ROBUST SPEED CONTROL METHOD FOR DC MOTOR DRIVES BASED ON A NEURAL NETWORK CONFIGURATION

fllEN-fllENT^TINHOC

ROBUST SPEED CONTROL METHOD FOR DC MOTOR DRIVES BASED ON A NEURAL NETWORK CONFIGURATION

• DAO THI MO - NGUYEN THI NGA - NGUYEN THUY MAY - BUI THI HOA - PHAM THI MIEN

ABSTRACT:

This paper proposes a novel robust speed control method for DC motor drives based on a two-layered neural network plant estimator (NNPE) and a two-layered neural network PI controller (NNPIC). The NNPE is used to provide a real-time adaptive estimation of the unknown motor dynamics. The projection algorithm is used as the learning algorithm for these neural networks to automatically adjust the parameters of die NNPIC and to minimize the differences between the motor speed and die speed predicted by the NNPE. The simulation and experimental results demonstrate that the proposed robust control scheme can improve the performance of an DC motor drive and reduce its sensitivity to parameter variations and load disturbances.

Keywords: Robust, speed control mediod, DC motor drives, a neural network configuration.

1. Introduction

In the past, DC motors were extensively used for variable speed control, e.g., industrial robots and numerically controlled machinery [i], due to their ease of control. However, DC motors have certain disadvantages to the commutator.

Recently, an induction motor can be controlled like a dc motor by using a field-oriented control approach [2], [3]. Also, because of the advances in power electronics and microprocessors [4], the induction motor drive used in variable speed and position control have become more and more attractive. Vector-controlled induction motors with a conventional PI speed controller is used extensively in industry [5], [6]. The conventional

PI controller is easily implemented and is highly effective if the load changes are small and the operating conditions do not force the system too far away from the linearizing equilibrium point [7]. However, in certain applications, e.g., rollingmill drives or machine tools, the drive operates under a wide range of changing load characteristics and the system parameters vary substantially. Thus, ensuring a specified dynamic response, independent of the parameter's variations, requires developing an adaptive speed control. Self-tuning control is an adaptive control strategy that has received widespread acceptance in industrial process control [7], [8]. Robust controllers that guarantee both the transient and

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steady-State response of dc servo mechanism systems within specified bounds under large plant uncertainty due to parameter and load variations have become an important issue [9], The multi- loop feedback control method supplemented by a complementary controller is used to improve the performance of an induction motor drive and reduce sensitivity to parameter variations and load disturbances [2], [10]. Neural network concepts have been an active research area in recent years. Due to the adaptive ability of a network's learning process, applying neural networks to the dynamics of system identification and control has become a promising alternative to process control [11], [12]. In this research, we propose a two-layered NNPE with a load torque observer used to provide a real-time adaptive estimation of the unknown motor dynamics.

Secondly, a novel model reference complementary controller for robust speed control of the induction motor, based on a two-layered NNPIC, is proposed. The widely used projection algorithm is used as the learning algorithm [13], [ 14], in order to automatically adjust the parameters for NNPIC and effectively reduce the system's sensitivity for both the parameter variations and the load torque disturbances, subsequently generating an adaptive control signal I This control signal can accurately bring the motor speed o^ fJtJ to a speed command oi\(k).

2. Model of field-oriented induction motor drive

Based on reference frame theory, the induction motor drive can be controlled like a separately excited dc machine using the indirect field-oriented control method [3]. The system configuration of an indirect field-oriented control induction motor drive is shown in Fig. I (a), which consists of an induction motor, a bang-bang current-controlled pulse widdi modulated (PWM) inverter, a field- orientation mechanism, a coordinate translator and a speed controller. Generally, the dynamic modeling of an induction motor drive is performed based on die reference-frame theory and die linearization technique [3]. By using die indu^ct field-oriented cond-ol, the dynamic model of die induction motor drive is significanUy simplified and can be reasonably represented by die block diagram shown in Fig. l(b)[3],[15].

The electromechanical dynamics induction motor drive can be written as

dt ^vB<o-. i<^U (1) where

By using the Laplace transformation, the transfer function for (I) is

0),is)=K,igJs)'T[_(s) (2) Js + B

Fig. 1. Indirect field-oriented Induction motor drive system: (a) system configuration and (b) block diagram

3-pha9e.

220V ; 60 Hz

— convener -r-

T.

speed -T" coniroller

C '-

'ds

^ 1 ^

sind PWM invota

\TAT\

cuiinit controller

t ' - 1 ; - 1

cooTdnaiE traiulalor

•M h

sinftos generalQr

•w.

—

T r \ I ^

Ei»»

^J

•>i

;

er

t

G,(s) T

rs+B j r

(b)

where i^^ is the stator torque component of the current, i^^ is the stator flux component of the current, QJ^ the motor load-shaft actual velocity, J the inertia constant of the motor and mechanical load, B the damping constant of the motor and mechanical load, T^ the electromagnetic torque, Ti the toad torque and P the number of poles.

3. Proposed robust speed control scheme The block diagram for die proposed robust speed control scheme of an induction motor drive is shown in Fig. 2, where two mdependent conQ-ollers are used. The model reference complementary conti-oller determine die sensitivii\ to die parameter and load variations and die servo-loop

HIEN-flIENTtf-TIN HOC

controller determines the overall performance indices, such as speed response, damping characteristics and steady-state error [2], [ 10],

A two-layered NNPE provides a real-time adaptive estimation for the unknown motor dynamics. A novel robust speed control for the induction motor is based on a two-layered NNPIC.

The projection algorithm is used as the learning algorithm in this network to automatically adjust the parameters for the NNPIC on-line, based on minimizing the difference between the motor speed Mr (k) and the estimated speed of the NNPE (U^ (k), so that the motor speed (o^ (k) can accurately follow the speed command to'^ (k), in spite of system parameter variations and load torque dismrbances.

Fig. 2. Block diagram of ttie robust speed control sctieme for an Induction motor drive

Model reftrence complementoy cmitroller

3.1. Neural Network Plant Estimator With Load Torque Observer

By applying the zero order hold to convert die electro mechanical dynamics of the induction motor drive, (2) can be discretized and described using [16].

,.,/,! _ d,i,i,(z) + d2Tiiz}

d (3) where

C/ = rf,-

z-c, I-z'ci

°"'(^)

Kt(l-ci) 'TL(Z)

Tm=— mechanical time constant Is sampling period

Allow the motor to be identified as the form [13]

0}^k) = CiO}/k-l} + d,i^Jk-l)

= cjco^k-l) + d2[-K,i^/k-l) + Ti_(k-l}} (4)

= ^(k-DMk-l)

Where Cj, dj and d2 are scalar parameters that are unknown. Besides, (j)(k-l) = [oy^k-l), -K^^Jk-I) -\- Tifk-1)}''''' IS the network input-output measurement vector and ^k-l) = [c/, d]\^ denotes a parameter vector.

If the load torque is constant, then the unknown parameter of (4) belongs to a linear estimation process. However, when the load torque is unknown or varies over time and the load disturbance sequence is not known, the estimation process becomes nonlinear due to the urdcnown Tifk-1) term, which multiplies the unknown parameter J2'

For resolving the preceding problem, we constructed a two-layered NNPE to estimate the unknown parameters and combine them with a simple torque observer to resolve the above difficulty. Fig. 3 depicts die network structure of the NNPE. The weight vector of Fig. 3 at time k is defmed by

e{k-\)=[e,{k-\)A.{k-\)J =[cj,] (5) is updated using the projection algorithm [13]

9(*) = 9 ( * - I ) + (6)

6+«>,(t-l)(»(t-l) Where ^ic-I) in this case is expressed by

nii-i)=i^,(k-i},i^ii-iir (7)

= [a^lc-l}. - K,i,iJk-l) + TL(k-l)I)'

a E (0,2) IS the reduction factor and cjk) = m^ic) - fflr (Ic). The constant b is chosen to be close to zero, thereby avoiding division by zero in (6) if f<k-im-J)=0.

As Fig. 3 indicates, any mismatch between the motor speed co/k) and the estimated speed of the NNPE wr(lc) would automatically produce an error Cjjk) = (B/y - dir (k). This error will be used to adjust die weights of the NNPE. The estimated speed is calculated as follows:

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",(*)=Z<*.(*-')«,(*-')

⁽⁸⁾

Equations (5)-(8) satisfies the following properties [13], [14]

(i) p{k)-e4<le{k-\)-e,l<\\e{oye,\\.k>i

(ii) lim

M.

[b+f{k-i)</,{k-\j\'

(9)

where OQ is the weight vector that corresponds to perfect learning of the motor dynamics. That is, the NNPE can accurately estimate the motor speed.

It is worth noting that the load disturbance of a practical system is an unknown variable. To simplify the load disturbance estimation, diis research considered an actual system in which the load disturbance is continuous in nature and the observed period is shorter than the variation for T^.

However, once the parameters C/, d,, and J2 ^re estimated, the torque observer of the induction motor, should be estimating using the inverse dynamics of die motor drive to obtain the observed torque. Therefore, the residual sequence of Tifk-l) is obtained from (4), where the parameters Cj, d, and ^2 3re replaced by estimated values C;, d,, and d2 which are obtained from (5)

t{k-2) = i-[0,{k-l)-c,6},{k-2)yK,i^{k-2)(m d..

The Tifk'l) m the <l)(k-l) vector of (4) is replaced by fiik~2) from (10). Using the preceding recursive process, the observed load torque will quickly converge into its real values.

Fig. 3. Network structure of ttie NNPE fil(A-I)-

A(*-o

<>-«,(*)

3.2. Neural Network PI Controller

To implement robust speed control of an induction motor, a two-layered neural network is

used as a neural network PI controller (NNPIC).

The dieorem and system structure for the derivative procedure is similar to the derivation for die NNPE used above. In die following, we will describe the design procedure for the NNPIC and develop its projection training algorithm to automatically adjust the parameters of the NNPIC on-Une so that the motor speed co,. (k) can track the model reference output (o^<k) and Q)^k) can accurately follow the speed command o)'Jk) in spite of system parameter variations and load torque disturbances. Fhst, consider that the transfer function of a PI controller can be expressed as

i,Js) K^

~^J^) "' s ( I I ) where Kj,^ and K^,. are, respectively, the proportional gain and the integral constant of the PI controller and c„, = (o^- oi^ Using the j = ("c - l)/iz 1- 1) approximation, (U) c^" be discretized and rewritten in the following form:

yk) = i^,(k-}) + K^,(cJk)

- cJk-1)) + K,^ (cJk) + cJk-D) (12)

= f^(k-l)OJk-l)

Where ejk-l) = (i^Jk-l), cJk) - cjk-l), cJk) + c^ (k'l)]''' is a given input-output measurement vector of the neural network and djk-l) = [I, Kp^., K^^f denotes an unknown or various parameter vectors. To implement the design of the NNPIC.

we constructed a two-layered neural network with a projection algorithm to adjust the parameters /("„

and Ki^.. Fig. 4 depicts the network structure of the NNPIC, which indicates that the simple neural network has three input nodes and one output node.

The inputs are i^^ (k-1), cJk) - cJk-1) and cJk) + cJk-l), the related weights are a constant value 1, Kp^. and K,^.

The weight vector for Fig 4 at time is defined by

e,{k-}) = [6^,(k-i). e,2(k-i), e,3(k-i)f

= [l,K^,KJ' (13) is updated using die projection algoridim {13]

ejk} = 0Jk-l) + g<j}c(k-l)c^(k)

h + ^^lk-l)^^(k-l) (14) (Fig. 4. Network structure of the NNPIC) where <f>Jk-l) is expressed by

(l,Jk-l) = [^Jk-ll ii>^2(k-l). (I>c3(k-l)r (15)

= [igc(f^-l). cJk) - cjk-l), cJk) + cjk-l}f g e (0,2) is die reduction factor. The constant h is chosen to be close to zero, therebv avoiding

eiEN-SIENTt-TINHOC

Fig. 4. Network structure olttte NNPIC

^(*)+^(t-I).

division by zero in (14) if iji^Jk-l)^Jk-J).

The output of the NNPIC is calculated as follows:

V ( * ) = E ! * H ( ^ - 1 K , ( * - I ) (16)

4. Properties of the proposed robust control scheme

The proposed control system can be treated as a two-degrees-of-freedom control system consisting of two controllers: a model reference complementary controller and a servo-loop controller. The merit of this design method is that both controllers can be realized and designed independently [10].

In order to outline the characteristics of the complementary controller it is convenient to assume that the servo-loop controller has been disconnected. Under this condition, the analysis of the complementary controller with system parameter variation and load torque disturbance is described as follows.

Evaluating system inertia J with sufficient accuracy is occasionally difficult. Such inertia may vary with the load. Here, it is desirable to analyze the robustness against variations of the system's parameters and load disturbance. The transfer function of this complementary control system is obtained

-,(.0 = P{s)P,(.)H{s),P(.)

UH(s]P{.) 'A^)-1 + //(.)P(.) TAs) (17) where the plant dynamics are

P(s) K, Js-\-B the model reference is

Js + B Pm(^)

(18)

(19)

and the compensator is

S (20) Substituting (l8)-(20) into (17) and simplified.

H(s) = K^

we obtain

where

a=Kj-^)-K,

(22) A(s) = Js' + (B + K^p^)s + K,K^, (23) Because the motor speed can be rapidly estimated using the NNPE and the motor speed w^

and the estimated speed ta^ can accurately track model reference output w^ using the NNPIC, the control parameter Kp^. and K,^ of (21) could be rapidly adjusted and compensated using (14), which responds to variations in the system parameters and load torque disturbances. The effect of [asip,(s) + sTJs)]/A(s) term of (21) can be eliminated or reduced. The above analysis shows that the complementary controller reduces the sensitivity not only for the parameter vanations but also for the load torque disturbance. These characteristics are preferable for robustness and stiffness.

When the complementary controller with a simple and stable self-tuning neural network PI controller is designed and completed as above, the overall performances such as system response, damping ratio and steady state are determined by the servo-loop controller. Referring to Fig. 2, the design's purpose of the complementary controller is to insure that the behavior of the plant dynamics P(s) is the same as the behavior of the required reference model PJs). Therefore, the closed-loop transfer function of the overall system from Fig. 2 is deduced as follows:

0}/s) _ C(s)PJs) (24) 0}\(s) l-\-C(s)PJs)

The open-loop transfer function, can be wntten as

(25) K.K.s+KK,

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Thus (24) becomes

^r{s) jy+{B„+K„Kp)s + K^K. ⁽²⁶⁾ The parameters for Jm, Bm and Km are given, let us compare the characteristic equation for (26) and the standard second order characteristic equation. We obtained the natural frequency

[K~K. (27)

and damping constant

. ^ B„-\-K„,K, (28) 2 •jK„,KiJ^

5. Simulation results

In this section, we present some simulation results to evaluate the efi"ectiveness of the proposed robust speed control scheme for an induction motor with NNPIC. The parameters for the induction motor drive are expressed by (I)-(3) which were chosen to be 7 = 2.7 x 10^ NmsV rad, B = 6.9xia-*Nms/radand/r,= 1.8Nm/A.

There were two different control methods used in the simulation to verify the proposed robust speed control and compare their performance.

i) The proposed control scheme As Fig. 2 shows, the transfer function of the reference model was selected as

PJs) = 0.45/(0.000688s + 0.000515).

The servo-loop controller (PI controller) was designed to have zero steady-state tracking error, proportional gain of Kp = 0.0265 and integral gain of Kj = 0.0185, respectively. Both die NNPE and NNPIC learned using the projection algoridim, with a = 0.85, b = 0.01 and g = 0.25, h = 0.001 in (6) and (14), respectively. The value for a system's sampling period is taken as 0.002 s. The initial weight vectors for (5) and (13) were chosen to be

0{O)^[e,(O)A(O)J =[6,{0).1{0)J =[0S.0.5f

O(O)^[0„(O),d^,{Q).O^,(O)]' = [lKJ0).K^{O)J =[\\,0.5]' ii) Only servo-loop controller without reference model, NNPE and NNPIC (i. e., conventional PI conti-oller): The PI controller was designed to have damping ratio and natural frequency which was same as die proposed control scheme. Now, assume that die system parameter varies from to 3 and the external load

torque for 2.5 N-m applied to die induction motor.

Fig. 5(a) presents a variation of the external load torque for 2.5 N-m applied to the induction motor.

Fig. 5(b) presents the speed response of the two types of control methods when the rotor is operated at 850 rpm. As this figure reveal, the conventional PI control has difficulty in producing the ability to reject a load dismrbance. The speed response of the conventional PI control is easily affected by a change in the system parameters.

However, the proposed control scheme yields excellent load disturbance rejection ability and has a better speed response than the conventional PI control. The proposed control scheme has a good speed response, regardless of the variation in J . Fig. 5(c) presents the torque current of the two types of control methods when the rotor is operated at 850 rpm. This figure reveals that the stator currents of the conventional PI control scheme and the proposed control scheme are within a reasonable range. Fig. 5(d) displays the parameters of the learning process Kp^. and Kj^ for die NNPIC. Fig. 5(e) displays the errors c,^ and c^

given in Fig. 2. As these figures reveal, the NNPE can provide a real-time adaptive identification of the unknown motor dynamics. The NNPIC can produce an adaptive control force so that the motor speed can accurately track the model reference output.

Fig. 5.

(a) Variations of the external load torque, (b) speed response,

(c) corresponding torque current, (d) parameter learning processes K and K of the NNPIC

(e) errors e and e

V

z

l o

_{3 0.5}

(a).

1.5 2 Tim e(S)

HIEN-BIEN It-TIN HOC

0.5 1 1.6 2 (b). Time(S)

-50

14-Proposed <

' K j . . . j ' P l c -Proposed control

ICOQUOI

O.S 1 1.5 (c). Time(S)

^ 1

i

0.5,

K„i'

X^t

) 0.5 1 1.5 2

(d). Time(S) 100

0.5 1 1.5 (e). Time(S)

6. Experimental results

The indirect field-oriented induction motor drive and the control scheme in Figs. I and 2 were implemented using 586 microcomputer hardware and software, diereby verifying the vahdity of die previous computer simulations and showing the merits of the proposed control scheme. The sampUng time was 0.002 s. The rotor of the induction motor was coupled with a magnetic braking system used to vary die load torque. The encoder of 2000 pulse/turn was used to measure die motor speed. The converter and PWM inverter were implemented using a power diode and IGBT, respectively. The sin/cos generator was

implemented using an LM33I IC, CD4040 counter and 27C64 EPROM to generate sino)^ and cos(0/

waves. The coordinate translator was implemented with a 12-bit AD7541 digital-to-analog converter and TL074 IC to translate the current commands i'^^ and i'j^ in a synchronously rotating frame to the stator current command (^^^, i%^ and i"^^. The current comparator was implemented with an LF357 IC to generate the control signal of the PWM inverter.

The actual stator currents of the induction motor 'as- hs ^""^ ^cs were generated from the PWM inverter by comparing the actual stator currents with the stator current commands i^^^, i^^^ and i'^^

in the current comparator. The parameters of the induction motor drive and the controller are the same as the parameters of the simulation Fig. 6. Speed responses for a load disturbance 2.5 N-m at 0.5 s: (a) proposed control scheme and (b) conventional PI control scheme

^ :t900rpm

• h n . | . M , ) M M i . . i

t o rpm; iOJs:

• l " " l " " i "

U/TTSooip

rpm ' • i - ' " l " - ' l - " M "

tOrpm :

• ! • • • • ! • • . • | . . . . | M ,

(b)

For a speed command of 900 rpm to a load disturbance 2.5 N-m at 0.5 s, with the system parameters fixed at nominal values, the speed responses of the proposed control scheme and the conventional PI control scheme are shown in Fig.

6(a) and (b), respectively. These figures reveal diat the speed response of the proposed control scheme was influenced slightly by die load disturbance.

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Fig. 7. Speed responses for system parameter varies from J to 3J: (a) proposed control sclKme and (b) conventional PI control sctieme

'• t900iini ipm

• l " " l " " l " " l ' " . t . . . . i , . „ i „

TOqjin

<—>

0.5s

.+****t*.

PI control scheme did have a long recovery time.

Now, the system parameter varies from 7 to 37.

For a speed command of 900 rpm under a no load disturbance, the speed responses of the proposed control scheme and the conventional PI control scheme are shown in Fig. 7(a) and (b), respectively.

These figures reveal that the speed response of the proposed scheme was insignificantiy affected by a variation in J. However, the speed response of the conventional PI conti"ol scheme was affected considerably by the variations in /.

7. Conclusions

This paper proposed a novel robust speed control method for induction motor drives. First, a two-layered NNPE with a load observer was used to provide a real-time adaptive estimation of unknown motor dynamics. Secondly, a novel robust speed control method for the induction motor based on a two-layered NNPIC was proposed. The projection algorithm was used as the learning algorithm, in order to automatically adjust the parameters of the NNPIC and effectively reduce the systems sensitivity for both parameter variations and load torque disturbances. The simulation and experimental results demonstrate diat the proposed robust control method, based on NNPIC possesses fairly good adaptation capabilities under parameter changes and load torque disturbances. The proposed robust control scheme can improve the performance of an induction motor drive and reduce its sensitivity to parameter variations, nonUnear effects and load variations. Moreover, the proposed new approach was presented in a manner diat wdl contribute lo a better understanding of die neural network applications in speed-tracking control and robust control in an induction motor •

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Receiving date: May 28,2020 Reviewing date: June 10,2020 Accepting date: June 18,2020

Author's information:

1. Master. DAO THI MO 2. Master. NGUYEN THI NGA 3. Master. NGUYEN THUY MAY

College of Electrical and Electronic, Thai Binh University, Thai Binh, Viet Nam 4. Master. BUI THI HOA

College of Information Technology, Thai Binh University, Thai Binh, Viet Nam 5. Master. PHAM THI MIEN

University of Transport and Communications - Campus in Ho Chi Minh City

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PHLfONG PHAP DIEU KHIEN BEN VtfNG TOO DQ CHO HE TRUYEN DQNG D O N G CO MQT CHIEU D U A TREN

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• ThS. DAO THj Md

• ThS.NGUYlNTHjNGA

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• ThS. BUI THj HOA

Khoa Cong ngh$ thong tin, TrUflng E)gi hoc Thdi Binh

• ThS. PHAM TH! MIEN Phdn hieu TrUdng Eigi hoc Giao thflng Vdn tdi

tgi Thdnh pho Ho Chi Minh

T6MT1T:

Bai vig't nay de xua't m6t plltfdng phap dieu Idiien ben vi^ng tdc d6 clio lid truyln d6ng dpng cd mot cliieu difa tren cS'u true mang ndron iiai tang (NNPE) vh bp dieu Idii^n PI mang ndron hai tang (NNPIC). NNPE diidc sit dung de tao la dap u'ng thdi gian thi/c cho he dOng hoc dpng cd chiJa xdc dinh. Thuat todn di/a ra dlTdc sijf dung rpng rai nhif m5t hpc thuat cho cdc mang ndron 6 day d^ tif ddng dieu chinh cdc tham so cija NNPIC v& di gidm thieu sif khac biet giifa t^c do dpng cd va t6'c do dUdc dif bdo bdi NNPE. Cdc ket qua m6 phSng va thtj" nghipm chifng minh ring mo hinh di^u khien ben vifng difdc de xuat c6 th^ cdi thien hieu suat cho hd truyin dpng ddng cdDC vd Idm gidm do nhay cua no doi vdi sif bien d6i tham so va nhiSu tdi.

Tiif khoa; Dilu khien, phifdng phap dilu khien b^n vifng tdc dp, he truyen dpng cd mot chilu, cau tnic mang ndrpn.

So 15 - Thdng 6/2020