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The purpose of this study is to provide a micromixer for achieving effective mixing of two liquids. The mixing of two liquids is difficult to achieve in microfluidic chips because they cannot form turbulence at small dimensions and velocities.

In this paper, four kinds of passive micromixers based on splitting–recombination and chaotic convection are compared. First, a better E-shape mixing unit based on the previous F-shape mixing unit has been designed. Then, the E-shape mixing units are further combined to form three micromixers (i.e. E-mixer, SESM and FESM).

Finally, the mixing experimental results show that the mixing indexes of E-mixer, SESM and FESM are more than those of F-mixer when the Reynolds number range is from 0.5 to 100. And at Re = 15, the lowest mixing index of E-mixer is 71%, which is the highest of the four micromixers.

At Re = 80, the highest mixing index of F-mixer and E-mixer is 92 and 94 per cent, respectively, and then it begins to decrease. But the mixing index of SESM and FESM remains close to 100 per cent.

Steer-by-wire (SBW) system mainly relies on sensors, controllers and motors to replace the traditionally mechanical transmission mechanism to realize steering functions. However, the sensors in the SBW system are particularly vulnerable to external influences, which can cause systemic faults, leading to poor steering performance and even system instability. Therefore, this paper aims to adopt a fault-tolerant control method to solve the safety problem of the SBW system caused by sensors failure.

This paper proposes an active fault-tolerant control framework to deal with sensors failure in the SBW system by hierarchically introducing fault observer, fault estimator, fault reconstructor. Firstly, the fault observer is used to obtain the observation output of the SBW system and then obtain the residual between the observation output and the SBW system output. And then judge whether the SBW system fails according to the residual. Secondly, dependent on the residual obtained by the fault observer, a fault estimator is designed using bounded real lemma and regional pole configuration to estimate the amplitude and time-varying characteristics of the faulty sensor. Eventually, a fault reconstructor is designed based on the estimation value of sensors fault obtained by the fault estimator and SBW system output to tolerate the faulty sensor.

The numerical analysis shows that the fault observer can be rapidly activated to detect the fault while the sensors fault occurs. Moreover, the estimation accuracy of the fault estimator can reach to 98%, and the fault reconstructor can make the faulty SBW system to retain the steering characteristics, comparing to those of the fault-free SBW system. In addition, it was verified for the feasibility and effectiveness of the proposed control framework.

As the SBW fault diagnosis and fault-tolerant control in this paper only carry out numerical simulation research on sensors faults in matrix and laboratory/Simulink, the subsequent hardware in the loop test is needed for further verification.

Aiming at the SBW system with parameter perturbation and sensors failure, this paper proposes an active fault-tolerant control framework, which integrates fault observer, fault estimator and fault reconstructor so that the steering performance of SBW system with sensors faults is basically consistent with that of the fault-free SBW system.