Model predictive control (MPC) has gained widespread acceptance in the chemical process industry, as well as in other industrial sectors (Qin and Badgwell, 2003). Key attributes are its ability to accommodate dead time and multivariable interactions directly, and its explicit constraint-handling capability. Commercial MPC systems are generally implemented in conjunction with a linear programming (LP) or quadratic programming (QP) optimizer that utilizes a linear, steady-state model to generate feasible set-points for the model predictive controller (Qin and Badgwell, 2003; Yousfi and Tournier, 1991; Sorensen and Cutler, 1998). The LP or QP may optimize an economic objective function directly, or minimize the deviation from set-point targets generated by a real-time optimization (RTO) system. In the latter application, the RTO system typically employs a more complex, nonlinear model, and the key function of the LP or QP layer is to make appropriate adjustments to the set-points in response to higher-frequency disturbances. However, despite the apparent success of LP-MPC cascade systems, poor performance characteristics have also been reported (Shah et al., 2002; Kozub, 2002). This includes high variability in the computed set-points (observed to exceed that of the corresponding controlled variables), and unexpectedly high fluctuations in the set of manipulated variables at constraints. This paper explores the effects of several factors on the performance of the overall LP-MPC cascade control system.

First, two methods for the LP model bias update were evaluated and compared in a variety of scenarios with different plant/model mismatch, constraints and LP objective function. Application to case studies indicated superior stability and performance properties for a bias update scheme that used the steady-state model directly, even with quite significant plant/model mismatch.

A multi-input, multi-output (MIMO) case study based on the Shell Standard Control Problem (Prett et al., 1990) demonstrated that the selected control structure may have a significant effect on the stability and control performance of an LP-MPC cascade control system. Chattering of the set-points was observed when an auxiliary output was constrained but not controlled. The set-points stabilized with an increased LP execution frequency, but poor dynamic performance was observed. Changing the control structure to include the auxiliary output as a controlled variable resulted in superior performance.

Finally, the effect of high frequency disturbances on the two-level control system behavior was investigated. Analysis, verified by simulation studies, showed that in MIMO systems, the LP may have an effect of amplifying the system noise through the bias term which is used for the model update. This is dependent on the model gains and active constraint set. Such amplification may result in high variation of the LP set-points provided to the MPC, thereby degrading the overall performance of the two-level system.

References

Sorensen, R. and C. Cutler (1998). LP integrates economics into dynamic matrix control. Hydrocarbon processing, 77(9), 57-65.

Kozub, D.J. (2002). Controller performance monitoring and diagnosis. Industrial perspective. In: 15th Triennial World Congress of the International Federation of Automatic Control. Barcelona, Spain.

Shah, S.L., R. Patwardhan, and B. Huang (2002). Multivariable controller performance analysis: Methods, applications and challenges. In: Chemical Process Control VI, AIChE Symposium Series, 98, 190-207.

Yousfi, C. and R. Tournier (1991). Steady state optimization inside model predictive control. In: Proc. ACC. Boston. 1866-1870.

Qin, S.J. and T.A. Badgwell (2003). A survey of industrial model predictive control technology. Control Engineering Practice 11, 733-764.

Prett, D.M., C.E. Garcia and B.L. Ramaker (1990). The Second Shell Process Control Workshop. Butterworths, Stoneham, MA.