ABSTRACT
High-fidelity mathematical modeling, heterogeneous simulation, data-intensive analysis, robust control, and optimization have become important problems that need to be solved for MEMS and NEMS. This chapter evaluates MEMS and NEMS dynamics in the behavioral domain, examining and optimizing the steady-state responses and dynamic transient dynamics. It covers analog and digital control of MEMS emphasizing the application of PID control, linear quadratic regulator, Hamilton-Jacobi, and other concepts for linear and nonlinear nano- and microscale systems. Different approaches can be used to simulate MEMS in the MATLAB environment. The application of SIMULINK is illustrated. The chapter reports different methods to design control algorithms minimizing performance functionals, which depend on the system variables. Sliding mode control has direct analogies to the time-optimal control. In microsystems, digital ICs can be utilized to implement control algorithms making use of the sensor data. The chapter also covers the constrained optimization problem for multivariable discrete-time MEMS and NEMS.
