torque control Part 10 pot

Torque Control 170 From this equation, it can be seen that for constant stator flux amplitude and flux produced by the permanent magnet, the electromagnetic torque can be changed by control of the torque angle. The torque angle δ can be changed by changing position of the stator flux vector with respect to the PM vector using the actual voltage vector supplied by the PWM inverter (Dariusz, 2002). The flux and torque values can be calculated as in Section 3.1 or may be estimated as in Section 3.3 . The internal flux calculator is shown in Fig. 24. Ψ F i sA i sD i sd Ψ sd Ψ sD Ψ s i sB is C i sQ i sq Ψ sq Ψ sQ λ s θ r DQ To dq Ld Lq ABC To DQ dq To DQ Cartesian To Polar Fig. 24. Flux Estimator Block Diagram The internal structure of the predictive controller is in Fig. 25. ψ sref V sref ΔT e Δδ λ sref ϕ sref λ s ψ s i s VOLTAGES M ODULTOR PI Fig. 25. Predictive Controller Sampled torque error Δ T e and reference stator flux amplitude Ψ sref are delivered to the predictive controller. The error in the torque is passed to PI controller to generate the increment in the load angle Δδ required to minimize the instantaneous error between reference torque and actual torque value. The reference values of the stator voltage vector are calculated as: _ 22 1 __ _ tan sQ re f sref sD ref sQ ref sref sD re f V VV V and V ϕ − =+ = (18) Where: _ cos( ) cos sref s s s sD ref s sD s VRi T ψλδψλ +Δ − =+ . (19) _ sin( ) sin sref s s s sQ re f ssQ s VRi T ψλδψλ +Δ − =+ . (20) Where, T s is the sampling period. For constant flux operation region, the reference value of stator flux amplitude is equal to the flux amplitude produced by the permanent magnet. So, normally the reference value of the stator flux is considered to be equal to the permanent magnet flux. Torque Control of PMSM and Associated Harmonic Ripples 171 4.1 Implementation of SVMDTC The described system in Fig. 23 has been implemented in Matlab/Simulink, with the same data and loading condition as in HDTC with PI controllers setting as: Predictive Controller: Ki=0.03, Kp=1 Speed Controller: Ki= 1 Kp=0.04. The simulation results are shown in Fig. 26 to Fig. 29. As evidence from the figures, the SVM-DTC guarantee lower current pulsation, smooth speed as well as lower torque pulsation. This is mainly due to the fact that the inverter switching in SVM-DTC is uni-polar compared to that of FOC & HDTC (see Fig. 10, Fig. 20 and Fig. 28), in addition the application of SVM reduces switching stress by avoiding direct transition from +Vdc to – Vdc and thus avoiding instantaneous current reversal in dc link. However, the dynamic response in Fig. 9, Fig. 19, and Fig. 27 show that HDTC has faster response compared to the SVM-DTC and FOC. Fig. 26. SVMDTC torque response Fig. 27. SVMDTC rotor speed response Fig. 28. SVMDTC Line voltage (V ab ) waveform Torque Control 172 Fig. 29. SVMDTC Line current response of phase a Fig. 30. Stator flux response. 5. High Performance Direct Torque Control Algorithm (HP-DTC) In this section, a new direct torque algorithm for IPMSM to improve the performance of hysteresis direct torque control is described. The algorithm uses the output of two hysteresis controllers used in the traditional HDTC to determine two adjacent active vectors. The algorithm also uses the magnitude of the torque error and the stator flux linkage position to select the switching time required for the two selected vectors. The selection of the switching time utilizes suggested table structure which, reduce the complexity of calculation. Two Matlab/Simulink models, one for the HDTC, and the other for the proposed model are programmed to test the performance of the proposed algorithm. The simulation results of the proposed algorithm show adequate dynamic torque performance and considerable torque ripples reduction as well as lower flux ripples, lower harmonic current and lower EMI noise reduction as compared to HDTC. Only one PI controller, two hysteresis controllers, current sensors and speed sensor as well as initial rotor position and built-in counters microcontroller are required to achieve this algorithm (Adam & Gulez, 2009). 5.1 Flux and torque bands limitations In HDTC the motor torque control is achieved through two hysteresis controllers, one for stator flux magnitude error control and the other for torque error control. The selection of one active switching vector depends on the sign of these two errors without inspections of their magnitude values with respect to the sampling time and level of the applied stator voltage. In this section, short analysis concerning this issue will be discussed. Torque Control of PMSM and Associated Harmonic Ripples 173 5.1.1 Flux band Consider the motor stator voltage equation in space vector frame below:. s sss d VRi dt Ψ =+ (21) Equation (21) can be written as: s sss d dt VRi Ψ = − (22) For small given flux band Δ Ψ s o , the required fractional time to reach the limit of this value from some reference flux Ψ * is given by: 0 s sss t VRi ΔΨ Δ= − (23) And if the voltage drop in stator resistance is ignored, then the maximum time for the stator flux to remain within the selected band starting from the reference value is given as: 00 max 2/3 ss sdc t VV ΔΨ ΔΨ Δ= = (24) Thus if the selected sampling time Ts is large than Δ t max , then the stator flux linkage no longer remains within the selected band causing higher flux and torque ripples. According to (24) if the average voltage supplying the motor is reduced to follow the magnitude of the flux linkage error, the problem can be solved, i.e. the required voltage level to remain within the selected band is: max level kk s t VV T Δ = (25) Where V kk is the applied active vectors Thus, by controlling the level of the applied voltage, the control of the flux error to remain within the selected band can be achieved. For transient states, Δ Ψ s is most properly large which, requires large voltage level to be applied in order to bring the machine into steady state as quickly as possible. 5.1.2 Torque band The maximum time Δ t torque for the torque ripples to remain within selected hysteresis band can be estimated as: 0 0 * torque ref T tt Te Δ Δ= (26) Where, Δ T 0 ; is the selected torque band Torque Control 174 Te ref ; is the reference electromagnetic torque t 0 ; is the time required to accelerate the motor from standstill to some reference torque Te ref . The minimum of the values given in (24) and (26) can be considered as the maximum switching time to achieve both flux and torque bands requirement. However, when the torque ripples is the only matter of concern, as considered in this work, may be enough to consider the maximum time as suggested by (26). Now due to flux change by Δ Ψ s , the load angle δ will change by Δδ as shown in Fig. 31. Under dynamic state, this change is normally small and can be approximated as: 1 sin ss ss δ − Δ ΨΔΨ Δ≈ ≈ Ψ Ψ (27) δ Ψ s | Δ Ψ s | Δ δ D d q θ r Ψ F Fig. 31. Stator flux linkage variation under dynamic state The corresponding change in torque due to change ΔΨ s can be obtained by differentiation of torque equation with respect to δ. Torque equation can be rewritten as: 3 2sin ( )sin2 4 s eFsqssqsd sd sq TP L LL LL δ δ Ψ ⎡ ⎤ =Ψ−Ψ− ⎣ ⎦ (28) Where, then ees s TT T ψ δ δδ ∂∂Δ Δ= ⋅Δ≈ ⋅ ∂ ∂Ψ (29) Substitute (24) in (29) and evaluate to obtain: 3 cos ( )cos2 2 s Fsq s sq sd sd sq Vt TP L LL LL δ δ Δ ⎡ ⎤ Δ= Ψ −Ψ − ⎣ ⎦ (30) Where, Δ t=minimum ( Δ t max , Δ t torque ) Equation (30) suggests that Δ T can also be controlled by controlling the level of V s . Thus both Δ T and Δ Ψ s can be controlled to minimum when the average stator voltage level is controlled to follow the magnitude of Δ T. 5.2 The HP-DTC Algorithm The basic structure of the proposed algorithm is shown in Fig. 32. Torque Control of PMSM and Associated Harmonic Ripples 175 Fig. 32. The HPDTC system of PMSM 5.2.1 Vector selector In Fig.32 the vector selector block contains algorithm to select two consecutive active vectors V k1 , and V k2 depending on the output of the hysteresis controllers of the flux error and the torque error; φ and τ respectively as well as flux sector number; n. The vector selection table is shown in Table 4., while vectors position and flux sectors is as shown in Fig.15 φ τ V k1 V k2 1 1 n+1 n+2 1 0 n-1 n-2 0 1 n+2 n+1 0 0 n-2 n-1 Table 4. Active vectors selection table In the above table if V k >6 then V k =V k -6 if V k <1 then V k =V k +6 5.2.2 Flux and torque estimator In Fig. 32 the torque and flux estimator utilizes equation (21) to estimate flux and torque values at m sampling period as follows: () ( 1)( ( 1) ) DD D sDs mmVmRiT ψ ψ = −+ −− (31) () ( 1)( ( 1) ) QQ Q sQs mmVmRiT ψ ψ = −+ −− (32) 22 sDQ ψ ψψ =+ (33) 1 Q s D Tan ψ λ ψ − = (34) Where; the stationary D-Q axis voltage and current components are calculated as follows: 11 22 (1)( )/ DDkkDkk Vm V t V t Ts−= + (35) Torque Control 176 11 22 (1)( )/ QQkkQkk Vm V t V t Ts − =+ (36) (( 1) ())/2 DD D iim im = −+ (37) (( 1) ())/2 QQ Q iim im = −+ (38) The torque value can be calculated using estimated flux values as: 3 ( ()() ()()) 2 eDQQD TPmim mim=Ψ −Ψ (39) 5.2.3 The timing selector structure In Fig. 32 the timing selector block contains algorithm to select the timing period pairs of vectors V k1 and V k2 . The selection of timing pairs depends on two axes, one is the required voltage level and the other is the reflected flux position in the sector contained between V k1 and V k2 . The reflected flux position is given by: mod60 /6 ss ρ λπ = − (40) Where λ s ; is the stator flux linkage position in D-Q stationary reference frame. Fig. 34 shows the proposed timing table. In this figure, the angle between the two vectors V k1 and V k2 which is 60 0 , is divided into 5 equal sections ρ -2 , ρ -1 , ρ 0 , ρ +1 , and ρ +2 . The required voltage level is also divided into 5 levels. The time pairs (t k1 , t k2 ), expressed as points, (out of 20 points presenting the sampling period) define the timing periods of V k1 and V k2 respectively. The remaining time points, (t 0 =20-t k1 -t k2 ), is equally divided between zero vectors V 0 and V 7 . Fig. 34. Timing diagram for the suggested algorithm The time structure shown in Fig.34 has the advantage of avoiding the complex mathematical expressions used to calculate t k1 and t k2 , as the case in space vector modulation used by (Dariusz, 2002) and (Tan, 2004). In addition, it is more convenient to be programmed and executed through the counter which controls the period t k1 , t k2 and t 0 . The flow chart of the algorithm is shown in Fig. 35. Torque Control of PMSM and Associated Harmonic Ripples 177 Define timing table Load initial & reference values Read sensed values: currents, dc link voltage and speed/position Calculate i D , i Q , V D , V Q Eq.s(35-38) Calculate Ψ D , Ψ Q , λ s & T e Eq.s (31, 34, 39) Calculate Δ Ψ s , Δ T Find Hysteresis controllers output values φ and τ Find sector number n (Fig. 15) Calculate torque error level Δ T ε {Level 1 Level 5 } Calculate reflected position Eq.18 ε { ρ -2 , ρ +2 } Determine t k1 ,t k2 & calculate t 0 Get active vectors V k1 , V k2 . INVERTER SWITCHING Send V k1 , Delay t k1 /2 Send V k2 , Delay t k2 /2 Send V 7 , Delay t 0 /2 Send V k2 , Delay t k2 /2 Send V k1 , Delay t k1 /2 Send V 0 , Delay t 0 /2 ADC & Encoder Motor Sensed values START Fig. 35. A Flow chart of the proposed algorithm 5.3 Simulation and results To examine the performance of the proposed DTC algorithm, two Matlab/Simulink models, one for HDTC and the other for the HPDTC were programmed. The motor parameters are shown in table 2. The inverter used in simulation is IGBT inverter with the following setting: IGBT/Diode Snubber Rs, Cs = (1e-3ohm,10e-6F) Ron=1e-3ohm Forward voltage (V f Device,V f Diode)= (0.6, 0.6) T f (s),T t (s) = (1e-6, 2e-6) DC link voltage= +132 to -132. Torque Control 178 The simulation results with 100μs sampling time for the two algorithms under the same operating conditions are shown in Fig. 36 -to- Fig. 41. The torque dynamic response is simulated with open speed loop, while the steady state performance is simulated with closed speed loop, 70rad/s as reference speed, and 2 Nm as load torque. 5.3.1 Torque dynamic response The torque dynamic response with HDTC and the HPDTC are shown in Fig.36-a and Fig.36- b respectively. The reference torque for both algorithms is changed from +2.0 to -2.0 and then to 3.0 Nm. As shown in the figures, the dynamic response with the proposed algorithm is adequately follows the reference torque with lower torque ripples. In the other hand, the torque response with the proposed algorithm shows fast response as the HDTC response. (a) (b) Fig. 36. Motor dynamic torque with opened speed loop: (a) HDTC (b) HP-DTC Fig. 37 demonstrates the idea of maximum time to remain within the proposed torque band as suggested by equation (26). According to the shown simulated values, the time required to accelerate the motor to 2 Nm is ≈ 0.8ms, so if the required limit torque ripple is not to exceed 0.1 Nm, as suggested in this work, then, the maximum switching period according to Eq. (26) is ≈0.05ms which is less than the sampling period (Ts=0.1 ms). Fig. 37. Torque ripples and motor accelerating time Although the torque ripple is brought under control, the flux ripples still high as shown in Fig. 38 which, is mainly due to control of the voltage level according to the magnitude of torque error only. [...]... steady state torque response: (a) HDTC (b) HPDTC (b) 180 Torque Control (a) (b) Fig 41 Rotor speed response: (a) HDTC (b) HPDTC 6 Torque ripple and noise in PMSM algorithm One of the major disadvantages of the PMSM drive is torque ripple that leads to mechanical vibration and acoustic noise The sensitivity of torque ripple depends on the application If the machine is used in a pump system, the torque ripple... of torque ripple is critical For example, the quality of the surface finish of a metal working machine is directly dependent on the smoothness of the delivered torque (Jahns and Soong, 1996) Also in electrical or hybrid vehicle application, torque ripple could result in vibration or noise producing source which in the worst case could affect the active parts in the vehicle The different sources of torque. .. PMSM Torque Reference Flux Estimator Currents Speed/Position Fig 49 The basic structure of HDTC of PMSM with the proposed filter topology 185 Torque Control of PMSM and Associated Harmonic Ripples 6.1.4 Simulations and results To simulate the performance of the proposed passive filter topology under HDTC Matlab/Simulink was used Under base speed operation, the speed control was achieved through PI controller... after applying the filter topology 6.2 Method 2: active filter topology In this section an active filter topology will be proposed to reduce torque ripples and harmonic noises in PMSM when controlled by FOC or HDTC equipped with hysteresis 188 Torque Control controllers The filter topology consists of IGBT active filter (AF) and two RLC filters, one in the primary circuit and the other in the secondary... to Fig 54 (a) (b) Fig 52 Motor torque: (a) before (b) after applying the filter topology (load torque is 2Nm) (a) (b) Fig 53 Rotor speed: (a) before (b) after applying the filter topology In Fig 54-a the spectrum of the line current without connecting the filter shows that harmonics currents with THD of ~3% have widely distributed with a dominant harmonics 187 Torque Control of PMSM and Associated... bands are set to 0.01 for both the torque and flux hysteresis controllers The motor parameters are shown in Table 2 and the passive filter parameters are in Table 5 L1 C1 R1 20μH 52μF 56kΩ L2 C2 R2 30mH 5.1μF 2.2Ω L3 C3 R3 r3 30mH 12.5 μF 128 Ω 2Ω Table 5 Passive Filter Parameters The simulation results with 100 μs sampling time are shown in Fig 50 to Fig 55 Fig 50-a in particular, shows the motor line... AF is characterized by detecting the harmonics in the motor phase voltages and uses hysteresis voltage control method to provide almost sinusoidal voltage to the motor windings 6.2.1 The proposed active filter topology When the PMSM is controlled by HDTC, the motor line currents and/or torque are controlled to oscillate within a predefined hysteresis band Fig 56, for example, shows typical current... pulses appear in Fig 39-a Better waveform can be obtained by increasing the partition of the timing structure, however, when smoother waveform is not necessary, suitable division as the one shown in Fig 34 may be enough (a) (b) Fig 39 Motor line currents: (a) HDTC (b) HPDTC The torque response in Fig 40 shows considerable reduction in torque ripples from 3.2Nm (max -to- max.) down to less than 0.15 Nm when... the RLC filter 186 Torque Control The motor performance before and after applying the filter topology are shown in Fig 51 to Fig 54 In Fig 51, the motor line currents show considerable reduction in noise and harmonic components after applying the filter which reflects in smoother current waveform (a) (b) Fig 51 Motor line currents: (a) before (b) after applying the filter topology The torque response... section, the reduction of torque ripple and harmonics generated due to inverter switching in PMSM control algorithms using passive and active filter topology will be investigated Method1: Compound passive filter topology 6.1 The proposed passive filter topology Fig 42 shows a block diagram of basic structure of the proposed filter topology (Gulez et al., 2007) with PMSM drive control system It consists . and torque bands limitations In HDTC the motor torque control is achieved through two hysteresis controllers, one for stator flux magnitude error control and the other for torque error control. . High Performance Direct Torque Control Algorithm (HP-DTC) In this section, a new direct torque algorithm for IPMSM to improve the performance of hysteresis direct torque control is described selected torque band Torque Control 174 Te ref ; is the reference electromagnetic torque t 0 ; is the time required to accelerate the motor from standstill to some reference torque Te ref .