## 1 Introduction  
The high-speed motors operating in adverse locations involving high temperatures are often prone to motor breakdown. According to recent surveys, nearly 51% of motor breakdowns are only due to bearing failures, which result in the shutdown of industrial process involving electric drives. The subsequent motor-bearing failures may affect modern industrial progress, causing undesirable and unreliable conditions. Solving motor bearing breakdowns became the most challenging task for researchers for a decade. Extensive research has been going on developing bearingless technology by eliminating the conventional mechanical-bearing system. The bearingless concept is a plausible alternative to the magnetic bearing drives, as it provides numerous advantages like minimal maintenance, low cost, compactness and redundant, high-performance power amplifiers [1; 2; 3]. Compared with conventional switched reluctance motors, the levitation of the rotor at the centre point and suspension force control is an additional task for bearingless switched reluctance motors (BSRMs). Besides stable rotor suspension control of the BSRM, there exists another duty in controlling the rotor position and its displacement under parameter variations during acceleration and deceleration phases. The perfect realisation of the BSRM is difficult to simulate and control due to its nonlinear magnetisation characteristics. For these reasons, the BSRM will not be used in high-precision and high-performance industrial applications. Apart from the difficulty of the model, the BSRM should operate in a continuous phase-to-phase switching mode for basic motor workings [4; 5; 6]. Therefore, various complex controllers are required to realise the full potential of the BSRM and to overcome its drawbacks, as mentioned above. Hence, to get less rotor eccentric displacements and steady speed and torque profiles of the BSRM, a new robust controller, i.e., dynamic sliding mode controller (DSMC), is proposed in this paper. The DSMC has received considerable attention due to its dynamic properties. The DSMC provides asymptotic stability to the states of tracking error dynamics and stability to the internal states. The sliding manifold with a new dynamic is called a DSMC. The DSMC improves the order of the system by number. Further, the designed compensators may not only enhance the stability of the sliding system but, also, improve the desired characteristics and performance of the system [7; 8]. Practically at high speeds, the accurate controlling of the rotor position and its displacement through the sensors makes it unfair, and this setup will increase the space, cost and complexity in the controlling process [9; 10; 11]. Hence, in recent days, various direct and indirect sensorless methods are applied to BSRM drives. To avoid the mechanical sensors and to get accurate rotor position information, sliding mode observer (SMO)-based sensorless speed and displacement control technics are presented in this paper. The rotor displacement tracking error functions and speed error tracking functions are considered in the designing of the switching surface for the proposed dynamic sliding mode control. To get a healthy and stable operation of the BSRM, the proposed controller's tasks are divided into three steps. As the first step, the displaced rotor in any one of the four quadrants in the air gap has to pull back to the centre position successfully. The second step is to run the motor at a rated speed by exciting the torque phase currents, and finally, the third step is to maintain the stable and robust operation of the BSRM even under the application of different loads and changes of the motor parameters. Improved rotor displacement and speed controllers are proposed to the model derived for the existing 12/14 BSRM. The issues like modelling, simulation, control without position and displacement sensors, the implementation of a robust controller and observers are the significant contributions of this paper.