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Linear oscillatory machines are becoming more widely used in refrigeration compressors due to advantages of compact volume, little maintenance, and so on. In order to further increase the efficiency and reduce the cost of the whole system, both resonant frequency tracking control and sensorless control strategies should be implemented simultaneously. In this article, an adaptive full-order observer with simple structure and less computation is proposed, which can not only provide accurate displacement estimation signals for the system piston stroke control, but also achieve resonant frequency tracking control through the estimation of machine parameters. The system stability analysis proves the quick convergence of the proposed observer, and comprehensive simulation and experimental results demonstrate the effectiveness of the proposed algorithm.

In order to solve the constrained-input problem and reduce the computing resources, a novel event-triggered optimal control method is proposed for a class of discrete-time nonlinear systems. In the proposed method, the event-triggered control policy is applied to the globalized dual heuristic dynamic programming (GDHP) algorithm. Compared with the traditional adaptive dynamic programming (ADP) control, the event-triggered GDHP control can reduce the computation while ensuring the system performance. In this paper, a non-quadratic function is given to code the control constraints and the trigger condition with the stability analysis is provided. Neural networks (NN) are constructed in the GDHP structure, where the model network is designed to identify the unknown nonlinear system, the critic network is used to learn the cost function and its partial derivative, and the action network is designed to obtain the approximate optimal control law. Three simulation examples are presented to demonstrate the performance of the proposed event-triggered design for constrained discrete-time nonlinear systems.

For the linear compressor system driven by linear oscillatory machine (LOM), the piston stroke signal is very important to realize the efficient control of the motor. Since it is difficult to install a position sensor in the LOM, and the position sensor will increase the difficulty of system control, it is necessary to use an accurate and efficient position sensor-less method to estimate the piston stroke signal. In this paper, a novel position sensor-less piston stroke estimation method based on sliding-mode observer (SMO) is proposed. Besides, a self-adaptive band-pass filter (SABPF) is designed to filter the estimated piston stroke signal, which not only overcomes the pure integration problem, but also solves the chattering problem of SMO. Simulation results show that the proposed SMO has a good performance in estimation accuracy, and the chattering problem is well solved.