(523b) Optimal Controlled Variables From Measured Plant Data

A common obstacle for applying modern state-of-the-art optimization methods in industrial processes is that they very often rely on a complicated process model. However, in many cases it is too expensive to develop accurate first principle models which are used for finding optimal operational strategies, and there is a need for developing simple ways to improve process operation without investing much effort to develop a model.

The method presented in this work is based on the idea of self-optimizing control [1], where a set of controlled variables c is selected from all the measurements y, such that controlling c at a constant setpoint results in near-optimal economic performance under varying operating conditions. Thus, there is no need to re-adjust the setpoints when disturbances affect the process.

For systematically finding self-optimizing controlled variables, generally two pieces of information are obtained by studying and optimizing a process model: 1) The process gain, i.e. how the measurement values change with varying input values, and 2) How the operational cost and the measurements change with varying inputs and varying unmeasured disturbances.

The new method proposed here, does not require a process model for finding the controlled variables. Instead, the method relies only on past operation data and a few plant experiments. In a first step, plant experiments are performed to find the steady state gain from the inputs to the measurements. The second step is to fit a quadratic cost function to historical process data. This is done by partial least squares regression [2] in order to be able to extract the most important directions and handle collinearity in the data. This second step provides information about how the cost changes with respect to unmeasured disturbances and input changes.

Using the quadratic cost function approximation together with the steady state gain, we construct a measurement combination matrix H, such that controlling c=Hy to zero leads to near optimal performance in spite of disturbances.

Before implementing the controlled variable in closed loop on the actual process, it may be used in open loop for testing purposes. Moreover, since the optimal value of c=Hy is zero, the magnitude of the elements in c=Hy may be used by process operators as an indicator of how well the process is operated.

[1] S. Skogestad "Plantwide control: the search for the self-optimizing control structure", J. Proc. Control, 10, 487-507 (2000).
[2] S. Wold, M. Sjöström and L. Eriksson "PLS-regression: a basic tool of chemometrics". Chemometrics and Intelligent Laboratory Systems 58 (2): 109–130. (2001).