Fixed structure LQ design with applications

Abstract: This thesis deals mainly with the problem of designing structure constrained controllers (or fixed structure control design) which is a problem that occurs in many industrial control applications. In process industry for example, almost all control loops are closed with commercial PI controllers (which have specified structures). There are also other areas, such as automotive, aerospace and space applications where complexity (structure) of the controller must be constrained, often to a minimum. The thesis consist of an introduction and five papers, the first paper deals with sampled-data control for structure constrained LQ controllers. The proposed method produces a discrete controller that minimizes a continuous LQ criterion and thus take into account the intersample behaviour in the design. The measured output is sampled with an averaging sampler to circumvent the difficulties arising when sampling continuous white noise. The second paper deals with implementation issues of control. For certain badly formulated LQ problems it is actually possible that the optimal solution is fragile with respect to small perturbation of the controller coefficients. This means that if the solution is rounded off or otherwise when implemented it might happen that the performance become very poor. This paper presents a general procedure to overcome fragility in optimal design and furthermore applies this procedure on fixed structure LQ control design. The third paper deals with random delays in the feedback loop. This is a problem that probably will be more prominent in the future as communication networks become more and more frequent in feedback loops. It is also today a possible problem in time-sharing computers where several different control tasks (as well as other tasks) are run on the same computer. The presented method is suited for fixed structure control design, which thus makes it possible to design PI controllers that take into account randomly varying delays in the feedback. The fourth paper deals with an application where fixed structure LQ control is applied. The paper summarizes the first stage in an ongoing research project where active suppression of flutter on an aircraft wing is considered. The project is a collaboration between Saab Aerospace, Volvo Aero Corporation and Lule{\aa} university of technology. A small rigid wind tunnel model of an aircraft wing has been used as test object and the trailing edge flap of the wing has been used as a control surface. An LQG controller was developed for this system that stabilized the wing using only small flap movements. Several LQ controllers with low complexity was also designed using fixed structure LQ design. They had almost equal performance as the LQG controller. The results from the project indicates that it actually is possible to extend the flight envelope by exploiting an active suppression approach. The fifth paper deals with another application where fixed structure LQ design is used. In this paper it is shown that it is possible to utilize a fixed structure LQ sampled-data methodology to design discrete LQ optimized PI controllers which minimizes a continuous criterion. The methodology is applied on a simulation model of one the flotation processes found at Boliden's concentrator in Aitik. The simulation results show that this PI tuning technique can be used to enhance the closed-loop performance considerably. This theory can also be used as an alternative when the existing control architecture prevents implementation of multivariable controllers such as LQ or LQG controllers. The paper also discusses how it is possible to allow for online tuning demands in the proposed design technique.