Control of Z-Axis MEMS Gyroscope Using Adaptive Fractional Order Dynamic Sliding Mode Approach

Abstract

This paper proposes a states feedback control method for Z-axis MEMS gyroscopes using fractional calculus and adaptive dynamic sliding mode control method. A new sliding mode control method is proposed to achieve trajectory tracking by adding a fractional order term in the conventional sliding manifold. The new proposed sliding surface contains integer order terms as well as fractional order terms and thus can provide an extra degree of freedom. Besides, in the presence of unknown system parameters, some adaptive laws containing the new designed sliding manifold are proposed to online tune controller parameters. All adaptive laws are derived in the stability framework and the stability of the control system is also guaranteed according to the Lyapunov stability theory and. Simulations results on a Z-axis vibrating gyroscope are provided to illustrate the effectiveness of the control method.INDEX TERMS Adaptive control, dynamic sliding mode control, gyroscope, fractional order calculus.

MLP-Based Neural Guaranteed Performance Control for MEMS Gyroscope With Logarithmic Quantizer

“…Focusing on raising the measuring accuracy of MEMS gyroscope, tremendous advanced control schemes have been proposed, such as sliding-mode control [4]- [6], fuzzy logic control [5], [7], robust and adaptive control [7], [8], as well as neural networks (NNs) [6], [9]. As an example, in [7], the backstepping control, where the controller design contains several steps and, in each step, the virtual control law is recursively designed such that the ultimately uniformly bounded (UUB) properties of MEMS gyroscope can be achieved.…”

“…In [8], to deal with the issue of term explosion arising from multiple differentiating, the dynamic surface control (DSC) is explored, where a first-order low-pass filter is applied to approximate the time derivative of virtual control signal and meanwhile, NNs are employed to online identify the unknown dynamics by virtue of their universal approximation, such that, the robustness against uncertainties of MEMS gyroscope is greatly improved. Despite the fact that available works [4]- [9] for MEMS gyroscope are of great superiority, it is worth pointing out that almost all of them are subject to the following two serious problems. One is concerned with bandwidth restriction of actuator, i.e., the existing results for MEMS gyroscope are almost achieved under the unpractical assumption that the actuator of MEMS gyroscope can perform with arbitrarily high precision and the capacity of communication channel from control module to actuator is large enough to transmit continuous signal with infinite accuracy, which is in contradiction with the physical truth of MEMS gyroscope.…”

“…Logarithmic quantizer (LQ) [10], [11], one of the most employed quantizers in digital communication systems, can largely reduce the communication data size and meanwhile, it is capable of generating quantized signals with constant quantization signal-to-noise ratio (SNR) owing to its exponentially transformed quantization levels compared with uniform quantizer (UQ) [12], such that the robustness of system will not change along with the variation of control signal magnitude. Nevertheless, the introduction of input quantization typically induces unexpected quantization error, which will inevitably influence the tracking accuracy of MEMS gyroscope, while to the best of authors' knowledge, how to make a compromise between the tracking performance and bandwidth restriction is rarely studied in existing results [4]- [9]. Thus, it is an urgent and tough issue to eliminate the influence of quantization error and guarantee high-accuracy tracking performance for MEMS gyroscope in the existence of quantized input.…”

Optimal Second Order Integral Sliding Mode Based Composite Nonlinear Feedback Approach for an Electrostatic Micromirror

“…However, the system disturbances are inevitable which intensively interfere with the system stability and transient performance. Among the exiting control techniques, sliding mode control (SMC) is an efficient robust control approach [14] which is widely used in many field such as spacecraft [15], linear motor [16] and MEMS gyroscope [17].…”

Efficient Fractional Order Reference Model of Adaptive Controller Design for Multi-input Multi-output Thermal System

“…For example, the model-free adaptive fractional-order control was proposed for illustrating the online tuning technique suitable for linear time-varying systems [18]. The adaptive fractional-order sliding mode control was applied to a micro gyroscope for achieving trajectory tracking control [19], [20]. The adaptive fractional-order combined with sliding mode control and super twisting sliding mode control was implemented in motor speed control for increasing speed tracking precision and robustness to process uncertainties [21]- [22].…”