MPC is widely adopted in the process industry as an effective means to deal with large multivariable constrained control problems. The main idea of MPC is to choose the control action by repeatedly solving on line an optimal control problem. This aims at minimizing a performance criterion over a future horizon, possibly subject to constraints on the manipulated inputs and outputs, where the future behavior is computed according to a model of the plant.
MPC has been used in industry for more than 30 years, and has become an industry standard (mainly in the petrochemical industry) due to its intrinsic capability for dealing with constraints and with multivariable systems. Most commercially available MPC technologies are based on a linear model of the process. For processes that are highly nonlinear, the performance of an MPC based on a linear model can be poor. This has motivated the development of Nonlinear Model Predictive Control (NMPC), where a more accurate (nonlinear) model of the plant is used for prediction and optimization.
Predictive Constrained Control
PID type controllers do not perform well when applied to systems with significant time-delay. Perhaps the best known technique for controlling systems with large time-delays is the Smith Predictor. It overcomes the debilitating problems of delayed feedback by using predicted future states of the output for control. Currently, some commercial controllers have Smith Predictors as programmable blocks. There are, however, many other model-based control strategies have dead-time compensation properties. If there is no time-delay, these algorithms usually collapse to the PID form. Predictive controllers can also be embedded within an adaptive framework.
Most processes require the monitoring of more than one variable. Controller-loop interaction exists such that the action of one controller affects other loops in a multi-loop system. Depending upon the inter-relationship of the process variables, tuning each loop for maximum performance may result in system instability when operating in a closed-loop mode. Loops that have Single Input Single Output (SISO) controllers may therefore not be suitable for these types of applications. These types of controllers are not designed to handle the effects of loop interactions.
A multivariable controller, whether Multiple Input Single Output (MISO) or Multiple Input Multiple Output (MIMO) is used for systems that have these types of interactions. A model-based controller can be modified to accommodate multivariable systems. Loop interactions are considered as feed-forward disturbances and are included in the model description. Following SISO designs, multivariable controllers that can provide time-delay compensation and handle process constraints can also be developed with relative ease. By incorporating suitable numerical procedures to build the model on-line, adaptive multivariable control strategies result.
Model-Based Predictive Control
Model-Based Predictive Control technology utilizes a mathematical model representation of the process. The algorithm evaluates multiple process inputs, predicts the direction of the desired control variable, and manipulates the output to minimize the difference between target and actual variables. Strategies can be implemented in which multiple control variables can be manipulated and the dynamics of the models are changed in real time.
Dynamic Matrix Control
Dynamic Matrix Control (DMC) is also a popular model-based control algorithm. A process model is stored in a matrix of step or impulse response coefficients. This model is used in parallel with the on-line process in order to predict future output values based on the past inputs and current measurements.
Statistical Process Control
Statistical Process Control (SPC) provides the ability to determine if a process is stable over time, or, conversely, if it is likely that the process has been influenced by "special causes" which disrupt the process. Statistical Control Charts are used to provide an operational definition of a "special cause" for a given process, using process data.
SPC has been traditionally achieved by successive plotting and comparing a statistical measure of the variable with some user defined control limits. If the plotted statistic exceeds these limits, the process is considered to be out of statistical control. Corrective action is then applied in the form of identification, elimination or compensation for the assignable causes of variation.
"On-line SPC" is the integration of automatic feedback control and SPC techniques. Statistical models are used not only to define control limits, but also to develop control laws that suggest the degree of manipulation to maintain the process under statistical control. This technique is designed specifically for continuous systems. Manipulations are made only when necessary, as indicated by detecting violation of control limits. As a result, savings in the use of raw materials and utilities can be achieved using on-line SPC