A consensus PID (CPID) control algorithm for vibration control of piezoelectric smart structures

By combining the idea of PID control and the consensus control algorithm, a new consensus-PID (CPID) control algorithm was proposed, which was used for vibration control of piezoelectric smart structures. In this new approach, the inputs of PID controllers were the system output errors. The outputs of PID controllers and their variations in the sampling period were treated as the inputs of the consensus controller. The input voltages of each actuator were the outputs of the consensus controller. The vibration control equations of piezoelectric smart structures were derived from the finite element dynamic equations of a linear elastic piezoelectric smart structure. The CPID control algorithm was numerically investigated for the smart structure, i.e., a piezoelectric smart beam that was simply supported at its both sides. The finite element model of a piezoelectric smart beam for vibration control was established by ANSYS. Numerical results demonstrate that the CPID control law can successfully control the vibration of the piezoelectric smart structure. Comparing with the centralized PID control algorithm, the new CPID control approach can maintain higher performance for vibration control in the system of piezoelectric smart structures, even though some sensors fail.