Optimization of fixed-order controllers using exact gradients

Abstract

Finding good controller settings that satisfy complex design criteria is not trivial. This is also the case for simple fixed-order controllers including the three parameter pid controller. To be rigorous, we formulate the design problem into an optimization problem. However, the algorithm may fail to converge to the optimal solution because of inaccuracies in the estimation of the gradients needed for this optimization. In this paper we derive exact gradients for the problem of optimizing performance (iae for input and output disturbances) with constraints on robustness (M s , M t ). Exact gradients, give increased accuracy and better convergence properties than numerical gradients, including forward finite differences. The approach may be easily extended to other control objectives and other fixed-order controllers, including Smith Predictor and pidf controllers.

A Novel Process-Reaction Curve Method for Tuning PID Controllers

“…A set of PO PID controllers is obtained for each process model example (Es1-12) using the exact gradient optimisation method in Grimholt and Skogestad (2016b).…”

PID Control With Higher Order Derivative Degrees for IPDT Plant Models

“…In the difference to the feedback linearization [47] which transforms a nonlinear plant to a chain of integrators with the plant nonlinearity transformed to its input, in the considered approach this nonlinearity is locally "frozen" to a constant signal. Thus, since it is possible to design fully reliable controllers by using few appropriately chosen integral plant models, a question arises, when we actually need all different modeling and the subsequent optimization approaches as treated, for example, in [3], [46], [55]- [57].…”

Structured controller design for closed‐loop D ‐stability in convex/non‐convex regions: Mixed integer‐linear programming approach

“…Hence, relations (23)- (26) are actually mixed real-binary inequalities. To sum up, for any cell of the mesh write one equation in binary decision variables of the cell as equation (14), and eight inequalities in binary decision variables of the cell and the nodes of that cell as given in relations (19)- (22), and for any node of the mesh write four mixed real-binary inequalities as given in relations (23)- (26). At the end, add the following equality in binary variables to the set of existing relations…”

“…Step 2: Assign two binary decision variables to every node and five binary decision variables to every cell of the mesh as shown in Figure 5 Step 3: For every cell of the mesh write one equation in binary decision variables of that cell as Equation (14), and eight inequalities in binary decision variables of that cell and its nodes as (19)-(22).…”