A Comparative Study of Some Multivariable Pi Controller Tuning Methods

Tanttu, Juha T.; Lieslehto, J.

doi:10.1016/b978-0-08-040935-1.50062-4

Cited by 27 publications

(8 citation statements)

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“…For the proportional part of the controller, a suitable choice for the rough tuning gain is: assuming that Bd is invertible (Tanttu, 1987). A good choice for the integral part is the inverse of the steady-state gain matrix (Davison, 1976), that is, Finally, for the rough tuning matrix of the derivative part, the choice:…”

Section: Resultsmentioning

confidence: 99%

“…The method was modified by Penttinen and Koivo (1980), and adapted to Peltomaa and Koivo (1983). Tanttu (1987) applied the tuning procedure in a self-tuning controller.…”

Section: Controller Tuningmentioning

confidence: 99%

“…Here we follow the approach of Tanttu (1987). Consider an m-input/m-output process which can be described by the model:…”

Section: Controller Tuningmentioning

confidence: 99%

“…This procedure results in a bilinear model, which is fitted to the linear models at the respective operating points. The bilinear model captures the nonlinear behavior of the process satisfactorily in the operating range of interest.The control law used in the study is a simple robust tuning method for multivariable PID controllers that has been proposed in the literature (Davison, 1976;Penttinen and Koivo, 1980;Peltomaa and Koivo, 1983;Tanttu, 1987). Because the method is based on a linear process model, the controller parameters are updated at each sampling instant on the basis of a linearized form of the bilinear model.…”

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Multivariable nonlinear and adaptive control of a distillation column

et al. 1995

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In chemical process control, the processes typically exhibit nonlinear behavior. In spite of this, linear feedback laws often perform quite well as long as the process is being controlled at a fixed operating point. Linear controller designs based on linearized process models are therefore commonly used. The nonlinear process dynamics can be taken into account implicitly by treating them as part of the model uncertainties.If the nonlinearity of the process is too severe for a (single) linear control law to perform satisfactorily, one possibility is to describe the process by a set of different linear models, each valid at a given operating point. One can then derive a different linear feedback law for each operating point and use the feedback law corresponding to the prevailing operating point (Shamma and Athans, 1991). A potential difficulty with this approach is to decide which model and feedback law to use between the given set of operating points. Another possibility is to describe the process by a nonlinear model valid over the whole operating range of interest. The main difficulty with this approach is to find a suitable nonlinear model. Models derived from physical principles are in general much too complex for controller design, and therefore simpler models that capture the nonlinearities are required. If a nonlinear model is available, one can design a nonlinear controller based on this model for the whole operating range (Slotine and Li, 1991). However, it is also possible to use a linear controller whose parameters are updated at each sampling instant on the basis of a linearized form of the nonlinear model.For processes with poorly known or slowly time-varying dynamics, adfptive and self-tuning control are widely accepted approaches ( Astrom and Wittenmark, 1989). When applying adaptive control to nonlinear processes, care should be taken to handle the nonlinearities properly. Adaptive controllers are usually based on linear process models and linear design methods. Although adaptive controllers have the property of adapting their behavior to changing process properties, it is, however, somewhat unsatisfactory to not consider the fact that the process is nonlinear, and to let the adaptive controller retune itself (and the parameters of the linear model) whenever the operating point is changed. As above, possible remedies (including the same problems and difficulties) are to let the algorithm employ several linear process models, each valid at a given operating point, or a nonlinear process model valid over the whole operating range.In this article, multivariable nonlinear and adaptive control is applied to a binary distillation column (Waller et al., 1988). Previous investigations (Waller et al., 1988;Sandelin et al. 1991;Haggblom, 1993) have shown that the process has nonlinear dynamics. Although linear controllers can be used to control the process at any given operating point, it is difficult to control the process satisfactorily over the whole operating range of interest using a fixed linear co...

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Section: Resultsmentioning

confidence: 99%

“…The method was modified by Penttinen and Koivo (1980), and adapted to Peltomaa and Koivo (1983). Tanttu (1987) applied the tuning procedure in a self-tuning controller.…”

Section: Controller Tuningmentioning

confidence: 99%

“…Here we follow the approach of Tanttu (1987). Consider an m-input/m-output process which can be described by the model:…”

Section: Controller Tuningmentioning

confidence: 99%

mentioning

confidence: 99%

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Multivariable nonlinear and adaptive control of a distillation column

et al. 1995

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“…For example, Sarma and Chidambaram [7] proposed a centralised proportion integration (PI) controller design method by extending Davison's method [8], based on the pseudo‐inverse of the steady‐state gain matrix. It has a faster time response compared with that obtained by using the method proposed by Tantuu and Lieslehto [9]. Chen et al [10] came up with a static decoupling method based on the structure of internal model control (IMC), designing a Smith compensator of the non‐square systems.…”

Section: Introductionmentioning

confidence: 99%