Response Surface Tuning Methods in Dynamic Matrix Control of a Pressure Tank Systems

Aiping Jiang and Arthur Jutan

Ind. Eng. Chem. Res. 39 (2000) 3835-3843

The article used response surface methodology as a novel approach to select control parameters for dynamic matrix control (DMC) that implemented on a nonlinear, multivariable, experimental pressure tank. These control parameters are difficult to chose and no universal guidelines can be used to select these control parameters for different processes. Response surface methodology provides a more systematic approach to tune and helps ensure that the tuned parameters lie within an optimum range.

The ISE (integral of the square error) for tank pressure and flow rate was selected as response variable to characterize dynamic matrix controller performance.

Where e_p and e_f represent the errors of tank pressure and flow rate, respectively, and t_f is the final time of the experiment.

A k = 2 central composite design was used to estimate a second order model with ISE as response and based on the second model the optimum set point is m = 2 and f = 5.639. Then, the author noted that several experimental runs were made around the m = 2 and f = 5.639 point and found that m = 2 and f = 5 is a good choice for the optimum point.

From statistical experiment point of view, there are a number of flaws in the author's approach to find the optimum tuning parameters. First, the 16-run experiment was carried out with 4 center point runs, 4 axial runs and 8 factorial runs with 2 replicates in each factorial treatment combinations. This is not an orthogonal central composite design as claimed by the author because the correlation between x₁² and x₂² is 0.1429. An orthogonal central composite design for k = 2 should have 4 axial runs, 4 factorial runs with 8 center point runs. Also, a proper follow-up experiment should be conducted to find the true optimum. However, the final conclusion was based on several arbitrary experimental runs that made around the m = 2 and f = 5.639 point.

Yeak-Chong Wong

November, 2000