(520d) Model Maintenance for Industrial Process Control

Model-based control is widely used in chemical processes. Model fidelity is the key factor influencing the performance of these controllers. Usually, these process models are identified using open-loop step tests during the initial, commisioning phase of the control system. However, with the passage of time, mismatches develop between the process and its model. These could be caused, for example, by physical changes in the process and changes in the operating conditions. In general, this model-plant mismatch increases with time and leads to a degradation in the closed loop performance. In order to restore satisfactory performance, it might be necessary to repeat the identification exercise and retune the controller using the new model.

The disadvantage of using traditional open-loop step tests for this purpose is that they are time-consuming, affect the productivity and are prohibitively expensive. Closed loop identification provides an attractive alternative for re-identifying the models. It uses data collected when the process is under closed-loop control, i.e., the controller is regulating the process. One of the main advantages of using closed-loop identification is that the controller attempts to preserve the system performance to some extent, while ensuring that constraints are not violated. Additional advantages include disturbance reduction, safe operation and better control-relevant models. The price to pay is in terms of the inherent reduction in the excitation, which could lead to poor signal-to-noise ratios. In addition, there can be a significant correlation between the manipulated variables and disturbances affecting the system, and this could introduce a bias in the estimates. Nevertheless, in view of its advantages, closed-loop identification is receiving more attention from process engineers and is being considered as an alternative which can be used for restoring controller performance when significant model-plant mismatch occurs.

Among recent developments related to industrial applications, Zhu (1999) extended the asymptotic theory of Forssell and Ljung (1998) and developed practical guidelines for input signal design. In this approach, a high order ARX model was identified to capture the deterministic and stochastic effects. This was followed by a filtering-based, model reduction technique to obtain a low order, high fidelity approximation of the deterministic dynamics. Vuthandam and Nikoloau (1997) proposed an MPC relevant identification methodology, which explicitly incorporated the input excitation requirements in the objective function of the MPC. However, the bias introduced due to the correlation between disturbances and manipulated inputs has not been completely addressed in these papers.

In this paper, we study the direct identification method and the indirect, two-step method, for closed-loop identification, focussing on the issues of signal-to-noise ratio (SNR), disturbance input correlation, and order reduction in the presence of noise. We propose a modification of the conventional SNR definition so that it reflects both input as well as output variability, and seek to maximize this index. We study the issue of input signal design with the objective of introducing variability in the closed loop data. We approach this problem as a trade-off, between balancing operating goals and introducing enough excitation to facilitate model identification. To minimize bias in the identified model which is caused by noise-input correlation, we analyze the applicability of the projection method (Forsell and Ljung, 1999) in the MPC scenario. Forsell and Ljung (1999) proposed a modified, two-step method for closed loop identification, wherein a non-causal structure for the sensitivity is used. We show that such a non-causal structure can be theoretically realized in an MPC framework, and can provide the benefit of minimizing the bias. In addition, we propose and discuss an alternate method of breaking the noise-input correlation by exploiting the nature of the MPC regulator. A few MPC regulators classify outputs to be restrained within zones/ ranges instead of trying to regulate them at desired values. We propose the use of a dynamic, active constraint set based strategy in the MPC optimization problem, which can be coupled with the above rangecontrol formulation. This yields a time-varying controller, which minimizes the input-noise correlation while accommodating some of the closed loop objectives, and results in better quality models.

We analyze these algorithms by applying them on a simulation case-study, the benchmark Shell Control Problem (Prett and Morari, 1987) and on a laboratory-scale quadruple tank experimental set up (Johansson, 2000). We will present results from these case-studies which demonstrate the practicality of closed-loop identification techniques for model maintenance in advanced process control.

References: 1. Prett and Morari, 1987. The Shell Process Control Workshop, Butterworth Publishers.

2. Johansson, 2000. The quadruple-tank process: A multivariable laboratory process with an adjustable zero, IEEE Trans. on Cont. Sys. Tech. , Vol 8, No. 3.

3. Ljung, 1999. System identification: Theory for user, Prentice Hall, NJ.

4. Vuthandam and Nikolaou, 1997. Constrained Model Predictive Control and Identification: A Weak Persistent Excitation Approach, AIChE J., 43, 9, pp 2279-2288.

5. Forsell and Ljung, 1999. Closed-loop identification revisited, Automatica, Vol 35, pp 1215-1241.