Dimensional transformation: A novel method for gain-scheduling and robust control

This thesis focuses on developing a technique of dimensional transformation to solve advanced controller design problems, specifically gain-scheduling and robust control methods. The developed technique reformulates the system representation in preferential dimensionless form that is more tenable for gain scheduling and robust control designs. The current work shows that the dimensionless formulation gives advantage in terms of reducing complexity and conservativeness of the control synthesis as compared to the dimensional form.; The complexity of a gain scheduling control design increases exponentially with the number of scheduling parameters. This thesis presents a method called dimensional transformation that reduces the number of scheduling parameters by reformulating the dynamic representation in dimensionless form. The choice of dimensionless description is usually preferred because any transformation to dimensionless representation is guaranteed to reduce variable dependence: the number of dimensionless parameters is always less than or equal to that of the classical representation (a result of the classic Pi-theorem). However, dimensional transformations are not unique. Some transformations---while reducing the total number of system parameters, scheduled or unscheduled---may have a negative effect on a gain-scheduling control algorithm because they may inadvertently increase the number of scheduling parameters. This work explores in detail conditions necessary such that dimensional transformation are guaranteed to present the minimum number of gain scheduling parameters for a control system design.; The same principle of dimensional transformation is explored as a method to reduce the size of parametric uncertainty block in robust controller synthesis. This simplification is performed using the dimensional transformation by appropriate matrices followed by LFT reformulation in the dimensionless domain. This reduces the conservativeness of the robust control synthesis. For example, in the mu-synthesis framework, if the uncertainty block size is greater than three, then only the upper bound can be computed, and this upper bound can be arbitrarily larger than the actual structured singular value resulting in a more conservative controller synthesis. Through the method of dimensional transformation, the size of a given uncertainty block can be reduced by up to three or more dimensions. Depending on the problem, this might allow for current techniques of robust control synthesis to be extended into significant new problems.; This thesis also discusses methods for a robust simultaneous control technique for systems whose system parameters are inherently coupled. The current work shows the potential of the proposed method for designing a unified robust controller that can be implemented through parametric adaptation. The goal is to obtain a robust, adaptive and modular controller for a group of systems. When considering collective group of systems, passenger vehicles for example, coupling is present due to optimization inherent in vehicles and engineering and natural systems. When such general coupling exists, the systems as a group can be represented in a more dense collection that gives advantage for robust controller synthesis. This approach is tested using a problem focusing on the lateral control of a scaled-vehicle-system on a rolling-roadway simulator.