader range of nonlinear behavior.

Although data-based modeling is an accepted approach, developing models requires cooperation with the operating plant to perform tests with enough excitation to reveal the dynamics of the systems of interest at each operating point.

Modeling with first principles

First-principles modeling involves an understanding of the chemistry and physics of the process to develop its governing equations. The models can be expressed as partial differential equations (PDE), ordinary differential equations, or differential algebraic equations (DAE). PDE models provide highly accurate results and localized operating conditions in a process. However, they require the most domain-specific knowledge as well as knowledge of the system geometry and are not always ideal for control system design. DAE models involve algebraic terms that take into account constraints such as mass and energy balances. DAE equations provide accurate system results in the form of lumped parameter models. Like PDEs, these models require domain knowledge but are suited for control system design as they are based on differential equations.

Typically, first-principle models are expressed in simulation software as flow-sheet diagrams (sometimes called block diagrams). These diagrams depict the system schematically, which works well for control system design. Engineers build the system model from libraries of predefined unit operations and mathematical operators. The library blocks let engineers build a simulation model that maps to the structure of the process, making it easy for others to understand the process architecture of the plant. DAE editors supplement the libraries, helping develop customized unit operations based on first principles to capture specialized processes or functions not already available in the software. Additionally, flow-sheet diagram software often supports importing data-driven models and reduced order PDE models from computational fluid dynamics software.

gPROMS flowsheet simulation model of a distillation column.
Source: Process Systems Enterprise Limited

Refining the model through parameter tuning is critical to first-principles simulation. It involves adjusting the simulation until it exhibits the same behavior as the actual process. Nonlinearities in the system can be parameterized, but the parameters may not be known before running the simulation. (For example, the coefficient of a reaction rate will depend on multiple operating inputs, which are unknown before the simulation begins.) Software simulations employ optimization methods that can tune parameters in the model using measured data from the actual system, bringing the models closely in line with the actual process operation.

Improving the control system

With proven process models, control system analysis becomes more systematic, so time-domain and frequency-domain analyses can be performed. For single loops, engineers can perform more rigorous loop tuning using classical control or optimization-based methods based on time and frequency constraints. For coupled loops, optimization approaches can yield controller gains that satisfy stability requirements. A more common approach is to develop a decoupling expression between the coupled loops to cancel their mutual effects on each other.

Some control problems require tuning multiple loops where constraints such as pressure or temperature limits exist. Model predictive control is an effective advanced process control strategy for obtaining better performance while maintaining loop stability. This approach requires developing an internal model through system identification or, if supported by the simulation software, a linear model of the process. Verifying the controller using simulation lets engineers avoid problems that are more expensive and difficult to fix once the actual process is implemented.

System level simulation model for a combined cycle power plant developed in Thermolib, a library of Simulink blocks.
Source: EUtech Scientific Engineering GmbH

Once a new control system strategy is verified via simulation, the distributed control system (DCS) can be reconfigured or supplemented with a supervisory control system, as in the case of a model predictive controller. Before plant startup, a company may optionally verify the DCS configuration by connecting the control system to the process simulation via an OPC connection if the simulation supports an OPC client.

In the race for greater process precision and speed, simulation is a cost-effective way to validate control systems, find and eliminate problems before implementation, and optimize plants already in operation. Desktop simulation software, already fully capable of performing such validation and optimization, continues to improve yearly as new features are added, helping engineers meet a rapidly expanding set of plant control challenges.


Tony Lennon (Tony.Lennon@MathWorks.com) is the Industry Marketing Manager for the industrial automation and machinery market at MathWorks, where he leads the marketing effort to foster industry adoption of MathWorks products and Model-Based Design.