Finite time sliding mode control for piezoelectric actuators / Ahmed Abood Faraq Al-Hadad - Amed Abood Faraq, Al-Haddad (2018)
The piezoelectric actuator (PEA) is a device which performs very small displacements within the range of less than or equal to 100 μm. However, the PEAs suffer from the inherent non-linearity because of the hysteresis, creep and vibrations effects. These effects may cause a displacement error as high as 15% of the total range. This high error shows the necessity of a controller. Due to Sliding Mode Control (SMC) simple design steps, high robustness and low sensitivity to disturbances, it has been implemented to overcome and minimize the error. This research project has successfully accomplished the following three objectives. The first is to overcome the robustness and accuracy issue by applying the SMC method which is robust and accurate, using the mathematical model of the PEA which includes all the uncertainties and disturbances. The second is to apply the Terminal Sliding Mode Control (TSMC) concept to overcome the global infinite time stability to reach convergence or zero error in finite time. The third is to reach chattering free non-singular system. Chattering and singularity phenomena reduce the service lifetime of the PEA and create unwanted noise in the control input single. To reduce the chattering, sigmoid (sig) function has been used in the sliding function. This method is called continues terminal sliding mode. To overcome the singularity problem, the sliding function and the derivative of the sliding function does not result in terms with negative (fractional) powers which mean there will be no singularity. The chattering free nonsingular finite time system has been proved mathematically and in the simulation.