This paper presents three observer/Kalman filter identification (OKID) approaches and develops a robust observer-based optimal linear quadratic digital tracker (LQDT) for the five-degree-of-freedom (five-DOF) sampled-data active magnetic bearing (AMB) system with various disturbances. The more detailed objectives are: (i) to construct both an equivalent linear time-invariant discrete-time model and its state estimator via the proposed OKID approaches for the AMB system, which might be an unknown nonlinear time-varying unstable system with both a specified rotation speed and a sampling rate; (ii) to provide an adaptive disturbance estimation scheme, which establishes an equivalent input disturbance (EID) estimator for the AMB system with unexpected disturbances; and (iii) to develop a robust observer-based optimal LQDT for the sampled-data AMB system with both a pre-specified time-varying speed and unexpected disturbances. The developed LQDT is able to recover the displacement of the rotor to the pre-specified trajectory position whenever it deviates from such trajectory.

The design of adaptive chattering‐free sliding mode controller (SMC) for chaotic systems with unknown input nonlinearities is studied in this paper. A smooth hyperbolic tangent function is utilized to replace the discontinuous sign function; therefore, the proposed adaptive SMC ensures that not only the chaos phenomenon can be suppressed effectively but also the chattering often appearing in the traditional discontinuous SMC with sign function is eliminated, even when the unknown input nonlinearity is present. A sufficient condition for stability of closed‐loop system is acquired by Lyapunov theory. The numerical simulation results are illustrated to verify the proposed adaptive sliding mode control method.

This paper presents a generalised optimal linear quadratic analog tracker (LQAT) with universal applications for the continuous-time (CT) systems. This includes: (1) a generalised optimal LQAT design for the system with the pre-specified trajectories of the output and the control input and additionally with both the input-to-output direct-feedthrough term and known/estimated system disturbances or extra input/output signals; (2) a new optimal filter-shaped proportional plus integral state-feedback LQAT design for non-square non-minimum phase CT systems to achieve a minimum phase-like tracking performance; (3) a new approach for computing the control zeros of the given non-square CT system; and (4) a one-learning-epoch input-constrained iterative learning LQAT design for the repetitive CT system.