Robust Speed Control of Induction Motor Drives Using ... - IEEE Xplore

This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TIA.2014.2330062, IEEE Transactions on Industry Applications

Robust Speed Control of Induction Motor Drives Using First-order Auto-Disturbance Rejection Controllers Jie Li, Hai-Peng Ren, Member, IEEE, and Yan-Ru Zhong

Abstract -- A novel robust control scheme employing three first-order Auto-Disturbance Rejection Controllers (ADRC) is presented for the speed control of induction motor drives. Compared with the existing high-order ADRC based speed control structures, the proposed method does not need to estimate the rotor flux. As a result, the implementation of the proposed scheme on Digital Signal Processor (DSP) is easier, and the runtime of the proposed ADRC control algorithm is shorter. The simulation results show that the proposed control scheme can cope with the internal disturbance and external disturbance, such as the motor’s parameter variations, the load disturbances, etc. A TMS320F2812 DSP based prototype using the proposed control scheme was developed. The comparative experimental results show that the robustness of the proposed ADRC system are obviously better than the conventional PI system when various disturbances occur, and the scheme is feasible and effective. 1 Index Terms-- induction motor; auto-disturbance rejection controller; robust control; vector control

I.

INTRODUCTION

Induction motors can be controlled similarly as DC motors using the field-oriented control (FOC) (also called vector control) approach, and the performances of the controlled induction motors with FOC are comparable to those of the DC motors. With the development of the power electronics elements and the high performance microprocessor, induction motor drives employing FOC and conventional proportional-integral (PI) regulators have been commercialized. However, the performances of the PI regulator based FOC suffers from the induction motor parameters’ mismatch or variation with time [1]. In addition, when the load disturbances present, the PI controller scheme has a long recovery period. Generally speaking, the requirements of the motor speed control system are the accuracy, the rapidity, the robustness, and so on. To satisfy these performance requirements of the industry drive system, electrical engineers use two ways: one way is using the on-line parameter identification to estimate the corresponding parameters in the FOC; the other way is using the robust controller to replace the conventional PI regulator to get better performance. During the past few decades, many on-line parameter identification methods have Jie Li, Hai-Peng Ren, and Yan-Ru Zhong are with the School of Automation and Information Engineering, Xi’an University of Technology, 710048 Xi’an, China (e-mail: [email protected]; [email protected]). This work is supported in part by NSFC (50907054); SRFDP (20126118110008); IRT of Shaanxi Province (2013KCT-04); NSRP of Educational Affairs Committee of Shaanxi Province (2013JK0995); SRICP of Shaanxi Province (2013KW05-02); SFKD of Shaanxi Province (00X901).

been proposed for FOC [2]. But, the parameters of the system are inherently dependent on each other, as the result, more parameters are needed to be identified, which increases the complexity of the algorithm and the difficulty of real time applications. In order to directly aim at the original goal, i.e. to improve the control performances of the drive systems, researchers attempted various kinds of robust controllers to cope with the parameter uncertainty, at the same time, not to degrade the accuracy and the rapidity of the speed control. For example, an adaptive robust control strategy was proposed in [3] to increase robustness to parameters variation and load disturbance for sensorless field-oriented controlled induction motor drives. A back-stepping controller based on the exact model of induction motors was proposed in [4], meanwhile, the Extended State Observer (ESO) was employed to improve the robustness to the uncertainty of the system. The neural-network based robust control schemes were proposed to obtain a robust speed control of induction motor drives in [5][6]. The ADRC was proposed by Han in 1998 [7-9]. The ADRC is a nonlinear controller for an uncertain system, it estimate and compensate the external disturbances and parameter variations, as a consequence, the accurate model of the plant is not required. It means that the design of ADRC is inherently independent of the controlled system model and its parameters. Bogdan M. Wilamowski, former editor-in-chief of IEEE Transactions on Industrial Electronics, pointed out “ADRC turns modern control theory on its head. The implication of this change of direction proved to be enormous both in theory and practice.”[9] As one of the simple robust control methods to deal with the uncertainty, ADRC attracts much attention in many technical fields [10-25], especially in the field of the motor control [14-25]. A second order ADRCs was proposed for the speed control of the Brushless DC motor [14, 15]. ADRC was used for direct torque control of permanent magnet synchronous servo motor [16]. Besides speed control, ADRC was also applied to speed estimation to improve the robustness of the estimation algorithms [17]. Many ADRC-based research works have been done to improve the robustness of the induction motor speed control [18-25]. The ADRC based speed control scheme for the induction motor drives has the advantage of good robustness to parameter uncertainty and external disturbance. The first scheme of speed control of induction motor based on ADRC was proposed in [18] and applied in [19-21]. In this scheme, two first-order ADRCs were used to control the rotor speed and the quadrature component of the stator current, respectively, and one second-order ADRC was used to

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regulate the rotor flux. A four-ADRCs configuration was proposed for the speed control of the induction motor fed by a matrix converter (MC) [22]. Two second-order ADRCs were used to regulate the rotor speed and the quadrature component of the stator current, respectively, and one thirdorder ADRC was used to regulate the rotor flux in [23] to achieve robust speed control of induction motor. Two second-order ADRCs were employed for the speed and rotor flux control of the induction motor [24]. Two conventional PI regulators were used for the torque current and magnetizing current control, meanwhile two second-order ADRCs were used for speed control [25]. Most of the aforementioned works on induction motor control are limited to simulation results. All these existing schemes using ADRCs require the estimation of the rotor flux, therefore, the real time computing cost is increased when the algorithms are implemented on Digital Signal Processors (DSPs). Furthermore, the existing works usually use the second-order (or third-order) ADRCs including the third-order (or fourth-order) dynamical equations for ESO. Consequently, the complexity of the entire control algorithm is dramatically increased. In this paper, a novel control scheme based on three firstorder ADRCs is presented. The rotor flux estimation is

removed to reduce the runtime of the proposed ADRC control algorithm. Because the order of ADRC is low and the flux estimation is removed, the DSP code implementation of the proposed method is easier, and the code running time is shorter as well. Simulation results show that the proposed simplified ADRC robust speed control scheme provide strong ability to resist the uncertainties, such as external load disturbances and motor parameter variations. Experimental results also show the feasibility and effectiveness of the proposed method. This paper is organized as follows: the robust control scheme using three first order ADRCs is given for induction motor speed control in Section Ⅱ; The robust performances of the proposed scheme are tested by simulation in Section Ⅲ; Experimental results on experimental bench are given in Section Ⅳ to show the effectiveness of the proposed method. Conclusion remarks are given in Section Ⅴ. THREE FIRST-ORDER ADRCS CLOSED-LOOP SPEED CONTROL OF INDUCTION MOTORS

II.

For the FOC scheme of induction motors, three control loops, including the quadrature axis (q-axis) current loop, the direct axis (d-axis) current loop and the speed loop, are udc

* ψ d2 +

− * + iq1 − iq1

ωr* + −

ωr

usα*

* ud1

αβ

Sa Sb Sc

usβ*

* uq1

isα

dq

abc αβ

isβ

isa isb isc

^

θ ^

usα usβ

ψ d2

Sa,b,c udc

(a) Example of control systems using high order ADRCs

udc * iq1 +

ωr* +

−

ωr ωr*

ψ d2*

usα*

* ud1

− * 1 id1 + Lm −

iq1

αβ * uq1

id1

dq

Sa Sb Sc

* sβ

u

isα

isβ

abc αβ

isa isb isc

(b) Proposed scheme based on three first-order ADRCs Fig. 1 Comparison of the scheme using higher order ADRC and our proposed scheme



considered. Figure 1(a) shows an example of the induction motor speed control system using high order ADRCs, which consists of two second-order ADRCs for the speed control and q-axis current control, respectively, and one third order ADRC for the d-axis current control. Meanwhile, the flux estimator is needed to get the information about flux and rotor angle. Figure 1 (b) gives the proposed scheme using three first order ADRCs for the speed control of induction motors, where three first order ADRCs are used for the three control loops of the system. It can be seen from Fig.1 that the proposed control scheme is simpler in the sense of using lower order ADRCs, which means the lower order of dynamical equation to be solved, and that the removal of the flux estimator further reduces the complexity of the control algorithm. The proposed speed control scheme employs three different first-order ADRCs for rotor electrical angular speed ωr regulation, direct component of stator current id1 regulation and quadrature component of stator current iq1 regulation. It means that the proposed control scheme use open loop control for the rotor flux. The motivation of using open loop flux control is to reduce the complexity of the control algorithm when it is implemented on DSP.

v

x1

e1

z1

u0

u

y

z2

Fig. 2 Block diagram of first-order ADRC

As shown in Fig. 2, each first-order ADRC is composed of three parts: 1) Nonlinear Differentiator (ND), 2) ESO, and 3) Nonlinear State Error Feedback control law (NLSEF). The ESO in the ADRC can be treated as a kind of dynamic feedback linearization mechanism. Its structure and performance are not determined by the model of the system under control, but only by the range of its variation rate. Therefore, the ESO is robust to the system model uncertainty. The role of ND is to define a desirable transition response for the step input. The ND can smooth the sudden change of the input signal in order to decrease the overshoot of the output response during the transient state. These factors make ADRC get a good balance between the fast transient response and the small overshoot. On the contrary, for the conventional PID controller, it is hard for tuning parameters to achieve this point. The NLSEF gives the control law u0 to drive the state trajectory to track the desired reference. Now, we explain how to design the three first-order ADRCs as follows: A. ADRC for Speed Regulation The mathematical model of the speed control loop is

ω& r = k1ψ d 2iq1 + w1 (t ) ,

(1)

where k1 = P 2 Lm / JL2 and w1 (t ) = − PTL / J , ψd2 is the d-axis rotor flux linkage, iq1 is the q-axis stator current, P is the number of pole pairs of the motor, J is the rotor inertia, Lm is the mutual inductance, L2 is the rotor inductance, and TL is the load torque. The load torque TL and the coupling term between the speed loop and flux loop can be treated as the “disturbances” when we design the ADRC for the speed loop. These disturbances can be compensated by the ESO given as e( k ) = z1 ( k ) − y ( k ) ⎧ ⎪ ⎨ z1 (k + 1) = z1 ( k ) + h( z2 ( k ) − β1 fal (e( k ), α1 , δ1 ) + bu ( k )) , ⎪ z 2 ( k + 1) = z 2 ( k ) − hβ 2 fal (e( k ), α1 , δ1 ) ⎩ (2) where function fal(e(k),α,δ) is a nonlinear function given as

⎧⎪ e( k ) α sgn(e( k )), e( k ) > δ , fal (e( k ), α , δ ) = ⎨ 1−α ⎪⎩ e( k ) / δ , e(k ) ≤ δ y(k) is the output signal of the system (plant) to be controlled. For the speed loop, y(k) is the speed ωr (as shown in Fig. 1), z1(k) is the estimation of the system state, z2(k) is the estimation of the disturbances. ESO has four adjustable parameters: α1, δ1, β1 and β2. The range of α1 is from 0 to 1; the smaller the α1 is, the better the ability of the ESO against the uncertainty of the induction motor model and the disturbances is. δ1 is the width of linear area of the nonlinear function. The system dynamic performances are affected tremendously by the β1 and β2. β1 mainly has effect on the estimation of the system state, and β2 mainly affects the estimation of the disturbances. The larger the β1 and the β2 are, the faster the estimation converges, on the other hand, if the β1 and the β2 are too large, the estimation might not converge. The ND is given as x1 ( k + 1) = x1 ( k ) + hx2 ( k ) ⎧ , ⎨ ⎩ x2 (k + 1) = x2 ( k ) + hfst ( x1 ( k ) − v( k ), x2 ( k ), r , h0 )

(3)

where the nonlinear function can be represented by ⎧ ra ( k ) / d , a (k ) ≤ d , fst ( p1 ( k ), p2 ( k ), r , h0 ) = − ⎨ ⎩ r sgn(a ( k )), a ( k ) > d 1

ytd ( k ) = p1 ( k ) + h0 p2 ( k ) , a0 ( k ) = ( d 2 + 8r ytd ( k ) ) 2 ,

⎧ p2 ( k ) + ( a0 (k ) − d ) / 2, ytd ( k ) > d 0

a (k ) = ⎨

⎩ p2 ( k ) + ytd (k ) / h0 , ytd ( k ) ≤ d 0

,

d = rh0 , d 0 = dh0 , v(k) is the reference signal of the ADRC, for the speed loop, v(k) is the speed reference ωr* (as shown in Fig. 1), x1(k) is the tracking signal of v(k), x2(k) is the derivative of x1(k), also approximately the derivative of v(k), h is the step size. ND is used to arrange transition procedure when tracking the



⎧ e1 ( k ) = x1 ( k ) − z1 (k ) ⎪ ⎨u0 ( k ) = β 3 fal (e1 (k ), α 2 , δ 3 ) , ⎪ u (k ) = u (k ) − z (k ) / b ⎩ 0 2

(4)

where u(k) is the control output of the ADRC, for the speed loop, u(k) is the q-axis stator current reference iq1* (as shown in Fig. 1). α2 and δ3 possess the similar meanings as that of α1 and δ1 in (2). β3 governs the speed of the system response, however, if β3 is too large, a big overshoot would appear. B. ADRC for q-axis Current Loop The mathematical model of the q-axis stator current is (5) i&q1 = − k2 iq1 + w2 (t ) + uq1 / Lσ , where k2 = ( R1 L22 + R2 L2m ) / Lσ L22 , w2 (t ) = − Lmψ d 2ωr / Lσ L2 − id 1ω1 , Lσ = L1 − L2m / L2 , uq1 is the q-axis stator voltage. R1, R2 are stator resistance and rotor resistance, respectively. L1 is the stator inductance, Lσ is leakage inductance. ωr is rotor angular speed. ω1 is synchronous angular speed. It can be seen from (5) that the “disturbance” w2(t) contains the coupling terms, i.e., the product of the rotor flux ψd2 and the rotor angular speed ωr, and the product of the daxis stator current id1 and synchronous angular speed ω1.If a PID controller was used, the performances of the system will be degraded because of this nonlinear coupling terms. However, the ADRC can estimate the disturbance and cope with the effect of this coupling term to get better performance. The ADRC used in q-axis current loop is similar to that of the speed loop ADRC except the input and output shown in Fig.1 (b).

C. ADRC for d-axis Current Loop The mathematical model of the d-axis stator current control loop is i&d 1 = −k2 id 1 + w3 (t ) + ud 1 / Lσ , (6) where w3 (t ) = k3ψ d 2 + iq1ω1 , k3 = R2 Lm / Lσ L22 , id1 is the d-axis stator current, ud1 is d-axis stator voltage. Here, w3(t) is treated as disturbance, which contains the coupling term, i.e., the product of the synchronous angular speed ω1 and the q-axis stator current iq1. The rotor resistance is also considered in the disturbance, and it is subjected to the variations of operation conditions of induction motors. ADRC can automatically estimate all these disturbances and compensate them to achieve better performance. The ADRC

for d-axis current loop is designed using the similar way as that in the speed loop, which is omitted for simplicity. III.

SIMULATION RESULTS

To show the performance of the proposed control scheme, an MATLAB/Simulink model [26] has been established for a 1.1kW induction machine driven by a Voltage Source Inverter (VSI) using the proposed scheme. Each first-order ADRC is written by an S-function with C code. The parameters of the squirrel-cage induction motor are listed as following: PN=1.1kW, UN=380V, IN=2.67A, fN=50Hz, R1=5.27Ω, R2=5.07Ω, RFe=1370Ω, L1=479mH, L2=479mH, Lm=421mH, σ =0.228, TN=7.45Nm, P=2, nN=1410r/min. We have investigated the robustness of the proposed scheme under the following three cases 1) load disturbance; 2) the motor parameter variations; 3) the model uncertainty. The proposed method is compared to the vector control based on the traditional PI regulators. In the simulation, both the adjustable parameters of the ADRC and those of the PI system have been manually tuned to their desirable values. It can also be done by the method proposed in [15]. A.

Load Disturbance Performance

Speed/(r/min)

reference signal. There are two adjustable parameters in the ND: r and h0. r is the convergence rate coefficient. The larger the r is, the faster the procedure that x1(k) converges to ωr* is. h0 is a filtering factor used for the noise filtering. According to the output of the ND and the ESO, the NLSEF gives the control to the corresponding loop:

(a)

(b) Fig. 3 Comparative simulation result when load torque disturbances occur with speed reference is 1300 r/min, (a) load torque steps up from no load to the rated load at 1.5s, (b) load torque steps down from the rated load to no load at 3s.

Figure 3 shows the comparative simulation results when the load torque disturbance occurs, Figure 3 (a) shows the speed response when the load torque steps up from no load to the rated load (1pu) at 1.5s, and Figure 3 (b) shows the speed response when the load torque steps down from the rated



B. Parameter Variation Performance To evaluate the rapidity and the accuracy of control algorithms, the step response of reference variation or the step response of disturbance is usually observed, because the step signal contains the most abundant frequency components. For induction motor drive systems, if wound-rotor induction motors were selected, the rotor resistance maybe suddenly increases or decreases. Although, the rapid parameter variation is not the general case, the step variation of the rotor resistance is still chosen here to do the comparative simulation, in order to evaluate the proposed ADRC scheme under the worst operation condition. A simulation motor model [26] with a varying rotor resistance is used to simulate the performance of the proposed scheme. Figure 4 shows the comparative simulation results when the motor parameter varies. The solid line, i.e. the smoother one, is the speed response of the proposed ADRC scheme, and the dash line, i.e. the oscillating one, is the speed response of the conventional PI controller. The operation

Speed/(r/min)

condition is same for both controllers, i.e. the speed reference is 1pu, and the load torque is 1pu. The motor parameters are given as the foregoing parameter list. The rotor resistance steps up from 1pu to 1.5pu at 4s and down to 1pu again at 6s. In fact, it is almost impossible in the practical situation that the rotor resistances suddenly increase or decrease for the squirrel-cage induction motor. But for the purpose of evaluating the robustness, step changes of the rotor resistance is chosen in simulation. As seen in Fig.4, when the rotor resistance suddenly changes, the proposed scheme is more robust than the conventional PI control. The ADRC system is able to quickly complete the adjustment process, and stabilize at the reference speed again, while, the PI control demonstrates a speed oscillation when the motor parameter changes. Comparative simulations under the conditions that other motor parameters change have been done, the conclusion is that the ADRC is more robust than the PI control when the motor parameters change.

Fig. 4 Comparative simulation result when rotor resistance steps up and down

C. Model Uncertainty Performance The motor model considering the iron loss [26] is used to simulate the model uncertainty [19]. Both PI controller and the proposed ADRC(s) are designed according to the ideal motor model (i.e. without considering the impact of the nonideal factors such as magnetic saturation and iron loss). In fact, an actual motor cannot behave as we expect, so the electrical engineers have to use more robust control method to get the desirable performance under the undesirable condition.

Ψq2/Wb

load to no load at 3s. In Fig.3, the speed reference is 1300r/min, The motor parameters are constant during the simulations. As seen in Fig.3, in the steady-state performance aspect, the ADRC system can always settle down to the speed reference value without steady-state error, while the steady-state error of the PI system increases when the load is heavier, even up to 1.3% under rated load. This shows that the ADRC system has better robustness compared with the PI System from viewpoint of load disturbances. In the dynamic performance aspect, the ADRC system always has larger overshoot than the PI system in the simulation results, the reason is the linearization mechanisms of them are essentially different: the PI regulator depends on the field oriented to realize the decoupling of the torque control and the flux control, when the rotor flux direction coincides with the daxis, under this circumstance, the induction motor can be treated as a ‘linear’ system. However, in ADRC control scheme, the ESO, a core component of ADRC, estimate the internal and the external disturbances as the “total disturbance” in real-time, then compensate it. As a result, the system is dynamically linearized. In simulation model, the PI system use the exact parameters, which means that the parameters used in the vector control scheme match very well with the motor, so the dynamic performance could be perfect if the parameters of the PI regulators optimized. On the contrary, the dynamic performance of the ADRC depends on the dynamic performance of its ESO, when the load suddenly increases or decreases, the disturbances in (1), (5) and (6) of the three ADRCs will also change suddenly, the ESOs will undergo transient state to estimate the disturbance and to track reference. Therefore, even the ADRC parameters are good, the simulation results will inevitable overshoot when load torque steps up or down heavily in high speed range. In practice, the experimental results in Section IV show that when load torque steps up or down, the PI system also overshoot because of inexact parameters used in the PI controller, i.e., the parameter mismatch.

Fig. 5 Comparative simulation result when modeling error exists

Figure 5 shows the comparative simulation results when the iron loss exists in the model, while the controller design procedure did not take into it account. The solid line is the



response of the proposed scheme, and the dashed line the PI system. The operation condition is same for both schemes, i.e. the speed reference steps up from 0.4pu to 0.8pu at 5s, and the load torque is full load throughout the simulation. The motor parameters including the iron loss equivalent resistance are set as the parameters listed above. If the flux control and the torque control of the induction motor are decoupled completely, the q-axis component rotor flux should be zero at the steady state. As seen in Fig.5, both the ADRC and the PI control do not make the q-axis component rotor flux to be zero, but the steady-state error of the q-axis rotor flux of the ADRC is obviously less than that of the PI control. It means that the decoupling degree of the proposed scheme is better than that of PI control. IV.

TD: r = 60, h0 = 0.01; ESO: α1 = 0.5, δ1 = 0.2, β1= 20, β2= 400, b0 = 11; NLSEF: β3= 10, δ2 = 0.2, α2 = 0.75. 2) q-axis current loop ADRC controller TD: r = 400, h0 = 0.01; ESO: α1 = 0.5, δ1 = 10, β1= 10, β2= 600, b0 = 300; NLSEF: β3= 10, δ2 = 10, α2 = 0.75. 3) d-axis current loop ADRC controller TD: r = 200, h0 = 0.01; ESO: α1 = 0.5, δ1 = 0.1, β1= 30, β2= 600, b0 = 940; NLSEF: β3= 1, δ2 = 0.1, α2 = 0.75.

EXPERIMENTAL RESULTS

The experimental bench is built based on the core of TMS320F2812 DSP, the actual motor has the same nominal parameters as that used in the simulations. The ADRC algorithm was written in mixed C language and assembly language in order to improve the execution speed, the execution time of each ADRC is about 50μs. The sampling periods of the current loops and the speed loop are 250μs so that the code for ADRC can be real time executed.

(a)

Disturbance occurs

Rotor speed

(400r/min)/div Stator current

1 2

5A/div

1s/div (b)

Fig. 6 Photo of the experimental bench

Compared with the conventional PI regulators, the ADRCs have more parameters to be tuned. But, once these parameters are set appropriately, it is effective all over the speed range and load condition. For the conventional PI systems, it always need several proportion coefficient and integral coefficient sets to obtain the desired speed control performance in different speed ranges for the same induction motor. From this point of view, the ADRC also has its superiority. On the other hand, some parameters in the ADRCs have their empirical values, e.g. α1, α2, h0 etc., so the tuning procedure of the ADRC parameters is easier than our imagination. Using trial and error method, the ADRCs parameters are set as follows: 1) Speed ADRC controller

Fig. 7 Comparative experimental results when load torque disturbance occurs (speed reference is 1300 r/min, load torque steps down from rated load to no load, (a) ADRC system (b) PI system)

Figure 7 shows the comparative experimental results of the proposed scheme and the conventional PI control. The speed reference is 1300 r/min, load torque steps down from the rated load to no load at the marked places in the figures. In Figs. from 7 to 10, CH1 is the measured rotor speed curve and CH2 is the measured stator current curve. It can be seen from Fig. 7 that because the speed is relatively high, and the load torque perturbation is relatively strong, as mentioned in Section III, the ADRC system will inevitable overshoot when load torque steps up or down heavily in high speed range. On the other hand, different from the simulation results, the PI control overshoots obviously even more than the proposed scheme. The reason is that in simulation model, the parameters of the plant and the controller are matched well, but in practice, it is impossible. Under this practical case, the proposed method has better performance.



In the middle speed range and the low speed range, the ADRC system shows very attractive performances, it is much better than the PI system. When load torque disturbances occur, the PI system still needs relatively longer settling time and the speed variation is obvious during the transient state, on the contrary, the speed of the ADRC system almost does not vary when load is stepped up or down. Figure 8 gives the comparative experimental results under the condition that the speed reference is 1000 r/min, and load torque steps up from no load to 0.8pu load. The speed of the ADRC system seems to be fluctuated to a very small extent, but, the PI system spends more than 3s to settle down and has about 80 r/min transient speed decreasing. The similar situation can be observed in the Figure 9 and the Figure 10. Figure 9 shows the comparative experimental results under the condition that the speed reference is 700 r/min, and load torque steps up from no load to 0.6pu load. Fig. 10 shows the comparative experimental results under the condition that the speed reference is 700 r/min, and load torque steps down from rated load to no load. It can be seen that, when the speed reference is in the middle speed range or in the low speed range, the ADRC system has a very short settling down time and far smaller speed fluctuation amplitude than those of the conventional PI control. Therefore, the conclusion can be drawn that the performance of the control system has been improved via the state observation, the real-time “disturbance” estimation and compensation, the ADRC controller indeed plays a role of “anti-disturbance”.

(a)

Disturbance occurs

1

Rotor speed

(400r/min)/div

Stator current

2

5A/div

1s/div (b) Fig. 9 Controlled experimental result when load torque disturbance occurs (speed reference is 700 r/min, and load torque steps up from no load to 0.6pu load, (a) the proposed scheme (b) conventional PI control)

Disturbance occurs Rotor speed (400r/min)/div Stator current

1 2

5A/div

1s/div (a)

(a)

Disturbance occurs

1

Rotor speed

(400r/min)/div

Stator current

2

5A/div

1s/div (b)

(b)

Fig. 8 Controlled experimental result when load torque disturbance occurs (speed reference is 1000 r/min, and load torque steps up from no load to 0.8pu load, (a) the proposed scheme (b) conventional PI control)

Fig. 10 Controlled experimental result when load torque disturbance occurs (speed reference is 700 r/min, and load torque steps down from rated load to no load, (a) the proposed scheme (b) conventional PI control)



Parameter varies

the upper curves in both (a) and (b) are the measured rotor speed and the lower curves in both (a) and (b) are the measured q-axis stator current. It can be seen that the proposed scheme has obviously shorter settle down time and smaller speed fluctuation amplitude than the conventional PI control when rotor resistance disturbance occurs.

Rotor speed

(400r/min)/div

V.

q-axis stator current 1 2

2A/div 100ms/div (a)

(b) Fig. 11 Controlled experimental result when rotor resistance steps up from 1pu to 2pu (speed reference is 1410 r/min, load torque is 1pu, (a) the proposed scheme (b) conventional PI control)

As mentioned in Section III, practically, it is unlikely that the rotor resistance can suddenly increase or decrease for squirrel-cage induction motor. In order to experimentally evaluate the robustness against the parameter variation, there are two choices: 1) replace the squirrel-cage induction motor used in the experiments with a wound-rotor induction motor, then, the rotor resistance can be changed by connecting a three-phase symmetric resistance in series with the rotor; 2) replace the induction motor used in the experiments with a soft motor, that is DSP program simulating the behaviors of the induction motor. The soft motor uses D/A of DSP to give the outputs representing currents, voltages and speed of the real motor, etc. That is semi-physical simulation. Here, we choose the latter one. The program module of the soft motor comes from the official website of TI company, and the correctness of the program module had been verified via comparison study. By this way, step variations of the rotor resistance can be implemented by the soft motor to test the performance under parameter variations. Here, we used the variation from 1pu to 2pu to simulate the extreme case of the parameter variation, which did not indicate that the practical motor can behave like this. If, in this extreme case, the proposed scheme could get nice performance, the small amplitude of the variation can also be solved by the proposed scheme. Figure 11 shows the semi-physical motor experimental results when the rotor resistance in DSP simulated induction motor suddenly increases from 1pu to 2pu. The operation condition is the rated speed and rated load torque. In Fig.11,

CONCLUSIONS

A novel control scheme employing three first-order ADRCs is presented in this paper for the robust control of induction motor drives fed by VSIs. Because the orders of the ADRCs are the lowest ones and the removal of the flux observer, the corresponding ADRC algorithms are simpler and have faster running speed compared to the existing ADRC(s) schemes. This is very important for real time application. Simulation and experiment results show that the robustness of the proposed method with the reduced order ADRCs is better than the conventional PI control under the variant internal and external disturbances. This simple ADRCs scheme is suitable for improving the commercial DSP based inductor control system performance without increasing the hardware cost. REFERENCES [1] [2] [3]

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Jie Li was born in Shaanxi, China, in 1976. She received the B.S. degree in applied electronics technology from Xi’an University of Technology, Xi’an, China, in 1997. She received the M.S. and the Ph. D. degrees in electrical engineering in 2000 and 2006, respectively. She is currently an Associate Professor with the Department of Electrical Engineering, Xi’an University of Technology, Xi’an, China. Her research interests are in high performance ac drive systems and its efficiency optimization. Hai-Peng Ren (M’06) was born in Heilongjiang, China, in 1975. He received Doctoral degree in electrical engineering from Xi’an University of Technology, Xi’an, China, in 2003. He currently works as a full professor in Xi’an University of Technology. He worked as a visiting researcher in the field of nonlinear phenomenon of power converters in Kyushu University, Kyushu, Japan, from April 2004 to October 2004. He worked as post PH.D. research Fellow in the field of time-delay system in Xi’an Jiaotong University from December 2005 to December 2008. He worked as an honorary visiting professor in the field of communication with chaos and complex networks in University of Aberdeen, Scotland, from July 2010 to July 2011. He obtained National Invention Award (second class) of China, 2013. He obtained 3 science and technology awards from the government of Shaanxi province. He was awarded Fok Ying Tong Education Foundation in 2008. He is the author or the co-author of more than 80 papers. His field of research is the complex system analysis and control. Yan-Ru Zhong was born in Xi'an, China, in 1950. He received the B.S. degree in electrical engineering from Xi'an Jiaotong University, Xi'an, in 1975 and the M.S. degree in electrical engineering from Xi'an University of Technology, Xi'an, in 1983. In 1983, he joined Xi'an University of Technology. In 1987, he was a Visiting Scholar with the Electrical Engineering Department, Sophia University, Tokyo, Japan. Since 1993, he has been a Professor with Xi'an University of Technology. He is engaged in research on power electronics, particularly inverters and ac drive systems.
