Dynamic ‘back‐off’ analysis: use of piecewise linear approximations

Abstract

SUMMARYThe operating point of a process is usually computed by optimizing an objective function, e.g. the profit, subject to some plant characteristics. Typically, the resulting point lies on the boundary of the operating region. At this point, the presence of disturbances can easily cause constraint violations and make the process move to the unfeasible region. Then, it is necessary to move the operating point away into the feasible region by considering the effect that the expected disturbances will have on the operation of the plant. The purpose of this paper is to present an efficient algorithm to modify the operating point in order to keep feasibility (both in steady-state and along transitory) in the process operation against the disturbances.

On the tuning of predictive controllers: Impact of disturbances, constraints, and feedback structure

“…The impact of this soft constrained MPC formulation is that if c s is sufficiently large, then h s will be very close to zero, except for cases in which the original MPC would be infeasible. In those cases, the constraints of (40) are relaxed, by (46), to determine a "reasonable" response to the infeasible initial condition. By appropriate selection of the terms within c s , one can set priorities with regard to constraint relaxation.…”

“…[28][29][30][31][32][33][34][35][36][37][38][39][40][41] Operating point selection methods can also be divided into subcategories. Methods employing a constant-in-time uncertainty perspective [42][43][44][45][46][47][48] are akin to deterministic flexibility analysis. Those with a time-dependent uncertainty perspective [49][50][51][52][53][54][55] are related to the stochastic flexibility and chance constrained approaches.…”

Simultaneous BOP selection and controller design for the FCC process

“…During the design phase it is customary to develop an economic based profit function, which will guide the selection of equipment as well as the associated nominal operating conditions. Efforts aimed at developing back-off selection schemes, under the assumption of an a priori designed controller can be found in [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. Efforts considering the simultaneous back-off controller design problem can be found in [20][21][22][23][24][25].…”

On the Tuning of Predictive Controllers: The Minimum Back-Off Operating Point Selection Problem

“…In the context of Figures 4 and 5, we see constraints (4) describe the set of available BOPs within the constraint polytope, which also includes the steady-state operating line (constraint 3). Additionally, constraints (7) and ( 8) define the standard deviation ellipse around a candidate BOP. Finally, constraints (5) and (6) ensure that the ellipse does not extend beyond the constraint polytope.…”

“…As stated above, Narraway et al first advocated the notion of a BOP. This deterministic framework was then extended by Romagnoli et al, , Contreras-Dordelly and Marlin, and Figueroa et al , Stochastic versions of the problem were presented in refs −11. These define the EDOR based upon the covariance ellipsoid generated by a given confidence interval.…”