(40g) Data-Based Sequential Design of Decentralized PID Controllers

Kumar, A. - Presenter, National University of Singapore

The contemporary process industries need to adhere to stringent product specifications and environmental regulations, thus making high control performance more important than ever. With incessant technological advancements, the processes have become more complex and hence difficult to model, which is essential to the conventional model-based design methods. On the other hand, the availability of a plethora of process data has recently led to the development of data-based controller design methods, wherein controller design is carried out without resorting to a process model. One such method is the Virtual-Reference-Feedback-Tuning (VRFT) method, which uses a desired reference model to formulate an optimization problem based on process input-output data (Campi et al., 2002). The key idea is to achieve a pre-specified closed-loop response via the design of a desired reference model, which is incorporated in the aforementioned optimization problem, and its optimal solution determines the controller's parameters.

Though the VRFT design method has been studied extensively, the existing design methods have been predominantly developed for single-input and single-output (SISO) control systems. However, most industrial chemical processes deal with multiple controlled and manipulated variables referred to as multi-input and multi-output (MIMO) system. In this work, decentralized PID controllers are considered as they are commonly used in process industries. For a decentralized control system, process interaction is inherent and causes difficulties for feedback controller design. As a result, the achievable control performance of a decentralized control system is inevitably degraded or even becomes unstable.

Despite few results being available for decentralized controller design under the VRFT design framework, there have been some notable attempts on the subject nonetheless (Nakamoto, 2004; Campestrini et al., 2016; Da Silva et al., 2016). However, these methods are independent design methods, which can design decentralized controllers in a straightforward manner at the cost of being a conservative design approach. In this work, a design alternative termed sequential design method is adopted as it innately takes into account the process interactions and can utilize the information about the controller designed in the previous step. This gives sequential design the advantage of being less conservative than independent design methods.

Owing to the aforementioned reasons, a sequential design procedure in the z-domain has been employed in this work under the VRFT design framework. The rudimentary mechanism is to treat multiple control loops as a sequence of single loops. For instance, a 2x2-control system can be tuned via the following steps:

  • Tune one of the loops based on open loop data
  • Using the controller parameters obtained in step 1, close the first loop and tune the second loop with the second loop open
  • Using the controller parameters obtained in step 2, close the second loop and tune the first loop with the first loop open
  • Repeat 2 and 3 till the controller parameters for both loops converge to a fixed value

Additionally, instead of the typically used first-order or critically damped reference model, a second-order reference model has been used in this work. In order to evaluate the performance of the proposed method, simulation results of controlling Wood and Berry distillation column (Vu and Lee, 2010) were used in a comparative study with benchmark methods including model-based Dahlin’s controller and existing VRFT reference models. The results show that the proposed method provides better or comparable performance to that of the benchmark decentralized controllers.


Campestrini, L., D. Eckhard, L. A. Chía and E. Boeira (2016). Unbiased MIMO VRFT with application to process control. Journal of Process Control 39(Supplement C): 35-49.

Campi, M. C., A. Lecchini and S. M. Savaresi (2002). Virtual reference feedback tuning: a direct method for the design of feedback controllers. Automatica 38(8): 1337-1346.

Da Silva, G. R. G., L. Campestrini and A. S. Bazanella (2016). Multivariable VRFT: an approach for systems with non-minimum phase transmission zeros. Control Applications (COCA), 2016 IEEE Conference on, IEEE. pp 1324-1329.

Nakamoto, M. (2004). An application of the virtual reference feedback tuning for an MIMO process. SICE 2004 Annual Conference. pp 2208-2213 vol. 2203.

Vu, T. N. L. and M. Lee (2010). Independent design of multi-loop PI/PID controllers for interacting multivariable processes. Journal of Process Control 20(8): 922-933.