Best achievable low order decentralized performance

Abstract

The fixed order decentralized performance problem is formulated as a quadratically constrained control problem in terms of a stable map and the degrees of freedom of the controller. This problem is of the same type as the decentralized and/or simultaneous performance problems that have been discussed in our earlier work, thus the same truncation-based solution procedure can be employed. The proposed approach is demonstrated through an example where the optimal parameter setting for decentralized P and PI control are identified.

A Class of Optimal Decentralized Controllers for Open Loop Stable Processes

“…Solving problem 1 subject to (6) is very hard due to the non convex nature of the constraints that (2) imposes on Q(z) (Sourlas and Manousiousthakis, 1995), (Goodwin et al, 1999), (Yuz and Goodwin, 2003). In (Sourlas and Manousiousthakis, 1995) an approximate solution to the related l 1 version of problem 1 is derived.…”

“…In (Sourlas and Manousiousthakis, 1995) an approximate solution to the related l 1 version of problem 1 is derived. However, no closed form of the optimal Youla parameter or controller is given.…”

“…Those advantages originate in their simplicity, their connection with classical single-input single-output control and in implementation and tuning issues (Conley, 2000), (Yuz and Goodwin, 2003). Nevertheless, that approach to control system design poses several fundamental questions (Sourlas and Manousiousthakis, 1995), (Goodwin et al, 1999), (Salgado and Conley, 2004). Among those questions are, firstly, how to select those measurements that will be used to generate every plant input, i.e., how to pair inputs and outputs, and secondly, once the pairing has been decided, how to synthesize, if possible, a stabilizing controller.…”

“…This approach is highly complex due to the non-convex nature of the associated optimization problem, as noted in (Sourlas and Manousiousthakis, 1995). In spite of the mentioned difficulties, in (Sourlas and Manousiousthakis, 1995) an approximation approach to solve the l 1 discrete time optimal control problem in the linear time invariant case is used. Due to the numerical nature of this solution, no closed form of the controller is given.…”

“…In (Sourlas and Manousiousthakis, 1995) the parameterization introduced in (Manousiousthakis, 1993) is used to state the decentralized model matching problem. This approach is highly complex due to the non-convex nature of the associated optimization problem, as noted in (Sourlas and Manousiousthakis, 1995).…”