Slider crank mechanism control using adaptive computed torque technique

Lin S.-L.Chiu Indexing ternis: Slider-crank mechanism, Adup rive computed torque technique Abstract: The position control of the slider of a slider-crank mechanism, which is driven by a

Trang 1

r-crank mechanism control using adaptive

uted torque technique

F.-J Lin

Y.-S Lin

S.-L.Chiu

Indexing ternis: Slider-crank mechanism, Adup rive computed torque technique

Abstract: The position control of the slider of a

slider-crank mechanism, which is driven by a

permanent magnet (PM) synchronous motor,

using an adaptive computed torque technique, is

studied First, the mathematical model of the

motor mechanism coupling system is described,

where the Hamilton principle and the Lagrange

multiplier method are applied to formulate the

equation of motion Secondly, assuming that the

parameters of the system are well known,

according to the computed torque technique, a

robust controller is designed to control the slider-

crank mechanism Then, considering the existence

of the uncertainties of the system, an adaptive

computed torque controller is designed based on

the Lyapunov stability Moreover, to increase the

execution rate of the control algorithms, a digital

signal processor (DSP)-based control computer is

devised to control the motor mechanism coupling

system

Introduction

Computed torque, or the inverse dynamics technique is

a special application of feedback linearisation of non-

linear systems A number of works related to computed

torque control of robotic manipulators have been pub-

lished [I] The computed torque controller is utilised to

linearise the nonlinear equation of robot motion by

cancellation of some, or all, nonlinear terms [l] How-

ever, the objection to the real-time use of such a con-

trol scheme is the lack of knowledge of uncertainties,

which include parameter variations and external distur-

bances of the system The adaptive control technique is

essential for providing a stable and robust performance

for a wide range of applications (e.g robot control,

inherently nonlinear with uncertainties [2-4] Therefore,

several adaptive controllers have tried to circumvent

the problem of uncertainties using adaptive

techniques [5-71 In Su and Leung [SI, a computed

torque control approach using the sliding mode tech-

0 IEE, 1998

IEE Proceedings online no 19982051

Paper first received 15th July 1997 and in revised form 23rd March 1998

The authors are with the Department of Electrical Engineering, Chung

Yuan Christian University, Chung Li 32023, Taiwan

process control, etc), and most of the applications are

nique is introduced, and the uncertainty bound is estimated by an adaptive scheme; Imura, Sugie and Yoshikawa [6] described an adaptive robust computed torque control, where a time-varying gain in the proposed robust controller is estimated using an adaptation law; Teshnehlab and Watanabe [7] proposed a

self-tuning computed torque controller, where the gains

of the computed torque controller are tuned by neural networks

The slider-crank mechanism is widely used Examples

of its application are found in petrol and diesel engines, where the gas force acts on the slider and the motion is transmitted through the links Steady-state solutions and the elastic stability of the motion of a slider-crank

mechanism were obtained in Jasinski et al [8], Zhu and Chen [9] and Badlani et al [lo] In addition, the response of the system has been found to be dependent upon the five parameters: length, mass, damping, external piston force and frequency in Viscomi and Arye [l 11 The transient responses have been investigated on the basis of the ratios, the length of the crank to the length of the connecting rod and the rotating speeds of the crank to the rotating speeds of the rod, etc in Fung [ 121 However, in the previous studies, the applications

of electric motors to drive the slider-crank mechanism were not considered and, moreover, no control theory was applied to control the position, velocity, or trajec- tory of the slider-crank mechanism

A slider-crank mechanism system actuated by a field-

orientated control PM synchronous motor drive [13, 141 is investigated in this study The slider-crank mechanism driven by a PM synchronous servo motor has applications in areas where the transfer of the rota- tion motion to the translation motion is needed, and high precision is required Since the application of the slider-crank mechanism has similar control problems to those of the robotic systems, the computed torque based robust and adaptive controllers are designed to control the motor mechanism coupling system in this study To achieve this objective, a robust controller based on computed torque control is designed to control the coupled mechanism in the nominal condition

In addition, an adaptive computed torque controller, in which the gains are tuned using adaptive scheme, is proposed to control the coupled mechanism considering the existence of uncertainties

With the great advances in microelectronics and very large-scale integration (VLSI) technology, today, high- performance microprocessors and DSPs can be effec- tively used to realise advanced control schemes [15] A DSP-based control computer, which is based on a per-

E E

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sonal computer (PC) and a TMS320C32 DSP, is

designed to provide a flexible environment with a high

execution rate for the field-orientated mechanism and

the control algorithms The field-orientated mechanism

and computer interface programs are implemented

using the Pentium-PC; the computed torque-based

robust and adaptive controllers are implemented using

First, the mathematical model of the motor mecha-

nism coupling system is derived Following that, under

the situation that the parameters of the coupled system

are well known, a robust controller based on computed

torque technique is designed to control the crank posi-

tion of the coupled mechanism In practice, the uncer-

tainties of the system can not be known exactly To

control the coupled mechanism with robust characteris-

tics, an adaptive computed torque controller is

designed to control the position of the slider of the

coupled mechanism considering the existence of uncer-

tainties The proposed adaptive controller maintains

the computed torque structure with a parameter esti-

mation scheme Finally, simulation and experimenta-

tion are performed to test the control performance of

the proposed robust and adaptive controllers

2 I Field-orientated PM synchronous motor

drive

A machine model of a P M synchronous motor can be

described in a rotor rotating reference frame as follows

[16]:

V q = R s 2 q + PA, + wsxd

V d = Rs2d + p x d + W A X q

(1) (2)

A, = L q % , ( 3 )

(4)

where

and

A d = L d a d + LmdIfd

In the above equations vd and vq are the d, 4 axis stator

voltages, id and i, are the d, 4 axis stator currents, Ld

and L, are the d, q axis inductances, Ad and A, are the

d, 4 axis stator flux linkages, while R , and U$ are the

er

stator resistancl: and inverter frequency, respectively In

eqn 4, Isd is the equivalent d-axis magnetising current, and L,, is the (Saxis mutual inductance

The electric torque is:

digital

filter

and the equation for the motor dynamics is:

In eqn 5 , P is the number of pole pairs, z, , is the load

torque, B, is the damping coefficient, w, is the rotor

speed and, J , is the moment of inertia The inverter

frequency is related to the rotor speed as:

The basic prinsciple in controlling a PM synchronous motor drive is based on field orientation The flux posi-

tion in the d-q co-ordinates can be determined by the

shaft position sensor because the magnetic flux generated from the rotor permanent magnetic is fixed in

relation to the rotor shaft position In eqns 4 and 5 , if

id = 0, the d-axis flux linkage Ad is fixed since Lmd and

Ifd are constant for a surfacemounted PM synchronous motor, and the: electromagnetic torque z, is then proportional to iq which is determined by closed-loop coii- trol In the field-orientated control of a PM synchronous mlotor, the d-axis rotor flux is provided by the PM mounted on the rotor; therefore, only the q-

axis torque current component iq is necessary to be generated by the drive Since the generated motor torque is linearly proportional to the q-axis current as the d-axis rotor flux is constant in eqn 5, the maximum torque per ampere can be achieved

The configuration of a general field-orientated PM synchronous motor drive system is shown in Fig 1, which consists of a PM synchronous motor coupled with a mechanism, a ramp comparison current-controlled PWM voltage source inverter (VSI), a unit vector (cos 0, + j sin Ox, where e,y is the position of rotor flux) generator, a co-ordinate 'translator, a speed-control loop and a position control loop The PM synchronous motor used in this drive system is a three-phase, four- pole, 750W 3.9A, 3000rpm type With the implementa- tion of field-orientated control, the P M synchronous motor drive system can be simplified to a control

;re = r, + B,w, + J mP w T (6)

( mechanism )

synchronous motor

i encoder inverter

3-phase

220v rectifier 60HZ

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system block diagram, as shown in Fig 2, in which:

I

I encoder ( I

I interface I

I and timer I

I

I _ _ _ _ _ _ - I

-

servo control card

1

J,s + B ,

=

linear scale interface

~

where iq* the torque current command A block dia-

gram of the DSP-based computer control system for

the field-orientated PM synchronous motor drive is

shown in Fig 3 The position of the slider is measured

by a linear scale The field-orientated mechanism is

implemented using the Pentium CPU, moreover, the

TMS320C32 floating point DSP from Texas Instru-

ments is chosen to realise the robust and adaptive con-

troller for the coupled mechanism A servo control

card is installed in the control computer, which

includes A/D, DIA, P I 0 and encoder interface circuits

Digital filters and frequency multiplied by 4 circuits are

built into the encoder interface circuits to increase the

precision of position feedback from encoder and linear

scale The current-controlled VSI is implemented by

IGBT switching components with a switching fre-

quency of 5kHz To reduce the calculation burden of

the CPU, and to increase the accuracy of the three-

phase command current, the co-ordinate transforma- tion in the field-orientated mechanism is implemented

by an AD2S100 AC vector processor

The dynamic modelling technique based on curve-fit- ting to the step response of the position loop is applied

to find the drive model of Fig 2 in the nominal condition (no parameter variations and z , = 0") The results are:

Kt = 0.6732 "/A, n = 1

B, = 1.53 x l o p 2 Nm s / r a d The '-' symbol represents the system parameter in the nominal condition

Fig 4 shows a PM synchronous motor system including a geared speed reducer with a gear ratio of:

(12)

n a 7 wT Q r

n = - = - = - = -

Substituting eqns 8 and 11 into eqn 6, the following applied torque can be obtained:

r = n (re - J,hr - B,w,)

= n ( Kti; - nJ,Q - nB,8 ') (13)

where z is the torque applying in the direction of w

'p PM synchronous motor drive system

Fig.2 Simpllfed control block diugrum

Fig,

J

3-phase

inverter

I - _

pentium

memory

320C32

mechanism

synchronous motor

I

DSP-based computer control drive system

linear scale

Trang 4

PM

synchronous

motor

xi- eqn.83

gear box

r - - - I

PM

O*

synchronous -

motor mechanism

- - - - - -

Fig 4 Schematic of motor-gear mechanism

2.2 Mathematical model of the coupled

mechanism

A slider-crank mechanism driven by a PM synchronous

motor is shown in Fig 5 , where m,, m2 and m3 are the

masses of the rotating disc, the connecting rod and the

slider, respectively; I is the length of the connecting rod

and 1' is the distance from point B to the mass centre of

the slider; R is the radius of the rotating disc, and r is

the distance from 0 to A Moreover, p is the coeffi-

cient of the dry friction between the slider and the

foundation Hamilton's principle and the Lagrange

multiplier are used to derive the differential algebraic

equation for the slider-crank mechanism in Appendix

9

't

t

FE

B

I

*

X

Fig 5 Slider-crank mechanism driven by PM synchronous motor

2.3 Reduced system (of differential equations of motion

The differential algebraic; equation of mechanical motion derived above is suimmarised in the matrix form

of eqn 14, anld in the constraint equation of eqn 59

The implicit method musl be employed to solve the equation of tlhe system Eqns 14 and 59 may be reordered and partitioned, according to the decomposi- tion of + = [IO @IT = [vT .TIT, which is the same as Wehage and Haug [17] If the constraints are independent, the matrix aq has fill-row rank, and there is always at least one nonsingular submatrix Bq of rank

2 The Gauss-.Jordan reduction of the matrix CD , with

v = [e], U = [#] so that 'Pv is the submatrix of CDp whose columns correspond to element v of +, and CDu 1s

the submatrix of aV, whose columns correspond to elements U of + The elements of the vectors v, U and matrices a,,, @, are detailed in Appendix 10 Thus, eqns 14 and 5'9 can be rewritten as:

(15)

(16)

double pivoting, defines a partitioning of qj = [v Y- uqT,

M""U + hlwwV + +TA = B"U + D" - N"

M""U + h'l""v + A +: = B"U + D" - N u

(17)

(18)

n

+bUU + cp,v = GT

or in the matrix form as:

where

& I ( V ) V + N(V, +) = Q u + D

M = M"" -

T

N = [ N"-+;(+,') Nu]

+ pVl""+il - Mu"Qi'] CT

(20)

The result is EL set of differential equations with only

one independent generalised co-ordinate v The equa-

by using the fourth-order Runge-Kutta method

The constraint position, velocity, and acceleration

61 and 69, the following equation in the matrix form is

obtained:

eqns' 59, 6o and 61 must be held By using eqns' 59, 60,

tion is an initial value pro,blem and can be integrated

3

The robust control system is shown in Fig 6, where

X;, XB, O*, and 8 are the command of slider position, slider position, command angle of crank, and angle of crank, respectively Since X, is the desired control objective and 8 is the state of the motor mechanism

1

(I4) This is a system of differential algebraic equations for

which the matrices element can be found in Appendix

9

B U + D ( $ ) - N ( @ , I I )

ff

robust cantroller

I errorfunction

_ _ - _ _ _ - - -

S(t)=e+h,e I

P T ' i

w

Fig 6 Schematic of robust control ofslider-crank mechanism driven by P M synchronous motor

361

Trang 5

coupling system, X,* and XB should be transformed to

8* and 8 by using eqn 83

Consider the second-order nonlinear, single-input-

single-output (SISO) motor mechanism coupling sys-

tem:

e ( t ) = .f(O, t ) + G(8, t ) U + W ( 8 , t ) ( 2 2 )

where

f ( 8 , t ) = -M-'N G(8, t ) = M-'Q

W ( 0 , t ) = M-lD

and U(t) is the control input iq* According to tqn 19,

M can be computed to ensure the existence of NI-'

Now, assume that the parameters of the system are

well known as the nominal condition Rewrite eqn 22

to be:

(23) where J,(@ t ) is the nominal value off(@ t); Gn(@ t) is

the nominal value of G(8, t); W,?(O, t) is the nominal

value of W(8, t ) where the external disturbance FE = 0

If the uncertainties occur (i.e the parameters of the sys-

tem are deviated from the nominal value and there is

an external disturbance added into the system), the

dynamic equation of the coupling system can be modi-

fied as:

e(t) = ( f n ( 8 , t ) + A f ) + ( G n ( 8 , t ) + AG) U

where Af, AG and AW denote the uncertainties Eqn 24

can be rewritten using the computed torque technique

as follows:

U(t) = GZ1 ( e , t ) d ( t ) ~ G i l (8, t ) ( f n ( 8 , t ) + Af)

e ( t ) = fn(B, t ) + Gn(O,t)U + Wn(O, t )

+ (Wn(8, t ) + AW) (24)

= d ( t ) + P f n ( B , t ) + y

(25)

( 2 7 )

where

P = -f?% t)Gil(Q, t ) ( f n ( 8 , t ) + A f )

7 = -G;'(O,t)(AGU + W n ( Q , t ) + A W ) (28)

Now, the tracking error e of the system and a error

function S(t) are defined as follows:

( 3 0 )

S ( t ) = i: + &e where 8, is the desired angle of crank; Ae is a positive

real value Substitute eqn 29 into eqn 30, then:

S ( t ) = s - e,,, (31)

where 1 9 , ~ ~ = 8!,- A,e denotes the reference speed In the nominal condition,

Af = o ( 3 2 )

y = -G,1(8,t)Wn(0,t) ( 3 7 )

Then, according to eqn 25 and the error function S(t),

the robust controller can be designed as:

(38) U(t) = ct8,,~ + / 3 f n ( B , t ) + y - K S ( t )

Substitute the above equation into eqn 25, then:

al,,,+Bfn(B,t) + y - K S ( t ) = a d + / ? f n ( Q , t ) + y

(39)

(40)

(41)

The above equation can be reduced to:

a! ( 8 - 8,,f 1 + K S ( t ) = 0 and

a S ( t ) + K S ( t ) = 0 Let K and a be the same sign, namely, sgn(Q = sgn(a),

then the controller will make the error function S(t)

converge to zero exponentially, and the coupling system is stable

4

To extend the usefulness of the computed torque controller, adaptive control techniques [ 2 4 ] can be employed considering the existence of uncertainties In this study, the uncertainties contain the variation of the

mass of the slider m3 and the external force FE With these uncertainties, an adaptive control law is designed

to stabilise the motor mechanism coupling system The proposed adaptive controller based on the computed torque technique for the motor mechanism coupling system is shown in Fig 7, and the adaptive controller is designed as:

U ( t ) ~Ei,,,(t) + B f n ( 8 , t ) + T - K S ( t ) (42) where 4 and denote the estimated parameters of /3

and y Substitute eqn 42 into eqn 25, then:

Design of an adaptive controller

a ! e , , f + p f , ( e , t ) + T - r i s ( t ) = a ! 8 + / 3 f n ( 0 , t ) + y

(43)

Fig 7 Schematic of adap five control of slider-crank mechunism driven by PM synchronous motor

Trang 6

and

(j - a> f,(O,t) + (+ - y) = cl (B - j r e f ) + K S ( t )

(44)

(45)

Rewrite the above equation:

where p = p - p and 7 = f - y Multiply sign(a) to

both sides of eqn 45, then:

(46)

a s @ ) = j f n ( 8 ; t ) + { : - K S ( t )

/alS(t) = s i g n ( a ) [/?fn(r9, t ) + ;i, - K S ( b ) ]

The above equation can be rewritten as:

Assumption: The speed of the variation of the system

parameters is much slower than the executing speed of

the adaptive algorithm and, during the adaptation, the

parameters of the system is considered as constants, i.e

p = p - p = p

- S / = ? - ; i = T . .

The adaptive algorithm for the parameters p and y i s

chosen as follows:

B = - s v ( a ) S ( t ) f n ( O , t ) (48)

;i/ = - s z g n ( a ) S ( t ) (49)

Theorem I : The motor mechanism coupling system will

be globally stable, if the adaptive controller is obtained

by eqn 42 with the adaptive algorithm eqns 48 and 49

Prooj Let the Lyapunov function be:

c2 - 2 >

1

V = - l a l S 2 + - p + y

Differentiate eqn 50 with respect to time:

Substitute the eqns 47, 48 and 49 into eqn 51, then:

V ( t ) = - / K l S 2 5 0 (54 Let function P(t) = -P(t) = 149, and integrate func-

tion P ( t ) with respect to time:

lil’P(t)dt = V ( 0 ) - V ( t ) (53)

Because V(0) is bounded, and V(t) is descent and

bounded, then:

(54)

Differentiate P(t) with respect to time:

P ( t ) = -2lKISS (55)

Since K, S and S are bounded, P(t) is uniformly con-

tinuous By using Barbalat’s lemma [2, 31, it can be

shown that lim,,,P(t) = 0 Therefore, S(t) -+ 0 as t -+

W As a result, the coupling system is globally stable

Moreover, the tracking error of the system will con-

verge to zero according to S ( t ) = e + &e = 0

The dynamic model formulation for the slider-crank

mechanism with a PM synchronous servo motor in

Section 2 is for general case However, to test the effec-

tiveness of the proposed mechatronics system and to

IEE Pror.-Control Tlzeory Appl., Vol 145, No 3 1998

verify the simulation results of the control system, an experimental mechanism is designed in this study For simulation andl experimental tests, a practical slider- crank mechanism is set up and its parameters (nominal value) are:

ml = 3.64 kg, ma = 1.18 kg, m3 = 1.8 kg,

(56)

(57)

I = 0.305 m

1’ = 0.055 m, R = 0.12 m, T = 0.1 m, p = 0.1

The physical meanings of the parameters can be referred to Seclrion 2.2 No.w, using Matlab package to simulate the motor mechanism coupling system with the robust controller The parameters of the robust controller are chosen as:

All the gains in the robuist controller are chosen to achieve the best transient performance in both siniula- tion and experimentation considering the limitation of

the control effort and the requirement of stability The control objective is to control the slider to move 0.lm Hence, the initial angle of 8 is 4.712 rad; the desired angle of 8 is equal to 5.760 rad, and the stroke of the

slider, AK,, is equal to 0 l m Three simulation cases

are addressed here First, the nominal case with external disturbance force FE = 0 is considered The responses of the crank angle, the error function, the slider position, and the control effort are shown in Figs 8-1 1 Next, the parametric variation case is increasing mass of m3 by a 1.4kg load and with exter-

nal disturbance force FE = 0, and the responses of the system are shown in Figs 12-15 Finally, Figs 16-19

I

5.5

H

5.0

4

time, s

Fig 8

Crank angle

Response twjectories of roliust contvol ,system (noniinul case M?th

FE ONt)

time, s Response trajectories oJ robust control systeni lnomind case

Fig 9

Error function

369

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I I

I

I 1 I I I

0.4C

XB

0.35

C

I

0.30

I

time, s

Fig 14

ation case with FE = ONt)

Slider position

Response trajectories of robust control system (parametric vari-

time, s

Fi .10 Response trajectories of robust control system (nominal case

w i z FE = PNt)

Slider position

r - - -

I

- - - -

- - - - , - - -

I

time s

time, s

Fig 15

ation case with ,FE = ONt)

Control effort iq

Fi I 1 Response trajectories of robust control system (nominul cuse

w i 3 FL- = ONt)

Contro? effort $

6.0

5.5

6 5.0

6.0

5.5

5.0

4.5

I

-1-

I

I -1-

I

e

I / : I I

time, s

Fig 16

ation case with FE = 5 N l )

Crank angle

time, s

Fig 12

ation case with Ft = ONt)

Crank angle

5

0

;;r -5

-10

-1 5

5

0

,

g -5

-1 0

-1 5

time, s

Fig 13

ation case with FE = ONt)

Error function

time, s Response trajectories of robust control system (parametric vari-

Fig 17

ation case with FE = 5Nt)

Error function

IEE ProccContuol Theory A p p l , Vol 145, No 3, May 1998

Trang 8

I I I I

I

0.01

I I I I I

I/

0.0

I

time, s

Fig 18

ation case with FE = SNt)

Slider position

Response trajectories of robust control system (parametric vari- Fi 22 Response trajectories of udaptive control system (nominal case

Slider position

wii! FE = pNt)

I-

8

4

i q

2

0

-2

r - - . r - - - r

-

I

time, s

Fig 19

ation case with FE = 5Nt i

Control effort i<,

Response trajectories of' robust control system (parametric vuri-

time, s

Fi 23 Response trajectories of adaptive control system (nominal case

Control effort iq*

w i z FE = ONtj

6.0

time, s

Fig 24

variation case with FF = ONt J

Crank angle

Response trajectories of adaptive control system (parametric

time, s

Fi 20 Response trajectories of adaptive control system (nominal case

w&FE = ONt)

Crank angle

I

-1

time, s

Fig 25

variation case with FE = ONt)

Error function

Response ,trajectories of udaptive control system (parametric

311

I

time, s

Fi 21 Response trajectories of adaptive control system (nominal case

Error function

Proc-Control Theory Appl., Vol 145, 3, 1998

wi%FE = O N t )

Trang 9

0.30

1

0.40

XB

0.30

time, s

Fig 30

variation case with FE = SNt)

Slider position

time, s

Fig 26

variation case with FE = ONt)

Slider position

8

6

i;l 4

2

I

2 t

time, s

Rmponse trajectories of adaptive control system (parametric

Fig 27

variation case with FE = VNt)

Control d r o r t iq*

time, s

Response trajectories of adaptive control system (pavametric

Fig 3 1

variation case with FE = 5Nt)

Control effort l q

nal disturbance force FE = 5Nt Furthermore, the adap-

tive control system shown in Fig 7 is also simulated by

using Matlab package under the same simulating conditions as the robust control system, and the parameters of the adaptive controller are chosen to be the same as the robust controller The simulation results in the nominal case, the parametric variation case and the parametric variation with the external disturbance case are shown in Figs 20-31 According to the simulation results, due to the robust control characteristics of the robust and adaptive controllers, smooth step-command tracking responses are obtained for both the crank angle and the slider position at both the nominal and parametric variation cases However, according to the existence of the steady-state error as shown in Figs 16-

19, the robust controller is inadequate when parameter variation with large external disturbance occurs On the other hand, the steady-state error is eliminated by the adaptive controller as shown in Figs 28-31 In the simulation results of the adaptive controller, all the control efforts are larger than the respective simulated control effort of the robust controller owing to the adaptation

of the and y parameters

Some experimental results are provided here to dem- onstrate the effectiveness of the proposed robust and adaptive controllers for step-command tracking The software flowcharts of the DSP-based computer control system are shown in Figs 32-35 The control processing is performed by the main program and three subroutines, two in the PC and one in the DSP

I

I >

5.1

I

~~

time, s

Fig 28

vurialion c a ~ c wilh FE = 5Nl)

Crank angle

i’ I I I

0

vj -5

-10

I

I -1-

I

time, s

Fig 29

variation case with FE = 5 N t )

Error function

Response trujectories of adaptive control system (parametric

IEE Proc.-Control Theory Appl., Vol 145, No 3, May 1998

Trang 10

main

parameters initialisation

I

a initialisation

interrupt intervals

enable interrupt monitor

disable interrupt

Fig 32

Main

Sojiware flowcharts of DSP-based computer control system

get XB from linear scale interface

synchronise

I DSP 1

g e t i i from

DPRAM

Fi 33 Software jlowcharts of DSP-based computer control system

1.4 1, T, = 1 ms

interface

calculate rotor flux position

output

to vector processor

W

Fig.34

ISR 2, T, = Software flowcharts 0.25 ms of DSP-based computer control system

Fig 35

DSP, T, = Sojiware flowcharts oj DSP-based computer control system I ms

In the main program, parameters and input/output (I/

0) initialisation are performed first Next, the interrupt intervals for the two interrupt service routines (ISRI and ISR2) are set After enabling the interrupts, the main program is used to monitor the control data The ISRl with 1"s sampling rate (T,) is used for linear scale interface to get the slider position (X,) and syn-

chronising the execution of the DSP, and then gets the

value of control effort (i;) from the dual-port RAM (DPRAM) if the execution of DSP ends The ISR2 with 0.25ms sampling rate is used to implement the field-orientated mechanism and control the vector processor Subroutine in the DSP first gets the value of

X , from the DIPRAM, and transfers X , to the crank

angle (e) by using eqn 25, and then performs the robust or adaptive control algorithm Two test conditions, the nominal case with no external disturbance force and the parametric variation case by adding a

7.4kg load on m 3 with no external disturbance force, are tested here The responses of the crank angle, the

slider position, and the control effort iq* with the

robust controller for the two test conditions are shown

in Figs 36-38 and 3 9 4 1 The responses of the crank

angle, the slider position, and the control effort iq* with

the adaptive calntroller for the two test conditions are shown in Figs 4 2 4 4 and 4 5 4 7 The results show that smooth step-command responses are obtained for the angle of the crank and the position of the slider, moreover, the tracking errors converge to zero within Is

Furthermore, the experimental results correspond to the simulation results

. .. .. ..

.. .. .. ..

Fig 36

Crank angle

Experimental results of robust control system (nominal case)

/ j ., .. : : : ' I

Fig 37

Slider position Experime,ntal results of robust control system (nominal case)

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