Adaptive control for six phase induction motor drives

(V ) 0.51 0.515 0.52 0.525 0.53 0.535 0.54 0.545 0.55 0.555 -500 0 500 Time (s) V co m 2 (V ) 0.51 0.515 0.52 0.525 0.53 0.535 0.54 0.545 0.55 0.555 -500 0 500 Time (s) V co m ( V ) 0.51 0.515 0.52 0.525 0.53 0.535 0.54 0.545 0.55 0.555 -500 0 500 Time (s) V co m ( V ) 0.51 0.515 0.52 0.525 0.53 0.535 0.54 0.545 0.55 0.555 -500 0 500 Time (s) V a p h as e v o lt ag e ( V ) 0.51 0.515 0.52 0.525 0.53 0.535 0.54 0.545 0.55 0.555 -500 0 500 Time (s) V a p h as e v o lt ag e ( V ) 9 Fig 2. 4: RCMV4S-CBPWM Vcommid technique: Va, Vab và six phase stator currnet, isαβ và isdq, VcomI, VcomII , Vcom Fig 2. 5: RCMV4S-CBPWM VcomOpt technique Va, Vab và six phase stator currnet, isαβ và isdq, VcomI, VcomII , Vcom The results in Fig 2.5 show that the instantaneous common-mode voltage value of the RCMV 4S-PWM technique with VcomOpt decreases within the limits, while the common mode voltage component also decreases within the above limit. The voltage of each 3P_VSI is controlled independently of the PWM to the limit of m = 0.866. In range (m> 0.866) from the modulation index m= 0.866 to 1, the offset voltages of the two VSI I, II will be constrained under the extreme condition of the Vcom function.Kỹ thuật RCMV4S-CBPWM với VcomOpt 0.51 0.515 0.52 0.525 0.53 0.535 0.54 0.545 0.55 0.555 -500 0 500 Time (s) V ab l in e v o lt ag e ( V ) 0.51 0.515 0.52 0.525 0.53 0.535 0.54 0.545 0.55 0.555 -500 0 500 Time (s) V ab l in e v o lt ag e ( V ) 0.51 0.515 0.52 0.525 0.53 0.535 0.54 0.545 0.55 0.555 -2 0 2 Time (s) S ta to r cu rr en t ( A ) 0.51 0.515 0.52 0.525 0.53 0.535 0.54 0.545 0.55 0.555 -2 0 2 Time (s) S ta to r cu rr en t ( A ) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -5 0 5 Time (s) St at or c ur re nt ( A ) is anpha is beta 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -5 0 5 Time (s) S ta to r cu rr en t ( A ) is anpha is beta 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 5 10 Time (s) S ta to r cu rr en t (A ) isd isq 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 5 10 Time (s) S ta to r cu rr en t ( A ) isd isq 0.51 0.515 0.52 0.525 0.53 0.535 0.54 0.545 0.55 0.555 -500 0 500 Time (s) V co m 1 (V ) 0.51 0.515 0.52 0.525 0.53 0.535 0.54 0.545 0.55 0.555 -500 0 500 Time (s) V co m 1 (V ) 0.51 0.515 0.52 0.525 0.53 0.535 0.54 0.545 0.55 0.555 -500 0 500 Time (s) V co m 2 ( V ) 0.51 0.515 0.52 0.525 0.53 0.535 0.54 0.545 0.55 0.555 -500 0 500 Time (s) V co m 2 ( V ) 0.51 0.515 0.52 0.525 0.53 0.535 0.54 0.545 0.55 0.555 -500 0 500 Time (s) V co m ( V ) 0.51 0.515 0.52 0.525 0.53 0.535 0.54 0.545 0.55 0.555 -500 0 500 Time (s) V co m ( V ) 10 CHAPTER 3: DESIGNING NONLINEAR CONTROLLER FOR SPIM DRIVES 3.1 Introduction In order to improve the quality of controllers, nonlinear control methods have recently been developed to replace traditional PID controllers. In this thesis, a new nonlinear control structure is proposed, in that the BS controllers are proposed for the outer speed and rotor flux closed loop controls, In addition, to further enhance the SPIM drives performance, the authors proposed a new structure combining BS and PCH, PCH controllers are proposed for inner current control loop to improve performance and ensure the stability, accuracy speed response for the drive system, enhance the robustness for the sensitivity of changes in machine parameters, load disturbance. The results of the research presented in this chapter are published in the articles [14], [16], [17] belong the list of publications. 3.2 BS_PCH nonlinear control structure 3.2.1 The proposed BS controller for outer speed control and rotor flux loops The tracking errors is defined as         t t * ' * * ' * ω r r ω r r ψ rd rd ψ rd rd 0 0 ε = ω - ω +k ω - ω dt; ε = ψ - ψ +k ψ - ψ dt  (3.1) The Lyapunov function is chosen:    2 2ω ψω,ψ 1 V = ε + ε 2 (3.2) To V' <0, the current stabilizing virtual commands are chosen:     * * ' *r l sq ω ω r ω r r t rd * * ' *rdr sd ψ ψ rd ψ rd rd m r dω T1 i = k ε + + + Bω + k ω - ω ; k ψ dt J dψτ 1 i = k ε + + ψ + k ψ - ψ L dt τ               (3.3) where, kω, kѰ are always positive design constants determining the dynamics of closed loop. We obtain:  ω,ψ 2 2 ω ω ψ ψ dV = - k ε - k ε < 0 dt (3.5) 3.2.2 The inner current loop controllers using PCH A PCH system with dissipation is a representation of the form:            T dx dH = J x - R x x + g x u dt dx dH =g x dx y x         (3.6) The Hamiltonian function of the system is given by 11      T -1 2 2 2 21 2 s sd s sq s 1 1 1 1 x = x D x = x + x = L i + L i 2 2 L 2 H (3.7) Suppose that with the expectation of systematic stability (19) around a desired equilibrium xo, a Hd (x) closed-loop energy function, which has a strict minimum at x0 (that is, Hd (x) > Hd (x0) for all x, is assigned to the system. The feedback stabilization theory of PCH system is given as follows [6]. Given J(x), R(x), H(x), g(x) and the desired equilibrium xo. Then a feedback control u = α(x), Ra(x) ,Ja(x) and K(x) vector functions can be found and they satisfy              d d a a dH J x - R x K x = - J x - R x x + g x u dx        (3.8) Hamiltonia closed system satisfies the conditions:      dd d dHdx = J x - R x x dt dx    . It will become an energy dissipation PCH system. We have: a a d dH K(x)= ; H (x)=H (x)-H(x) dx (3.9) where, Ha is an added energy into the system for this closed-loop system is gained a stable equilibrium at x0. From equations above, the control components of the current controller in the inner loop is determined as         * * * * * sd sd 1 sd sd 1 sq sq s s sq r rd * * * * * sq sq 2 sq sq 1 sd sd s s sd r rd = σ ai + r i - i - J i -i - L ω i - bR ψ = σ ai + r i - i + J i -i + L ω i + bω ψ u u            (3.10) 3.3 Research results These surveys are implemented based benchmark tests in [45], [47]. Nguồn AC 3P -+ -+ -+ PCHBS T2 T2 -1 BCL SPVSI DC link ĐKD isdq ĐKTĐ T6 -1 T6 isd isq usd usd usα isα isβ isq isd usβ * * Đ iều K hiển B S_PC H ( IF O C ) Phần Đ ộng L ực SPIM + + ʃ ωsl ω ωe θ e * Eq.(3.8) ψrd^ isq * * r -+ Eq.(4.4) ω * r ψ * r ω r Figure. 3.1 IFOC control of the SPIM drive with BS_PCH controller Case 1: The quality survey in the transitional mode was carried out. Comparing with the obtained results of SPIM drives using PI controllers, it is easy to see that the control quality in the transient mode of SPIM drives using BS-PCH controllers has been significantly improved as Fig 3.2. 12 Figure 3. 2: Speed and torque response during speed reveral Case 2: Two tests are examined based on recommend [47]. In test 1, the reference speed changes without load, the results are shown in Fig. 3.3. and in test 2, the speed is fixed at 1000rpm during the survey time, the load torque of 100% is rated at 7s (instead of 75% rated load as [47]), the results are shown in Fig. 3.3, Fig 3.4. The simulation results show that the dynamic performance of the BS_PCH controller is very good. It does not appear the speed and current ripple, the controlled value converges and follow very rapidly the reference value during the survey period. The convergence time of the speed is significantly improved compared to the controller proposed in [47]. Figure 3. 3: The responses of SPIM drive when the reference speed changes without load 0 0.5 1 1.5 2 -1000 -500 0 500 1000 Time (s) S p ee d ( rp m ) Reference Measured (PI) Measured (BS-PCH) 0 0.1 0.2 0.3 0 500 1000 Time (s) S pe ed ( rp m ) Reference Measured (PI) Measured (BS-PCH) 1 1.2 1.4 -1000 -500 0 500 1000 Time (s) S pe ed ( rp m ) Reference Measured (PI) Measured (BS-PCH)0.168s 0.102 0.1025s 0.135s 0 0.5 1 1.5 2 -10 0 10 20 Time (s) T or qu e (N m ) TL Te (PI) Te (BS-PCH) 0 0.5 1 1.5 2 -5 0 5 Time (s) S ta to r cu rr en t is a (A ) isa (PI) isa (BS-PCH) 0 0.5 1 1.5 2 -5 0 5 Time (s) S ta to r cu rr en t i sd q ( A ) isq (PI) isq (BS-PCH) isd (PI) isd (BS-PCH) 0 0.5 1 1.5 2 0 0.5 1 Time (s) R ot or F lu x (W b) Phi rd (PI) Phi rd (BS-PCH) 0 2 4 6 8 10 0 500 1000 Time (s) S p ee d ( ra d /s ) Reference Measured 0 2 4 6 8 10 0 0.5 1 Time (s) R o to r F lu x ( W b ) Phi rd Phi rq 0 2 4 6 8 10 -10 0 10 Time (s) T or qu e ( N m ) TL Te 0 2 4 6 8 10 -5 0 5 Time (s) C ur re nt i sq (A ) Reference Actual 0 2 4 6 8 10 -2 0 2 Time (s) C u rr e n t is a (A ) Reference Actual 0.5 0.502 0.504 0.506 0.508 0.51 -500 0 500 Time (s) V co m ( V ) 0 0.1 0.2 0 500 1000 Sp ee d (r ad /s ) 0.292 0.294 992 994 996 998 1000 1002 13 Figure 3. 4: The responses of SPIM drive when the fixed reference speed with rated load To further verify and confirm the robustness of the BS_PCH controller against load disturbance, another survey was conducted with both PI and BS-PCH controllers for SPIM drive vector control as Fig 3.5. Figure 3. 5: Speed and torque responses of SPIM drive using PI and BS_PCH controller when facing load disturbance. Case 3: This test is carried out according to recommended Benchmark tests in [45]. From the results in Fig 3.6a show that the dynamic performance of the BS_PCH controller is very good, faster start time, lower overshoot and better ability to follow the reference speed than the proposed controller in [45]. Case 4: The extreme conditions are surveyed with the rotor resistance value was setup increased Rr' = 3Rr as in [45]. Fig. 3.6b show the speed, torque and current responses of the proposed BS_PCH vector control scheme, respectively. The BS_PCH controller works effectively, real speed follows and converges very fast with reference speed, tracking error is very small at load and is almost unaffected by the change of Rr. 0 2 4 6 8 10 0 500 1000 1500 Time (s) Sp ee d (r ad /s ) Reference Actual 0 2 4 6 8 10 -2 0 2 4 6 Time (s) Cu rre nt is q (A ) isq isd 0 2 4 6 8 10 -10 0 10 Time (s) To rq ue ( Nm ) TL Te 0 2 4 6 8 10 -4 -2 0 2 Time (s) C ur re nt is a (A ) 0 2 4 6 8 10 0 0.5 1 Time (s) Ro to r F lu x (W b) Phi rq Phi rd 8.5 8.502 8.504 8.506 8.508 8.51 -500 0 500 Time (s) V co m ( V ) 0 0.5 1 1.5 2 0 500 1000 1500 Time (s) S p e e d ( rp m ) Reference PI BS-PCH 0 0.05 0.1 0.15 0 500 1000 Time (s) S p ee d ( rp m ) Reference PI BS-PCH 1.5 1.55 1.6 800 1000 1200 1400 Time (s) S p ee d ( rp m ) Reference PI BS-PCH 0 0.5 1 1.5 2 -10 0 10 20 30 Time (s) T o rq u e ( N m ) TL Te (PI) Te (BS-PCH) 1 1.05 1.1 1360 1380 1400 1420 Time (s) S p ee d ( rp m ) Reference PI BS-PCH 0.5 0.55 0.6 1000 1200 1400 Time (s) S p ee d ( rp m ) Reference PI BS-PCH 0 0.5 1 1.5 2 -5 0 5 Time (s) S ta to r cu rr en t is a (A ) isa (PI) isa (BS-PCH) 0 0.5 1 1.5 2 0 0.5 1 Time (s) R o to r F lu x ( W b ) Phi rd (PI) Phi rd (BS-PCH) 0 0.1 0.2 0 1000 8 8.05 -2 0 2 14 a. b. Figure. 3.6 BS_PCH vector control with setting: a. Nominal rotor resistance; b. Rr*=3Rr 3.5 Conclusion This chapter presents a new approach to FOC control of SPIM. A RCMV_4S_CBPWM Vcommid common mode voltage reduction algorithm also has applied in SPVSI of this proposed drive. Two nonlinear controllers, one of Backstepping control (BSC) and the other Port Controlled Hamiltonian (PCH) define a new control structure for vector control of SPIM drive systemt, enables very good static and dynamic performance of SPIM drives (perfect tuning of the speed reference values, fast response of the motor current and torque, high accuracy of speed regulation), and robust for the machine parameter variations, load disturbances. 0 2 4 6 8 0 20 40 60 80 Time (s) S pe ed ( ra d/ s) Reference Measured 0 2 4 6 8 0 20 40 60 80 Time (s) S pe ed ( ra d/ s) Reference Measured 0 2 4 6 8 -10 0 10 Time (s) T or qu e (N m ) TL Te 0 2 4 6 8 -10 0 10 Time (s) T or qu e (N m ) TL Te 0 2 4 6 8 -2 0 2 4 6 Time (s) C ur re nt is dq (A ) isd isq 0 2 4 6 8 -2 0 2 4 6 Time (s) C ur re nt is dq (A ) isd isq 15 CHAPTER 4: DESIGN AN ADAPTIVE SPEED OBSERVER FOR SENSORLESS VECTOR CONTROL OF SPIM DRIVES 4.1 Introduction MRAS-based on speed observers have been successfully applied in the medium and high speed regions. However, zero and low speed operation is still a large challenge .... In this thesis, the author proposes a the stator reference model (SC_MRAS) based on speed observer using neural network (NN) and sliding mode (SM) to improve the performance of the speed observer and SPIM drive, especially at zero and low speed regions. The relevant research results have been published in the articles [1-5], [8-14] of the list of publications. 4.2 NN SM_SC_MRAS speed observer Converting from the VM voltage model and the CM current model, we obtained:      x xx = A x + B u (4.1)      x s x sA T A T -1x x sX k = e X k-1 + e - I A B u k-1   (4.2) The mathematical equation describles the adaptive mode of NNSM_SCMRAS oberserver using two layer NN with improved Euler is shown as follows:                                   sα 1 sα 2 sα 3 rd 4 rq 5 sα 6 sα 7 rd 8 rq sβ 1 sβ 2 sβ 3 rq 4 rd 5 sβ 6 sβ 7 rq ˆ ˆ ˆi k = w i k-1 + w u k-1 + w ψ k-1 + w ψ k-1 ˆ ˆ + w i k-2 - w u k-2 - w ψ k-2 - w ψ k-2 ˆ ˆ ˆi k = w i k-1 + w u k-1 + w ψ k-1 - w ψ k-1 ˆ + w i k-2 - w u k-2 -w ψ k-2  8 rdˆ+w ψ k-2        (4.3) 2 2 s s s m s s m s m s s s s mm m 1 2 3 4 r 5 6 7 8 r s r r s s r r s r s s r r s s r r s r s 3T R 3T L 3T 3T L 3T L 3T R T T LTL TL ˆ ˆw =1- - ; w = ; w = ; w = ω ;w = + ; w = ; w = ; w = ω 2σL 2στ L L 2σL 2στ L L 2σL L 2σL 2στ L L 2σL 2στ L L 2σL L where: The weights w1, w2, w3, w5, w6, w7 are calculated offline, while w4, w8 are updated online. Rearranging we have the equation of the adaptive model obtained in the predictive mode as follows:  rˆA ω k-1 = B (4.4) 4.2.1 Rotor Speed Estimation Algorithm From (4.4) shows that Ax ~ b is the linear regression problem. LS algorithm is obtained by minimizing the energy function:     T X T Ax-b Ax-b E = 1- ξ + ξx x (4. 5) 16 By applying the gradient descent algorithm to solve to the extreme finding problem, we have:            2r r rˆ ˆ ˆω k+1 =ω k - βγ k a k + ξ βγ k ω k   (4.6) (MHTC) SPIM NN (MHTN) Giải thuật LS us SM Nhận dạng từ thông Ước lượng Rs ψ ^ r i ^ s ω ^ rZ-1 Z-1 Z-1 Z-1 Z-1 Z-1 w1 w2 w3 w4 w5 w6 w7 w8 w1 w2 w3 w4 w5 w6 w7 w8 i ^ sα i ^ sβ is Rs ^ ω r ^ Z-1 Figure 4.1 NNSM_ SC_ MRAS speed observer 4.2.2 Rotor Flux identification and Stator Resistance Online Estimation Algorithm 4.2.2.1 Rotor Flux identification The rotor flux identifier is defined by the structure as following: r r sˆ ˆˆ ˆ ˆz = F(ω )z + G(u,ω ,z) + ΛI (4.7) where Ʌ is the gain matrix and Is is a vector defined by:   T s 1 2I = sat(s ) sat(s ) (4.8) From current model (CM), the flux estimation algorithm based on sliding- mode theory is defined: m rd sα rd r rq ψ s r r m rq sβ rq r rd ψ s r r L 1 ˆ ˆ ˆ ˆψ = i - ψ - ω ψ + Λ I τ τ L 1 ˆ ˆ ˆ ˆψ = i - ψ + ω ψ + Λ I τ τ                             (4.9) To v’<0,  has been chosen: rd rq ψ 1 1 3 ψ ψ 2 2 4 Λ 0 δ ε ε 0 Λ = = 0 Λ 0 δ ε ε              (4.10) 4.2.2.2 Stator Resistance Online Estimation In particular Rs is estimated on the basis of the isD, isD measured and estimated stator current components , by means of the following update law:    s sα sα sα sβ sβ sβ ˆdR ˆ ˆ ˆ ˆ= -μ i -i i + i -i i dt     (4.11) 17 4.3 Research results In order to verify and evaluate the performance of the BS_PCH controller and NNSM_SC_MRAS speed observer for the sensorless vector control of SPIM drive system as shown in Fig. 4.2, Tests verify and evaluate the performance of NNSM_SC_MRAS observer based on recommended benchmark tests in [58], [120], [128] [131]. Test 1: A. Low Speed Operation The results in Fig 4.3, Fig 4.4 show that the estimated speed follows the actual speed quite accurately even at a very low speed in both survey cases. Figure. 4.2 Sensorless vector control of SPIM drive using BS_PCH control and NNSM_SC_MRAS observer a. NNSM_SC_MRAS observer b. BPN_NN_SC_MRAS observer Fig 4. 3: The performance of SPIM DRIVE at low speed: Step Response Hình 4. 1: The performance of SPIM drive at low speed: Ramp Responses 0 2 4 6 -4 -2 0 2 4 6 Time (s) Sp ee d ( rad /s) Reference Measured Estimated 0 2 4 6 -4 -2 0 2 4 6 Time (s) Sp eed (ra d/s ) Reference Measured Estimated 0 0.5 1 1.5 2 2.5 3 3.5 -20 0 20 Time (s) S p e e d ( r a d /s ) Reference Measured Estimation 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4 -5 0 5 Time (s) S ta to r cu rr en t (A ) is anpha real is anpha ets is beta real is beta est 2 2.5 3 3.5 4 -5 0 5 Time (s) St at or c ur re nt (A ) isq Real isq Est isd Real isd Ets 0 0.5 1 1.5 2 2.5 3 3.5 0 0.5 1 Time (s) R ot or f lu x (W b) Phird real Phird est Phirq real Phirq est 2.32.42.5 1.9 2 2.1 2.32.42.5 1.9 2 2.1 0.8 1 1.2 -0.5 0 0.5 1 1.5 0.8 1 1.2 -0.5 0 0.5 1 1.5 2.3 2.4 2.5 1.9 2 2.1 2.3 2.4 2.5 1.9 2 2.1 0.8 1 1.2 -0.5 0 0.5 1 1.5 0.8 1 1.2 -0.5 0 0.5 1 1.5 0.7 0.8 13 14 15 16 Time (s) 18 Case 2: Dynamic performance survey of SPIM drives The simulation results in Fig 4.4 shows that the estimated speed and rotor flux responses are very good, The real speed, estimated closely follow the reference speed values. Low speed reversal (b) high speed reversal Hình 4. 2: Đáp ứng tốc độ và từ thông rotor Fig 4.5, Fig 4.6 and Fig 4.7 show the effectiveness of the proposed new control structure during the reversal. a. b. Figure 4. 4: Speed and torque response during high speed reversal. The observer using: a. BPN_NN_SC_MRAS; b. OLS_NNSM_SC_MRAS a. b. Figure 4. 5: Speed and torque response during medium speed reversal. The observer using: a. BPN_NN_SC_MRAS; b. OLS_NNSM_SC_MRAS 0 0.5 1 1.5 2 -10 0 10 Time (s) Sp eed (ra d/s ) Reference Measured Estimation 0 1 2 3 -100 -50 0 50 100 Time (s) Spe ed (ra d/s ) Reference Measured Estimated 0 0.5 1 1.5 2 -2 0 2 Time (s) Sta tor cu rre n ( A) 0 1 2 3 -4 -2 0 2 4 Time (s) Sta tor cu rre n ( A) 0 0.5 1 1.5 2 -2 0 2 4 Time (s) Sta tor cu rre nt (A ) isq Real isq Est isd Real isd Est 0 1 2 3 -5 0 5 Time (s) Sta tor cu rre nt (A ) isq Real isq Est isd Real isd Est 0 0.5 1 1.5 2 0 0.5 1 Time (s) Ro tor flu x ( W b) Phird Real Phird Est Phirq Real Phirq Est 0 1 2 3 0 0.5 1 Time (s) Ro tor flu x ( W b) Phirq Real Phirq Est Phirs Read Phirq Est 0.9 1 1.1 1.2 1.3 1.4 -100 0 100 Time (s) Sp eed (ra d/s ) Reference Measured Estimated 0.197s 0.9 1 1.1 1.2 1.3 1.4 -100 0 100 Time (s) Sp ee d ( rad /s) Reference Measured Estimated 0.1s 0.9 1 1.1 1.2 1.3 1.4 -10 0 10 Time (s) Er ror (ra d/s ) 0.9 1 1.1 1.2 1.3 1.4 -10 0 10 Time (s) Er ror (r ad /s) 0.9 1 1.1 1.2 1.3 1.4 -50 0 50 Time (s) Sp ee d ( rad /s) Reference Measured Estimated 0.101s 0.9 1 1.1 1.2 1.3 1.4 -50 0 50 Time (s) Sp ee d ( rad /s) Reference Measured Estimated 0.052s 0.9 1 1.1 1.2 1.3 1.4 -10 0 10 Time (s) Er ro r ( rad /s) 0.9 1 1.1 1.2 1.3 1.4 -10 0 10 Time (s) Er ro r ( rad /s) 0.9 1 1.1 1.2 1.3 1.4 -10 0 10 i e (s) Er ror (r ad /s) 0.9 1 1.1 1.2 1.3 1.4 -10 0 10 Time (s) Er ror (r ad /s) 19 a. b. Figure 4. 5: Speed and torque response during low speed reversal. The observer using: a. BPN_NN_SC_MRAS; b. OLS_NNSM_SC_MRAS Case 3: Stator resistance variations Rs: This test is based on bandmark in [128] but the survey expanded RS value changed 150-200% nominal Rs values at 1.5s, 3.8s, respectively. The SPIM drive works with 100% rated load. Fig. 4.6 shows the speed response, estimation error, torque, estimated resistance, rotor flux. The system works stably. Observing the simulation results show that the performance of the SPIM drive system is quite good in this cases, the control and parameter estimation strategies give the good responses, sustainably with parameter changes. Simulation results confirm the dynamic performance of the proposed scheme. Figure 4. 3: Sensorless control under motor parameter variation condition (Rs) Case 4: Four Quadrant Operation From the simulation results in Fig 4.8, Fig 4.9 show that the speed response and the ability to track according to the reference speed, the estimation errors are well controlled, there is no flux and speed fluctuation in any of the recorded operating modes. The performance of the proposed drive in the four quadrants is very good. 0 0.5 1 1.5 2 -15 -10 -5 0 5 10 15 Time (s) Spe ed (ra d/s ) Reference Measured Estimated 0 0.5 1 1.5 2 -15 -10 -5 0 5 10 15 Time (s) Sp eed (ra d/s ) Reference Measured Estimated 0 0.5 1 1.5 2 -10 -5 0 5 10 Time (s) Spe ed e rror (ra d/s) 0 0.5 1 1.5 2 -10 -5 0 5 10 Time (s) Spe ed err or ( rad /s) 0 1 2 3 4 5 6 7 -5 0 5 10 15 20 25 Time (s) Sp ee d (r ad /s ) Reference Measured Estimates 0 1 2 3 4 5 6 7 1 2 3 4 5 6 7 Time (s) T o rq u e (N m ) Reference Measured 0 1 2 3 4 5 6 7 -5 0 5 Time (s) Sp ee d er ro r ( ra d/ s) 0 1 2 3 4 5 6 7 0 0.5 1 Time (s) Ro tor flu x ( W b) Phird Phirq 0 1 2 3 4 5 6 7 5 10 15 20 25 Time (s) St at or re si st an ce R s Reference resistance various Estimated resistance Rs 1.5 Rs 2 Rs 2.5 2.51 2.52 2.53 2.54 2.55 2.56 -500 0 500 Time (s) Vc om (V ) 2 2.5 3 3.5 4 -10 0 10 Time (s) To rq ue (N m ) Tl Te 2 2.5 3 3.5 4 -10 0 10 Time (s) Sp ee d (r ad /s ) Reference Measured Estimation 1.45 1.5 1.55 18 20 22 3.75 3.8 3.85 10 12 14 20 Figure 4. 4: SPIM drive operation in four quadrants Figure 4. 5: Speed response in the motor and regenerating mode a. NN_SC_MRAS observer using CM based on rotor flux identifier[130] b. NN_SC_MRAS observer using SM based on rotor flux identifier The robustness of the proposed SPIM drive under load disturbance effects has also surveyed as shown in Figure 4.11. Fig 4. 6: Speed and torque responses at 100 rad/s under load disturbance 4.4 Conclusion In Chapter 4, the author successfully built the adaptive speed observer using neural network, sliding control combination with BS_PCH controller and RCMV_4S_CBPWM Vcommid common mode voltage reduction algorithm for sensorless control of SPIM drive. Through simulation results have been proved that NNSM SC_MRAS speed observer has worked correctly at zero and low speed regions, there is no instability phenomenon in the regenerative mode, robust and stable working system, unaffected by changes of motor parameters and load disturbance. 2 2.5 3 3.5 4 -5 0 5 Time (s) St at or c ur re nt (A ) isq Real isq Est isd Real isd Ets 2 2.5 3 3.5 4 0 0.5 1 Time (s) Ro to r f lu x (W b) Phird real Phird ets Phirq real Phirq ets 2 2.5 3 3.5 4 4.5 5 -60 -40 -20 0 20 40 Time (s) Sp ee d ( rad /s) Reference Measured Estimated 2 3 4 5 -60 -40 -20 0 20 40 Time (s) Sp eed (ra d/s ) Reference Measured Estimated 0 2 4 6 8 0 50 100 Time (s) S p e e d ( ra d /s ) Reference Measured Estimated 0 2 4 6 8 -5 0 5 10 15 Time (s) T o rq u e ( N .m ) TL Te 0 1 2 3 4 5 6 7 8 -5 0 5 Time (s) E rr o r (R ad /s ) 0 2 4 6 8 -2 0 2 4 6 Time (s) C u rr en