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A broadband active self-tuning frequency piezoelectric energy harvester (AST-PEH) is proposed in this paper. It consists of a piezoelectric cantilever beam, an energy harvesting and control circuit (EHCC), a miniature stepper motor, a screw rod and a T-section mass. It can actively adjust the position of the T-section mass according to the ambient vibration frequency. It matches the AST-PEH's resonant frequency with the ambient vibration excitation frequency, and it widens the operating frequency range of the AST-PEH. The expression of the AST-PEH's resonant frequency function is constructed based on the dynamic and static theoretical analysis. The theoretical model of the AST-PEH under different position of the T-section mass is analyzed by ANSYS15.0 APDL, which is verified by two different materials and sizes. The tested two type substrate materials are steel and polylactic acid (PLA). The experimental results show that the frequency range of the two type harvesters are 4.8 Hz-6.3 Hz and 8.17 Hz-14.3 Hz respectively, and the widening rates of the working frequency are 31.25% and 75% respectively. The tested maximum output power of steel type AST-PEH is 0.32 mW at 6.3 Hz under 0.32 g acceleration and with a 100 KΩ load resistance.

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A nonlinear H,,, disturbance attenuation based solution of adaptive control for nonlinear systems with unknown (certain or uncertain) parameters is put forward. It is shown that the adaptive control law can be obtained by solving a reviced Hamilton-Jacobi-Isaacs inequlity (or equality) directly when an estimator can be obtained satisfying the presented conditons. Under some hyposises the asymptotical stability of the closed loop system can be guranteed when the estimate of the uncertain parameter convergences to the ture value or the stability when the estimate is bounded.