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Schnelle, David R. Operability-based determination of feasible control constraints for several high-dimensional nonsquare industrial processes. An overview on controllability analysis of chemical processes. Osvaldo J. Dynamic operability analysis of nonlinear process networks based on dissipativity. AIChE Journal , 55 4 , The steady-state region of attraction under linear feedback control: A numerical approach.

Journal of Process Control , 19 3 , Rojas, Peter Lee. Pair your accounts. Your Mendeley pairing has expired. Please reconnect. This website uses cookies to improve your user experience. By continuing to use the site, you are accepting our use of cookies. Read the ACS privacy policy. Hugh Durrant-Whyt RA for contributions with application to decentralized data fusion algorithms with application to simultaneous localization and navigation. Kazuhiro Kosuge RA for contributions to multiple robots coordination and human-robot interface. Ioannis Kanellakopoulos for contributions to the theory and practice of adaptive nonlinear control.

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Analysis and control of nonlinear process systems

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Unlike the linear case where LQR always stabilizes the system, it is seen that the stability region does not cover the entire operating region. Indeed, a simulation run in Fig. Note that an LQ controllers is structurally the same as a linear pole placement controller i. Therefore, undesired stable steadystates may also appear depending on the LQ-design.

Local asymptotic linearization stabilization 6ia feedback A nonlinear technique, feedback linearization is investigated in order to change the system dynamics into a linear behavior. Then, different linear controllers can be employed on the feedback linearized system. Exact linearization 6ia state feedback In order to satisfy the conditions of exact linearization, first we have to find an artificial output function u x that is a solution of the PDE Isidori, The results for two different weighting matrix selections are investigated.

Simulations showed that it is hard to numerically evaluate the functions h and i and the partially closed loop system produced infeasible large input signals considering the constrains on substrate flow rate. The system can be exactly linearized theoretically, but the feedback is hard to compute in practice. Moreover, in an engineering sense it is not practically useful to linearize such an output function as i. The static nonlinear full state feedback for achieving this goal is calculated as Fig.

Note that the above equation are exactly the same as the Eq. Let us choose the simplest possible output function again i. As we will see the key point in designing such controllers is the selection of the output h function where the original nonlinear state Eq. Controlling the biomass concentration.

The time-derivative of the Lyapunov function is shown in Fig. The state-space model of the system in the new coordinates is 3. Controlling the substrate concentration. The exactly linearized model may seem simple put if we have a look at the new coordinates we can se that they are quite complicated functions of x depending on both state variables.

The time derivative of the Lyapunov function of the closed loop system as a function of X and S is shown in Fig. Note that for this case it was proven see the zero dynamics analysis that the closed loop system is globally stable except for the singular points where the biomass concentration is zero.

Controlling the linear combination of the biomass and the substrate concentrations. The time derivative of the Lyapunov function of the closed loop system is shown in Fig. Note that in this case q1 and q2 are design parameters. E6aluation and comparison of the controllers The evaluation and comparison of the controllers is performed using the evaluation criteria introduced in the beginning of this section. The results are summarized as follows: Fig. Stability region Stability region has been investigated using the quadratic Lyapunov function.

Conclusion Different types of nonlinear controllers are designed and compared for a simple continuous bioreactor operating near optimal productivity. This operating point is close to a fold bifurcation point in this paper. A relatively simple cultivation model with constant volume and physico-chemical properties and with a substrate inhibited biomass growth rate expression is used to form an input-affine nonlinear state space model. Nonlinear analysis of stability, controllability and zero dynamics provides information not only in the vicinity of the desired operating point but also within the whole operating region.

Analysis of the zero dynamics shows that the best choice of output to be controlled generally narrows the stability region for the investigated model. Nonlinear stability analysis based on the Lynapunov technique is used to obtain a crude estimate of the stability region for the controllers. A wide range of controllers are tested including pole placement and LQ controllers, feedback and input — output linearizing controllers and a direct nonlinear passivation controller. Controllers using partial state feedback of substrate concentration and not directly depending on the reaction rate are recommended for the relatively simple bioreactor investigated.

Such controllers have a wide and predictable operating region and use the measurable state variable only. Passivity based controllers have been found to be globally stable, rather insensitive to uncertainties in the reaction rate, however they require full nonlinear state feedback. Acknowledgements This research is partially supported by the Hungarian Research Fund through grant No.

T which is gratefully acknowledged. References Boskovic, J. Comparison of linear, nonlinear and neural-network-based adaptive controllers for a class of fed-batch fermentation processes. Automatica, 31, — Isidori, A. Nonlinear Control Systems. Berlin: Springer. Johnson, A. The control of fed-batch fermentation processes —a survey. Automatica, 23, — Kuhlmann, C. On the controllability of continuous fermentation processes.

Bioprocess Engineering, 19, 53 — Kuhlmann, Ch. Robust operation of fed batch fermenters. Bioprocesses Engineering, 19, 53 — Seborg, D.