Model Predictive Controller

Despite many challenges in applying model predictive control (MPC) to a process control problem, it is worth the effort. Performance of this technology can be significantly better than more familiar control methods. Consequently, its use is becoming more important in achieving plants' production-and-efficiency goals—driven by today's environment of intense economic competition.

By Lew Gordon January 1, 2006
  • Process testing

  • Model structure

  • Relative performance

  • Operator impact

Despite many challenges in applying model predictive control (MPC) to a process control problem, it is worth the effort. Performance of this technology can be significantly better than more familiar control methods. Consequently, its use is becoming more important in achieving plants’ production-and-efficiency goals—driven by today’s environment of intense economic competition.

Most significantly, MPC’s ability to project paths for the controlled variables (CVs into the future makes it more capable of meeting the constraints of real-world process control. The same constraints typically are given a wider margin by less capable controls.

The most significant benefit gained in selecting MPC is its ease of integration with a process optimizer (subject of this series’ next two installments), generating significant economic benefits that are hard to achieve using conventional control strategies.

Obtaining good data during process testing is the most important step.

MPC for reactor control

Major steps in applying an MPC are:

  • Obtain data showing process response relationships;

  • Definition of the process model’s controlled, manipulated, and disturbance variables;

  • Process model development using model identification tools;

  • Integration of the process model into a final controller; and

  • Controller commissioning and finalization of performance.

Process testing. Initially, definition is lacking among meaningful controlled variables, effective manipulated variables, and significant disturbance variables. This is especially true if the process is complex. And dynamic interactions among these variables are often unclear. Process testing provides necessary information.

Process interactions are clear: both of the ingredient flows affect all three controlled variables; and steam flow only impacts product temperature.

Process testing requires stepping through the likely manipulated variables and recording their effect on the likely controlled variables—along with any variation in the likely disturbance variables. This often takes the form of a Pseudo-Random Binary Sequence (PRBS) test. Figure 1 illustrates some of the PRBS test data collected from the target reactor for this series. It shows randomly timed step changes in the flows of ingredients A and B and steam, and their effects on the controlled variables.

Model structure definition. This critical step is not as simple as it sounds. It is not always obvious which variables should be included in an MPC. The engineer must select the:

  • Controlled variables that are important to achieving product quality and throughput objectives; and

  • Manipulated variables that have the most effect on them.

The engineer must also identify the measured disturbances that have significant impact and variation. Test data provides quantitative proof, but process understanding is essential to properly identify relevant independent and dependent variables.

The engineer must specify the CVs as either set-point or constraint variables. Finally, if there are available degrees-of-freedom, the designer must specify which manipulated variables will have targets.

For the reactor example, variables include:

  • Three controlled;

  • Three manipulated; and

  • Two feed forward.

Reactor modeling of the effect of ingredient B’s flow on product temperature shows an inverse response.

Since there are set points for each of the CVs and only three degrees of freedom, no independent multi-variable (MV) targets can be defined.

Model identification. Because all MPC packages include tools for identifying process models from test data, some critical decisions must be made. These include:

  • What will be the prediction interval of the model? The prediction interval of the model defines the time interval between predicted values into the future. This value must be small enough to adequately resolve the process dynamics of the fastest controlled variable.

  • How many coefficients will be in the models? The number of coefficients in the model defines the history used to make predictions. It must be enough to span full process response; this is also the magnitude of time it takes for the effect of an input change to be complete.

  • What will be the model’s prediction horizon? This is the amount of time into the future for which predictions will be made. Unless the individual models have individual horizons, this value must be long enough to cover the full response of the controller’s slowest model.

If the process is multi-variable, some number of output-controlled variables will be affected by some number of input manipulated and disturbance variables. A matrix of individual input/output models is a convenient way to present a complete set of these input/output relationships. Figure 2 shows the complete set of step responses for the reactor model:

  • Left axis includes the CVs of product: composition, flow rate, and temperature; and

  • Top axis presents the MVs and FVs (feed forward variable)—ingredient flows of A and B, steam flow, and ingredient temperatures.

Controller integration with the control platform. While many details must be configured, this is the easiest part since the process is largely mechanical and procedural. Details vary with the particular control package used.

Controller commissioning . All prior efforts come together when the controller is applied to the process. One fundamental difference between traditional and model-based controls immediately becomes clear. Traditional controls are tuned when they are commissioned, and the full range of controller response is available through tuning constants that can be easily changed.

However, a model-based controller’s behavior is mostly determined by its model. If the model is accurate, the controller should perform well. If the model is inaccurate, the controller will yield poor results. Tuning weights only have a trimming effect on controller response. It is very difficult, if not impossible, to make up for a poorly developed model during commissioning. This makes obtaining good data—during process testing—the most important step in applying MPC.

Figure 3 compares performance of this MPC to previous control schemes showing that the performance of model-based control is superior to all earlier forms of control, in every category. For the most likely event, a change in production rate, the overall index is:

  • 3.3 times better than advanced regulatory control (ARC);

  • 62 times better than basic regulatory control (BRC); and

  • 103 times better than fuzzy logic control.

For changes in the product composition set point, the index is 9% better than that of ARC and 70% better than the index for fuzzy logic control.

MPC response for the reactor after introducing the same changes (applied in previous articles in the series).

Like ARC, MPC operates as a multi-variable controller. Although only one set point is changed, the controller moves all the manipulated variables. MPC gains its performance edge over ARC from its better understanding of process dynamics.

Most of the gain comes from better temperature control. With a better understanding of the temperature dynamics, it can deliver control action at a more appropriate rate. In the trend, the controller responds to a composition set point change by first driving the steam flow away from its final steady-state value. This properly compensates the inverse response in the process and holds temperature more constant.

Conversely, there is not much apparent difference among the index values for product composition response to a set point change. The index only varies from 1.7 to 2.7. Composition response is dominated by dead time; but there is nothing any controller can do to eliminate the effect of dead time. Even if a controller responds perfectly at the moment of set point change, there will still be a delay before the control action appears at the measurement. An error equal to the set point change will exist for at least one dead time. A minimum ISE is unavoidable.

For this error and dead time, this minimum ISE is approximately 1.5 units. Only the ISE greater than this value can be eliminated by any control. For BRC, this value is 0.29 units; for MPC it is 0.21 units. Compared to BRC, MPC reduces this portion of the index by 28%. Rule based control increases it by 413%.

Operator impact

Introducing MPC into the control room brings significant new challenges for the operator. In working with the controller, the operator primarily has to think in multivariable terms. The controller makes multiple changes simultaneously to accomplish multiple objectives; the combined effect may not be immediately clear. Furthermore, because the controller is aware of dynamic characteristics, such as inverse and delayed response, the logic of its control moves may not be immediately obvious to an operator.

Moreover, MPC introduces new kinds of control objectives. Some variables will be classified as constraint variables, which the controller will consider only when they approach their limits. Targets for manipulated variables may be an unfamiliar concept that requires careful explanation.

The human-machine interface for the controller may be unfamiliar to the operators. In addition to set points, the operator may have to enter constraint limits. Because of the number of variables in the controller, the information will likely be displayed in tabular format.

Additionally, controller state transitions are more complicated. A traditional PID controller has only two states—manual and automatic—and the transition is instantaneous. However an MPC must pass through several states, over a longer period of time, before it is fully in control. And, because MPC typically provides set points to lower-level regulatory controls, operators will see additional states and transitions for these controllers as well.

MPC reactor-control performance

Relative MPC performance Change production rate Change product composition
Control technology Composition ISE* Temperature ISE Total ISE Composition ISE Temperature ISE Total ISE
*Integral of the squared error
Basic regulatory control 0.53 0.28 0.81 1.79 0.55 2.34
Advanced regulatory control 0.015 0.028 0.043 1.83 0.08 1.89
Advanced fuzzy logic control 0.003 1.35 1.35 2.70 0.56 3.26
Model predictive control 0.011 0.002 0.013 1.715 0.005 1.72
Author Information
Lew Gordon is a principal application engineer at Invensys;