Quantitative-fuzzy Controller Design for Multivariable Systems with Uncertainty

This work serves as a pioneer contribution in terms of application of Quantitative Feedback Theory (QFT) methodology and fuzzy logic method to design a controller for MIMO systems. Due to the presence of uncertainty in multivariable dynamic systems, the application of robust control methods for achieving high accuracy in tracking is inevitable. On the other hand, application of QFT to MIMO uncertain systems still remains to be one of the most difficult control problems for engineers. In this paper, authors attempt to simplify the MIMO control problem by proposing a new algorithm which joins QFT and fuzzy techniques. In order to illustrate the utility of the proposed algorithm, its application on a two degree of freedom link robot manipulator is depicted. Initially, a QFT controller is designed for each link to overcome the track and disturbance rejection problems. Then, a bi-level tuned PD-fuzzy controller is employed as one strategy for curbing probable errors in the previous controller. The controller design was carried in the following stages; first, a linear PD controller independently applied to each actuator. Then, fuzzy rules were developed to design a fuzzy PD controller. Fuzzy controller normalizing parameters were regulated according to maximum PD control errors. In the second stage, named nonlinear tuning, other parameters of the fuzzy controller were tuned using genetic algorithms. Finally, nonlinear simulations of arbitrary path tracking shows that the proposed controller has a consistent tracking ability, and also it can clearly be seen that the mentioned approach is precise and very simple in comparison to other MIMO control techniques.