A Novel Sensorless Approach for Speed and Displacement Control of Bearingless Switched Reluctance Motor
A Novel Sensorless Approach for Speed and Displacement Control of Bearingless Switched Reluctance...
Nageswara Rao, Pulivarthi;Manoj Kumar, Nallapaneni;Padmanaban, Sanjeevikumar;Subathra, M. S. P.;Chand, Aneesh A.
2020-06-12 00:00:00
applied sciences Article A Novel Sensorless Approach for Speed and Displacement Control of Bearingless Switched Reluctance Motor 1 2 , 3 , Pulivarthi Nageswara Rao , Nallapaneni Manoj Kumar * , Sanjeevikumar Padmanaban * , 4 5 M. S. P. Subathra and Aneesh A. Chand Department of Electrical Electronics and Communication Engineering, Gandhi Institute of Technology and Management (Deemed to be University), Visakhapatnam 530045, Andhra Pradesh, India; dr.nageshpulivarthi@gmail.com or nagesh.pulivarthi@gitam.edu School of Energy and Environment, City University of Hong Kong, Kowloon, Hong Kong, China Department of Energy Technology, Aalborg University, 6700 Esbjerg, Denmark Department of Electrical and Electronics Engineering, Karunya Institute of Technology and Sciences, Coimbatore 641114, Tamil Nadu, India; subathra@karunya.edu School of Engineering and Physics, The University of the South Pacific, Suva, Fiji; aneeshamitesh@gmail.com * Correspondence: nallapanenichow@gmail.com or mnallapan2-c@my.cityu.edu.hk (N.M.K.); san@et.aau.dk (S.P.) Received: 2 May 2020; Accepted: 9 June 2020; Published: 12 June 2020 Abstract: The bearingless concept is a plausible alternative to the magnetic bearing drives. It provides numerous advantages like minimal maintenance, low cost, compactness and no requirement of high-performance power amplifiers. Controlling the rotor position and its displacements under parameter variations during acceleration and deceleration phases was not eective with the use of conventional controllers like proportional–integral–derivative (PID) and fuzzy-type controllers. Hence, to get the robust and stable operation of a bearingless switched reluctance motor (BSRM), a new robust dynamic sliding mode controller has been proposed in this paper, along with a sensorless operation using a sliding ode observer. The rotor displacement tracking error functions and speed tracking error functions are used in the designing of both proposed methods of the sliding mode switching functions. To get a healthy and stable operation of the BSRM, the proposed controller ’s tasks are divided into three steps. As a 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 torque phase currents, and finally, the third step is to maintain the stable and robust operation of the BSRM even under the application of dierent loads and changes of the motor parameters. Simulation studies were conducted and analysed under dierent testing conditions. The suspension forces, rotor displacements, are robust and stable, and the rotor is pulled back quickly to the centre position due to the proposed controller ’s actions. The improved performance characteristics of the dynamic sliding mode controller (DSMC)-based sliding mode observer (SMO) was compared with the conventional sliding mode controller (SMC)-based SMO. Keywords: asymmetric converter; bearingless; dynamic sliding mode control; sensorless; sliding mode observer 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. Appl. Sci. 2020, 10, 4070; doi:10.3390/app10124070 www.mdpi.com/journal/applsci Appl. Sci. 2020, 10, 4070 2 of 26 The subsequent motor-bearing failures may aect 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 [1–3]. 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 dicult 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 diculty of the model, the BSRM should operate in a continuous phase-to-phase switching mode for basic motor workings [4–6]. 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 [9–11]. 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 dierent 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. The proposed control methods have to achieve a quick and hassle-free start and better control actions on rotor displacement and speed. Such control schemes oer higher accuracy in sensorless operations for a wide speed range and help to reduce the torque ripple of the drive appreciably. The article is structured as follows: Section 2 briefly described the operation and modelling of the BSRM. In Section 3, the modelling of the proposed controller and observer is given. Results and discussion are presented in Section 4, the detailed comparison of the proposed controller is presented in Section 5. Lastly the conclusions were drawn and presented in Section 6. Appl. Sci. 2020, 10, 4070 3 of 26 Appl. Sci. 2020, 10, x FOR PEER REVIEW 3 of 26 2. Operation and Modelling of the Bearingless Switched Reluctance Motor 2. Operation and Modelling of the Bearingless Switched Reluctance Motor 2.1. Operating Principle 2.1. Operating Principle The BSRM has salient poles both in the rotor and stator, and the excitation is limited to stator The BSRM has salient poles both in the rotor and stator, and the excitation is limited to stator windings only. The excitation currents are unidirectional and discontinuous. The stator phases are windings only. The excitation currents are unidirectional and discontinuous. The stator phases are sequentially excited to obtain continuous rotation [12–14]. Hence, the design of the controllers for the sequentially excited to obtain continuous rotation [12–14]. Hence, the design of the controllers for the BSRM is more complicated due to its nonlinear magnetic field distribution. The basic 12/14 BSRM BSRM is more complicated due to its nonlinear magnetic field distribution. The basic 12/14 BSRM salient pole structure is illustrated in Figure 1. Two regulated individual DC voltages are given to the salient pole structure is illustrated in Figure 1. Two regulated individual DC voltages are given to suspension and torque coils to realise the decoupled performance between the net suspension the suspension and torque coils to realise the decoupled performance between the net suspension winding’s force and main winding’s torque. The suspension winding coils Is1 and Is3 produce the winding’s force and main winding’s torque. The suspension winding coils Is1 and Is3 produce the radial force in the Y-directional, and coils Is2 and Is4 produce the radial force in the X-directional. radial force in the Y-directional, and coils Is2 and Is4 produce the radial force in the X-directional. Positive suspension forces are produced from Is2 and Is1; similarly, Is4 and Is3 poles produce Positive suspension forces are produced from Is2 and Is1; similarly, Is4 and Is3 poles produce negative negative suspension forces. The resultant rotational torque will be produced from the stator main suspension forces. The resultant rotational torque will be produced from the stator main phase coils phase coils called phase-A and phase-B. The operating parameters and ratings of the 12/14 BSRM are called phase-A and phase-B. The operating parameters and ratings of the 12/14 BSRM are given in given in Table 1. Table 1. Is1 A1 B1 Y+ A2 B2 Rotor Is4 X+ Is2 Centre X- Position B4 Y- A4 B3 A3 Is3 Figure 1. Structure and winding pattern of the stator. Figure 1. Structure and winding pattern of the stator. Table 1. Operating details of the 12/14 bearingless switched reluctance motor (BSRM). Table 1. Operating details of the 12/14 bearingless switched reluctance motor (BSRM). Parameters Value Parameters Value Rated power(motor) 1 kW Rated power(motor) 1 kW Maximum motor Current/phase 4 amp Maximum motor Current/phase 4 amp Voltage/phase 250 volts Voltage/phase 250 volts Net torque 1 Nm Net torque 1 Nm Speed 9000 rpm Toque winding per phase resistance 0.86 ohms Speed 9000 rpm Suspension winding per phase resistance 0.32 ohms Toque winding per phase resistance 0.86 ohms Suspension voltage 250 volts Suspension winding per phase resistance 0.32 ohms Maximum suspension current 4 amp Suspension voltage 250 volts Maximum suspension current 4 amp Hence, the BSRM drive needs a total of six hysteresis controllers to regulate both the suspension force and torque. Out of six, two are used as individual phase current controllers, and the remaining four Hence, the BSRM drive needs a total of six hysteresis controllers to regulate both the suspension suspension force current controllers are used to control the suspension currents. The suspension force force and torque. Out of six, two are used as individual phase current controllers, and the remaining pole arc is carefully chosen not to be less than one-rotor pole pitch to maintain the continuous levitation four suspension force current controllers are used to control the suspension currents. The suspension force. Therefore, the pole arcs of both the suspension pole and rotor pole are equal in dimensions. force pole arc is carefully chosen not to be less than one-rotor pole pitch to maintain the continuous levitation force. Therefore, the pole arcs of both the suspension pole and rotor pole are equal in dimensions. Appl. Sci. 2020, 10, 4070 4 of 26 2.2. Rotor Modelling (Suspension Control) The suspension forces required for the levitation of the rotor in both the X and Y directions are given below at the standstill position: d x Fx = m +kx (1) dt d y Fy = m +ky + mg (2) dt Here, X , X , Y and Y are chosen as the state variables from Equations (1) and (2). Hence, the desired 1 2 1 2 tracking rotor displacement states are modelled as: X = X ; Y = Y 2 2 1 1 (3) k F k F y y x x X = X + + F ; Y = Y + + F + g 2 1 2 1 dx dy m m m m The net suspending forces produced in the X-Y directions are written in electrical equivalence, as given in Equation (4): 2 3 6 xp 7 6 7 " # " # 6 7 6 2 7 6 7 F K K K K i x xxp xyp xxn xyn yp 6 7 6 7 = 6 7 (4) 6 2 7 6 7 F K K K K i y yxp yyp yxn yyn 6 xn 7 6 7 4 5 xn By equating the above Equations (3) and (4), we get the following Equations (5) and (6): d x [ ][ ] F = m + kx = K I (5) x X x dt d y [ ][ ] Fy = m + ky + mg = K I (6) Y Y dt h i h i where K = diag Kxxp Kxyp Kxxn kxyn , K = diag Kyxp Kyyp Kyxn Kyyn and I = X Y x " # " # 2 2 I I xp yp and I = . 2 2 I I xn yn The equivalent desired tracking state space equations for rotor displacements are given as follows in Equation (7): 2 3 6 7 2 32 3 2 3 2 3 6 X 7 2 6 7 1 0 0 0 X 0 0 0 0 i 6 7 6 76 7 6 7 6 7 1 xp 6 7 6 76 7 6 7 6 7 6 7 6 76 7 6 7 6 7 6 7 6 k 76 7 6 7 6 7 6 7 6 76 7 6 7 6 7 0 0 0 X Kxxp Kxyp Kxxn Kxyn i 6 2 7 6 76 2 7 6 7 6 yp 7 6 7 6 76 7 6 7 6 7 = + (7) 6 7 6 76 7 6 7 6 7 6 7 6 76 7 6 7 6 2 7 6 7 6 76 7 6 7 6 7 0 0 1 0 Y 0 0 0 0 i 6 7 6 76 1 7 6 7 6 xn 7 6 Y 7 6 76 7 6 7 6 7 6 7 4 54 5 4 5 4 5 6 7 k 6 7 0 0 g 0 Y Kyxp Kyyp Kyxn Kyyn i 4 5 2 xn 2.3. The Speed Control of the BSRM The flux linkages vector “Y”, the voltage vector “V”, the phase current vector “i", the vector of the mutual inductance matrix “N” and phase resistances “r” are the modelled state space to get the perfect realisation of the BSRM and are given in Equation (8): dY dw T T B T d e l e = rN()Y + V + w ; = w + + w ; = w + w and i = N()Y (8) dt dt J J J dt Appl. Sci. 2020, 10, x FOR PEER REVIEW 5 of 26 for the two-phase torque winding control. The topology of the asymmetric converter circuit is shown below in Figure A1 (in Appendix A.1). The detailed switch numbers are given in Table 2. Table 2. Switch numbers for the 12/14 bearingless switched reluctance motor (BSRM). 12/14 BSRM Number of Power Switches Total Appl. Sci. 2020, 10, 4070 5 of 26 Torque winding (two-phase) 2 per phase 4 Suspending force winding (four- 2 per pole 8 phase/four poles) 2.4. Switching Control Strategy Fig The ure 12/2 14 sho bearingless ws the over SRM all in drive dependen system t suspen only needs sion cont 12 power rol swit switches. ching scheme dia As discussed gram of in tthe he operating principle, the 12/14 BSRM is total a six-phase drive. Therefore, eight power switches are BSRM. The selection of suspending force windings is mentioned in Table 3. From Table 3, the swit requir ching ed for stat contr e 1 ind olling icatthe es th four e magnet -phaseis suspension ation mode windings, and the switching state 0 me and four power switches ans the fr are r eew equir heelin ed for g the two-phase torque winding control. The topology of the asymmetric converter circuit is shown mode. below in Figure A1 (in Appendix A.1). The detailed switch numbers are given in Table 2. Table 3. Switching state rule of the hysteresis control method for the bearingless switched Table 2. Switch numbers for the relu 12 ctance m /14 bearingless otor (BSRM) switched . reluctance motor (BSRM). Suspending 12/14 BSRM Number of Power Switches Total Desired Force Force Poles Enable Is1 Enable Is2 Enable Is3 Enable Is4 Torque winding (two-phase) 2 per phase 4 Selection Suspending force winding 2 per pole 8 (four-phase/four poles) If ≥ , ≥ Is1 and Is2 1 1 0 0 If ≥ , ≤ Is2 and Is3 0 1 1 0 If Figur ≤ e , 2 shows ≤ the overall independent suspension control switching scheme diagram of the Is3 and Is4 0 0 1 1 BSRM. The selection of suspending force windings is mentioned in Table 3. From Table 3, the switching If ≤ , ≥ Is4 and Is1 1 0 0 1 state 1 indicates the magnetisation mode and the switching state 0 means the freewheeling mode. Note: and are suspension forces in X and Y directions; Is1, Is2, Is3, and Is4 are the suspension winding coils. Figure 2. Figure 2. Swit Switching ching states statesof t of the he hysteresis control method. hysteresis control method. Table 3. Switching state rule of the hysteresis control method for the bearingless switched reluctance 3. Modelling of the Proposed Controller and Observer motor (BSRM). 3.1. Design of the DSMC Suspending Force Poles Desired Force Enable Is1 Enable Is2 Enable Is3 Enable Is4 Selection Generally, the conventional sliding mode controller (SMC) uses a practically high value of gains If F 0, F o Is1 and Is2 1 1 0 0 x y to slide the trajectories on the predetermined sliding mode surface [15,16]. The key advantage of the If F 0, F o Is2 and Is3 0 1 1 0 SMC is x its robust y ness, and it does not allow the parametric variations when the system states are on the switching surface. Furthermore, the sliding mode condition can be reached in finite time due to If F 0, F o Is3 and Is4 0 0 1 1 x y If F 0, F o Is4 and Is1 1 0 0 1 x y Note: F and F are suspension forces in X and Y directions; Is1, Is2, Is3, and Is4 are the suspension winding coils. x y Appl. Sci. 2020, 10, 4070 6 of 26 3. Modelling of the Proposed Controller and Observer 3.1. Design of the DSMC Generally, the conventional sliding mode controller (SMC) uses a practically high value of gains to slide the trajectories on the predetermined sliding mode surface [15,16]. The key advantage of the SMC is its robustness, and it does not allow the parametric variations when the system states are on the switching surface. Furthermore, the sliding mode condition can be reached in finite time due to its noncontinuous control law function. However, the SMC at high speeds has drawbacks such as chattering and the steady-state error due to its high switching gains [17,18]. These particular attributes make the SMC less attractive to the bearingless drives, even though it oers robust and stable activities. To avoid the prominent problems of reaching time and the chattering in the control scheme of the SMC, a new dynamic sliding mode control (DSMC) is implemented. The DSMC guarantees the system robustness and disturbance rejection capability [19,20]. The main features of the dynamic sliding mode controller are given by: (a) The system will achieve stability even with incomplete information from the state observer or absence of the state observer. (b) The system will get stability even under the accommodation of unmatched disturbances. (c) The chattering can be reduced to a great extent. Defining the state tracking errors and the switching functions are e = x x , e = y y , x y d d S = (C e )+e and S = (C e )+e , respectively, where C > 0 and C > 0, and it must be x x x x y y y y x y Hurwitz. The first-order derivative of the switching functions is given by: ( ) ( ) k F k F y y x x S = C e + X + + F X ; S = C e + y + + F + g Y (9) x x x y y x 1 dx d 1 dy d m m m m where e = x x and e = y y (the design of C and C are given in Appendix A.2.1). x d y x y The new dynamic sliding mode switching functions are given by = S + S and = S + S x x x x y y y y ( > 0 and > 0). When = 0 and = 0, S + S = 0 and S + S = 0 are asymptotically stable; x y x y x x x y y y therefore, the error and its first-order dierential functions tend to zero. (The design of and are x y given in Appendix A.2.2). The stability analysis is given as follows from the above Equations (10) and (11): ( ) k F x x = S + S = C e + X + + F X + S (10) x x x x x x 1 dx d x x m m ( ) k F y y = S + S = C e + y + + F + g Y + S (11) y y y y y y 1 dy d y y m m Therefore, the rotor X and Y displacement control equations are given by Equations (12) and (13): ( ! ) k C k x x x x ( ) ( ) ( ) U = m x + C + x + x + u C + x C e sgn (12) x 2 x x x x x 2 x x x x d d x m m m m ( ! ! ) k C k y y y y U = m y + C + y + y + u C + y C e sgn (13) y y y y y y 2 y y y y 2 d d m m m m The above dynamic feedback controller Equations (12) and (13) guarantee the asymptotic convergence of rotor displacements X and Y to their desired values as t tends to infinity (the designs of , and , x y 2 2 are given in Appendix A.2.2). The motor speed tracking control dynamics based on e = w w , e = w w , = S + S w w w w w w d d and 0 are given as shown in Equation (14). Appl. Sci. 2020, 10, 4070 7 of 26 8 9 ! ! > > > > > > <