Limited Coding-Length-Based Sliding Mode Control with Adaptive Quantizer's Parameter

In [1], an interesting issue was investigated on how an existing controller can still achieve the same control performance under the quantization case by designing the online adjusting strategy for the quantizer's parameter. However, the above work ignored the limitation of the coding length in the practical transmitting procedure such that the desirable performance may not be achieved due to the inevitable coding errors. Hence, this work will further consider the above issue under the limited coding length. Different coding rules are designed for the quantized states and the adaptive quantizer's parameters. The minimum bound of coding errors is explicitly given, which are dependent on the coding length and the coding range. Moreover, the relation between the coding length and the control performance is established, that is, the coding length has a direct effect on the convergent upper bound of the system state and the sliding domain around the specified sliding surface. Finally, an operational amplifier circuit system is provided to verify the proposed method.