H∞ Fuzzy PID Control under Try-Once-Discard Protocol

Abstract

In this paper, the robust $H_{\\infty }$ fuzzy proportional-integral-derivative (FPID) control problem is investigated for discrete-time fuzzy systems subject to the Try-Once-Discard (TOD) protocol scheduling effects. A shared and constrained communication network is employed between sensors and controllers for data transmitting. In consideration of the limited bandwidth in real practice, requiring that only one sensor node is allowed to access the network at each time instant, the TOD protocol is employed to arrange the order of each node gaining the access to the shared network. Based on the prescribed performance requirements, a novel FPID controller is developed where the integral-loop is generated by utilizing the past measurements with the limited and fixed length to improve the computational efficiency. Sufficient conditions are obtained to guarantee the stability as well as the prescribed $H_{\\infty }$ performance. Furthermore, the desired controller gains are derived directly by solving a set of linear matrix inequalities. Finally, the correctness and effectiveness of the results are demonstrated by a simulation example.