Quantitative feedback design for control systems with large plant uncertainty

A new robust control design framework, quantitative feedback design (QFD) method, is developed to consider large plant uncertainties and desired quantitative performance specifications simultaneously. For SISO uncertain control systems, a new single loop sensitivity-based QFD scheme is generated to provide a more systematic way for designing robust controllers to meet predefined quantitative specifications. By loop shaping techniques, the optimal solution can be obtained (if possible) in the QFD-design scheme. Such a single loop QFD-design method has been successfully applied to design a robust compensation for controlling the back angle of C135 aircraft and to robustly suppress undesired chaotic vibration of a nonlinear fluid-elastic system with large parameter variations. For MIMO uncertain control systems, based on non-negative matrix theory, an effective almost decoupling mechanism using an internal model reference loop (IMRL) concept is developed. One unique feature of such an IMRL almost decoupling mechanism is that not only can the achievement of sufficiently generalized diagonal dominance be assured, but also the reduction of the uncertainty in the resultant inner loop system is obtained. Hence, the IMRL almost decoupling mechanism makes it easy to proceed with the design of decentralized controllers for the resultant inner loop system. Combining the IMRL almost decoupling mechanism and the single loop QFD-design method, a new robust decentralized control design framework--model reference quantitative feedback design (MRQFD) method is proposed for MIMO uncertain control systems to meet quantitatively defined stability and performance specifications. The MRQFD design method is much simpler to work with than the existing quantitative decentralized control design techniques. The design procedure can be carried out in the direct or the inverse plant domains as in the Rosenbrock Nyquist array. Robust polynomial assignment may be used as an intermediate design step if necessary. A complete sensitivity analysis is provided. Two multivariable uncertain examples are presented to demonstrate the effectiveness of the proposed design methodology. The MRQFD method has been also successfully applied to design robust decentralized controllers for the Allison PD-514 turbofan engine covering totally six operating points without gain scheduling.