Model-Based Feedback Control: Effect Of Constraints On Controller Structure In Three Case Studies



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In the first section, focus is an instance of the problem, in which the steady-state gain sign may change as a result of large unmeasured external disturbances entering a process with input multiplicities. The conventional approach to design a linear controller for a nonlinear system recommends that the controller must be tuned sluggishly. However, such a recommendation resulted in the instability of closed loop. To explain and anticipate closed-loop behavior a theoretical analysis based on nonlinear operator theory is used to provide controller design guidelines. Moreover, it has been demonstrated that linear control can be effective for a wide range of operating conditions, if designed correctly. Numerical simulations using a dynamic model calibrated on plant (industrial NOx reduction unit) data are used to illustrate the proposed controller design approach. The second section proposes a novel, simple and effective scheme to debottleneck level control in a system of three tanks in series. Level control often involves two conflicting issues, rejection of disturbance and the minimization of outlet flow variations. Normally, the level controller is intentionally designed to response sluggishly to reduce flow oscillations in downstream. However, constraints in level variations restrict sluggish tuning of level controller. The proposed scheme translates system of tanks in seris; from multiple, single input single output into a single system of multiple inputs multiple outputs. Feedback controls based on a linear PI controller, are used and generalized tuning charts are prepared. Further, the performance of the proposed control structure is compared to the control structures derived from numerical optimization. In the last section, the model predictive control concept has been proposed to design an optimal central bank interest rate. The optimization problem which relies on dynamic programming technique can only produce numbers but cannot provide interest rate rules. A multiparametric model predictive control framework is employed to derive rules for central bank interest rates bounded by zero. It has been found that rules are actually piecewise linear, finite in number and follow the celebrated Taylor-rule forms (Taylor 1993). Rules with or without inertia are included in the derivation. The proposed approach is illustrated through simulations on US economy data.



Nonlinear systems, Steady-state gain sign, Input multiplicity, Optimal control structure, Tanks in series, Constrained optimization, Taylor rule, Zero lower bound, Liquidity trap, Model predictive control, Multi-parametric programming