Nonlinear adaptive control with integral-PID adaptive law

This paper focuses on designing a novel adaptive control approach, where a proportional-integral-derivative (PID) control law and a integral-PID adaptive law are proposed. The design idea is first demonstrated by a first-order nonlinear system, and then extended to the high-order systems with Brunovsky canonical form (BCF). The stability of closed-loop system is analyzed by Lyapunov method. Compared with the conventional adaptive control approach, the proposed control approach possesses the better transient performance and the faster convergence speed by choosing suitable coefficients of PID terms.