intelligent actuator

Automatica, Vol. 29, No. 5, pp. 1315-1331, 1993 0005-1098193 $6.00 + 0.00 Printed in Great Britain. 1993 Pergamon Press Ltd

Intelligent Actuators Ways to Autonomous Actuating Systems*

ROLF ISERMANNt and ULRICH RAABI-

The integration of microelectronics within the actuator allows the addition of more intelligent functions. Based on parameter and state estimation and nonlinear models with hysteresis, adaptive control and fault diagnosis are demonstrated for an electromagnetic and pneumatic actuator.

Key Words--Actuators; intelligent control functions; nonlinear adaptive control; supervision; fault diagnosis.

Abstract--The integration of microelectronics within the actuator allows not only replacement of the analog position controller but addition of several functions which give the actuator more intelligent functions. The actuator control is performed in different levels and includes adaptive nonlinear control, optimization of speed and precision, supervision and fault diagnosis. The actuator knowledge base comprises actuator models based on parameter estimation, controller design and a storage of the learned behavior. An inference mechanism makes decisions for control and fault diagnosis, and a communication module operates internally and externally. After a short review of important actuator principles and their properties, as examples, electromagnetic and pneumatic actuators are considered and it is shown how the control can be improved considerably by model-based nonlinear control, taking into account time varying nonlinear characteristics and hysteresis effects. Supervision with fault detection indicates faults in the electrical and mechanical subsystems of the actuator. Several experimental results are shown including the implementation on a low-cost microcontroller.

1. INTRODUCTION

FROM THE BEGINNING actuators and sensors play an important role in automatic control systems. They must operate precisely and function reliably as they directly influence the correct operation of the control system. In many cases actuators manipulate energy flows, mass flows or forces as a response to low energy input signals

* Received 3 February 1992; revised 27 August 1992; received in final form 24 November 1992. The original version of this paper was presented as a plenary paper at the IFAC Symposium on Intelligent Components which was held in Malaga, Spain during May 1992. The Published Proceedings of this IFAC Meeting may be ordered from: Pergamon Press Ltd, Headington Hill Hall, Oxford OX30BW, U.K. This paper was recommended for publication in revised form by Associate Editor C. C. Hang under the direction of Editor P. C. Parks. Corresponding author: R. Isermann. Tel. (49) 6151 162114; FAX (49) 6151 293445; Telex 419579.

t Technical University of Darmstadt, Institute of Automa- tic Control, Laboratory for Control Engineering and Process Automation, Landgraf Georg Str.4, D-64283 Darmstadt, Germany.

1315

like electrical voltages or currents, pneumatic and hydraulic pressures or flows. Basic components are usually a power switch or a valve, an electrical, pneumatic or hydraulic amplifier or motor, sometimes with feedback to generate a specific static and dynamic behavior, and a sensor for the actuator output, like a position or force. Because of the continuous motion or changes and the power amplification, actuators usually undergo wear and aging. Hence their properties change at least gradually with time and the performance may diminish. Faults may appear and develop until a failure occurs.

Industrial sensors usually show a different dependence on life time than actuators. The influence of wear and aging may be less. However, this very much depends on the environment and it is difficult to make a general statement. Sensor failures seem to occur randomly and suddenly (Halme and Selk~iinako, 1991; Henry and Clarke, 1991).

Figure 1 shows the scheme of a classical actuator without and with analog position control. The analog command signal UR is the reference value for the position controller. Dependent on the actuator type, one distinguishes proportional actuators (e.g. piezoelectric or

electromagnetic actuators) integral actuators with varying speed (e.g.

pneumatic/hydraulic cylinders or d.c. motors) integral actuators with constant speed (e.g.

a.c. motors) actuators with quantization (e.g. stepper

motors) (Isermann 1989, 1991a). The goal of the position controller is to obtain

precise positioning, independent of disturbances like power supply voltage, shaft and gear friction, backlash or reactive forces from the

1316 R. ISERMANN and U. RAAB

-~"] ~ Z ~ . u . ~ l l ~ , ~ actuator ~- I lP ,~o~r., L~ I-- I ......... , , ';

FIG. 1. Classical actuator control: (a) feedforward position control, (b) analog feedback position control.

manipulated mechanism or medium. Because the analog position controllers are mostly linear P, PI or PID controllers, the reachable control performance is not very high since the actuators frequently show nonlinear behavior.

The position control also masks faults of the actuator up to a certain size. If the faults of an actuator are large enough, they may be detected indirectly by monitored variables like the power supply current or the control deviation of the position controller or of the superimposed controller or, of course, by inspection.

Further development of actuators will be determined by the following requirements: larger reliability and availability higher precision of positioning faster positioning without overshoot simpler and cheaper manufacturing.

The design and the manufacturing of classical actuators has reached a very high standard. If the numbers of produced pieces are high, the prices are relatively low. Therefore no significant changes are to be expected from this side. However, new impacts can be expected from new actuator principles and the integration of microelectronics. New actuator principles are, for example, piezoceramic and magnetostrictive effects of electrochemical reactions (e.g. Raab and Isermann, 1990a). A stronger influence may come from the integration of microelectronics on (classical) actuators, as the prices for the microcontrollers are now low enough. Then, not only the analog position controller can be replaced but many more functions can be added. This may lead with time to actuators with more 'intelligent' properties.

Saridis (1977) considers intelligent control as a next hierarchical level after adaptive and learning control to replace the human mind in making decisions, planning control strategies and learning new functions by training. Merrill and Lorenzo (1988) define intelligent control systems as those which integrate traditional control concepts with real-time fault diagnostic and prognostic capabilities. According to ~,str/Sm (1991), an intelligent control system possesses

the ability to comprehend, reason and learn about processes.

Care should be taken in using the word 'intelligence' for automatic control in order not to expect too much in comparison to a really intelligent human operator. Here, only a very low degree of 'intelligence' is meant, with 'ability to model, reason and learn about the actuator and its control'. Figure 2 shows the different modules of the information flow of a 'low-degree intelligent actuator'. They comprise: control in different levels

--self-tuning/adaptive (nonlinear) control --optimization of the dynamic performance

(speed vs. precision) --supervision and fault diagnosis

knowledge base analytical knowledge: --parameter and state estimation (actuator

models) -----controller design methods heuristic knowledge: --normal features (storage of learned

behavior) inference mechanism

---decisions for (adaptive) control --decisions for fault diagnosis

communication channels

~ I for ~ ~ -- ' , "~ ~ault diagnosis :~; ~',

E : ; = decisions internal I

~ , for communication i ~ ! contro ,

FIG.

l-'! normal features

i controller design

L r ~md state estimation

~,~

.... i

~ j supervision

..... /

L

actuator

i~ posi~o. I U R power sensor - - , manip~Jlal~on

E

3

UA v

powof supply

2. General scheme of a (low-degree) intelligent actuator.

Intelligent actuators--ways to autonomous actuating systems 1317

communication --internal: connecting of modules , messages ----external: with other actuators and the

automation system. Hence, the 'intelligent' actuator adapts the

controller to the mostly nonlinear behavior (adaptation) and stores its controller parameters in dependence on the position and load (learning), supervises all relevant elements and performs a fault diagnosis (supervision) to request for maintenance or if a failure occurs to fail safe (decisions on actions). In the case of multiple actuators, supervision may help to switch off the faulty actuator and to perform a reconfiguration of the controlled process. Other names for low-degree intelligent actuators would be 'smart actuators' or 'autonomous actuators'.

In the following, model-based methods of self-tuning and adaptive digital control and supervision with fault detection (diagnosis) are described. The models are based on the physics of the actuator and also contain nonlinear characteristics as hysteresis effects. Their mostly unknown and time-varying parameters are obtained by parameter estimation. Applications to different drives show practical results and also how the methods can be implemented on cheap standard microcontrollers.

2. ACTUATOR PRINCIPLES

The actuators considered transform electrical inputs into mechanical outputs such as position, force, angle or torque. The output energy level is much higher than the input signal, so usage of a supporting energy such as electricity, pneumatic or hydraulic pressure is required. With regard to the important actuator concepts, a class- ification and evaluation can be concentrated on three major groups (Fig. 3.): electromechanical actuators fluid power actuators alternative actuator concepts. A further subdivision leads to different operating principles.

Based on the power constraints of the supporting energy and on related construction

eleotromec~nical actuators

d.c. motor

a.c. motor

stepper motor

electromagnet

linear motor

fluid power aotuators

hydraulic actuator concepts

pneumatic actuator concepts

altema~ve actuator concepts

plezoelectrlcal concepts

magnetoslrictive concepts

eleotrodlmnieel actuators

thermo-bimetel actuators

memory-metel actuators

FIG. 3. Low-power actuator principles (


pi~oo~, a~ulW

d.~./,,c.

hydm~ ~m~x

low pm~. emam~

mp~. mo~

IWat~0l

FIG. 6. Power to weight ratios for common actuator principles (without power supply).

by piezoelectric actuators, but only for very small positioning ranges.

The power to weight ratio, in Watt/kg, is presented in Fig. 6. It underlines the leading position of fluid power systems as well as the restricted ratios _of electromagnetic and electromechanical concepts (if the power supply is not considered).

Discussing actuator applications implies a specified closed-loop performance in terms of accuracy, dynamics, positioning ranges etc. Therefore, system characteristics such as the static I/O-behavior, nonlinear effects (friction, backlash, hysteresis) and (time) varying process parameters are important. They are obtained by an evaluation of the uncontrolled actuating device and are presented in Table 1.

The evaluated properties, such as friction, nonlinear characteristics and varying process parameters, are present especially in electro- magnets, pneumatic and hydraulic drives. They limit or hinder the overall performance of position control in a closed loop, especially if their influence is large as in case of low-cost

actuator production. Hence, classical actuator control for these types of actuators is not sufficient to deal with these major restrictions. Therefore, it is a challenging task to combine the given actuator hardware, a microcontroller and sophisticated control-software to improve the dynamics as well as the static characteristics of actuators and to add other, more intelligent functions.

3. MODELLING AND IDENTIFICATION OF ACTUATORS

Precise actuator models are of substantial importance for the design of model-based control algorithms and supervision with fault diagnosis. They are developed by theoretical modelling and describe the dynamic relations between the electrical input U and the mechanical output Y. For a more detailed approach considering electromechanical, pneumatic or hydraulic actuators see e.g. Pfaff (1982), Back6 (1988), Raab (1993) or Tomizuka et al. (1985).

For most actuator models there exist certain similarities. In the case of translational motions they have a SISO-structure, as shown in Fig. 7.

The actuator model describes the energy transducer, consisting of an amplifier with delayed dynamics and a following force gener- ator. Because of energetic boundaries and material properties, the static behavior between the electrical input and the generated force F~ is nonlinear to some extent. The dynamics can be simplified to a linear first-order system, e.g. a closed-loop controlled current subsystem (Fre- yermuth and Held, 1990), or a second-order system, e.g. servo-valves (Back& 1990).

TABLE 1. INPUT/OUTPUT BEHAVIOR OF IMPORTANT ACTUATOR TYPES

Varying process Nonlinear effects parameters

Static Characteristic linearity Friction Backlash Hysteresis Internal* Externalt

Actuator type d.c./a.c, motor .+ O- O- O O-

with feed Stepper motor + - - 0 - 0 -

with feed Electromagnet - - - 0 - Pneumatic - - 0

cylinder Hydraulic - - 0

cylinder Piezo-stack 0 - - -

actuator

+ = Good, negligible; O = average, common; - = bad, significant. * Caused by internal physics (position dependent parameters etc). t Caused by external influence (varying supporting energy potential, thermal

properties etc.).


transducer medlani~fl system

FIG. 7. Simplified actuator model for translational motions and proportion I/O-behavior.

FG acts together with the sum of other forces on a mechanical spring-mass system. The resulting displacement is characterized by the position output Y and velocity dY/dt, and can be modelled by

m~'(t) = ~ F(t)

= FG(t) + FL(t) -- cY(t) - FF(I 2) (1)

where FL denotes external loads and Fv frictional forces. In the case of an integral I/O behavior the spring feedback, represented by spring constant c, does not exist.

In general the motion of the mass is influenced by frictional forces. Once the motion begins, this effect can be modelled by a superposition of Coulomb friction Fc and linear damping d ('viscous friction')

FF(Y :/: 0) = Fc:F sign (I?) + d:F- I;" (2)

where the index +/ - denotes coefficients for positive (+) or negative ( - ) motion directions. Equation (2) delivers a simple but, for practical purposes, adequate friction model. A more sophisticated approach, which describes stip- slick effects during slow motion, requires Stribeck's extended friction model (Stribeck, 1902; Maron, 1991).

If well known linear design methods are to be used, the model must first be linearized and the range of operation must be confined to a small range. A better approach is to use two differential equations for the actuator dynamics

y( t )=-~a* di "" i=l i+ -~iy(t)

+ ~ b*+ ~,u(t) + C~c+ (3) j=o J clt'

for dy/dt > 0 (positive motion) and

y(t) = - ~ * dj i=, ai_ -~y(t )

j~ , dj + bj_ -~ u(t) + CDc-

.=) (4)

for dy /d t. > y(k - n) (positive motion) and

y(k) =- ~ a~_y(k - i ) i=1

+ ~ bj_u(k - j) + CDc_ (7) j=l

for y (k )


is obtained by minimizing the loss function N

V = Z e2(k) = ere k =0

where

(10)

e(k) =y(k) - ~pr(k). ~ (11)

represents the equation error and 0 the estimated value of O. This results in the nonrecursive LS-estimation equation, which can be transformed to recursive algorithms Modifi- cations in the form of discrete square root filtering (DSFI) or adequate factorization methods show better numerical properties, e.g. Biermann (1977), Kofahl (1986) In the case of a discrete time model, the data vector ~p directly involves the measured I/O-data of u and y. For the identification of continuous time models, the unknown derivatives in the data vector must be determined by e.g. state variable filter techniques (see Young, 1981; Peter and Isermann, 1989).

If data processing can be performed off'line, usually better identification results are obtained by nonlinear parameter estimation methods. Based on an output error approach

e(k, O) = y(k) - yM(k, O) (12)

the minimization of the quadratic cost function

= min e2(k, (~) (13)

with a hill climbing method offers an improved robustness as well as reduced estimation bias (see Kabaila, 1983; Ljung, 1978; Drewlow, 1990). Using the discrete time representation, model output YM can be directly computed by equations (6) and (7). For the continuous time representation, an additional discretization of equations (3) and (4) in each iteration step is required. Although the computational effort is therefore high, the omission of state variable filter techniques may be an advantage (R~ab, 1993).

According to the proposed estimation methods, it is important to point out that the identification procedure for the actuator is carried out separately for both motion directions. As the models are only valid for velocities not equal to zero, only data vectors which fulfill the adequate conditions should be used. Therefore a sufficient excitation must be guaranteed, which can usually be obtained during a pre-identification period using special input signals. A suitable one, which delivers

>" 3

_~ 2

-1

-2

0.25 0.5 0.75 i 1.25 i 5 175

time [ see ]

FIG. 8. I/O-signals and related identification ranges for a proportional actuator with friction (simulation).

good identification results even in the case of high-order actuator models is shown in Fig. 8 (Raab, 1993). Note that only I/O-data within the shaded areas are used for the identification of the actuator model.

4. MODEL-BASED NONLINEAR CONTROL OF ACTUATORS

In order to obtain a specified I/O-performance in terms of accuracy, dynamics and robustness, actuating systems require a closed-loop position control. Assuming an approximately linear process behavior, the basic discrete time SISO-control algorithms are of type

u(k)=-~p i .u (k - i )+ ~ q j .e ,c (k - j ) (14) i=1 j -O

which include for example the P, PI or PID type.

ew(k) = W(k) - Y(k) (15)

denotes thereby the control error and u the controller action. If a state control is used

u(k) = -krx (k )= - [k ,k2 . . . kn]

[x , (k )x2(k) . . .x , (k ) ] 'r. (16)

x are the measured or observed state variables and k is a constant gain vector.

The design and tuning of these algorithms are based on identified parametric actuator models (see Section 3) and supported by appropriate software design packages. The use of computer- aided controller design and system analysis is described in e.g. Isermann (1984a, 1991a).

Because actuator properties such as friction, hysteresis, nonlinear characteristics and time- varying process parameters are present (see Section 2), even well-tuned linear control


g

[ con~o. ~cmnnnu,~y p,o~,,~ [

FIG. 9. General structure of a series correction (compensation) for nonlinear process statics.

I f~o" L. F L I-~---------I_

[ p,'oce~ w~ rr~on or_ - l

FIG. 10. General structure for friction compensation.

algorithms do not give satisfactory results (Raab and Isermann, 1990b). Therefore these nonlinear effects are taken into account for the design of the actuator position controller.

Correction of nonlinear static characteristics Nonlinear static characteristics are present in

most of the actuators, either in specific local areas or over the whole range. This leads to a loss of control performance or even closed-loop instability.

The objective is to compensate the main static nonlinearity f by an approximate inverse function f*, which can be implemented in the microprocessor (Franz, 1973; Lachmann, 1983). According to Fig. 9, the regular actuator input U is then substituted by the 'corrected' value

U* =f*(U, x) (17)

such that the I/O-behavior U -Y becomes (approximately) linear. Gp1 usually represents here the dynamics of the energy transducer, Gp2 the mechanical system and x the involved process states.

Assuming an actuator model as shown in Fig. 9, the nonlinear static relation f* follows from

x2 = U*-Kp, . f(x) (18)

and

x2 = K .u . (19)

K describes the determined gain of the 'linearized' system and Kp~ the gain of the input system Gp~ (Raab, 1993).

In practical cases the dynamics of module Gp~ are often negligible compared to the time constants of Gp2 (e.g. energy transducer vs. mechanical system dynamics). If f (x) offers then a precise approximation, good and robust compensation results are obtained.

Friction compensation The main control problem with friction occurs

when high positioning accuracy is required. If the process stops within the hysteresis width before the setpoint is reached, only the integral part of the control algorithm can compensate for

the offset. This leads to a significant loss of control performance and accuracy, especially during small position changes.

The basic idea of friction compensation is to compensate the relay function of the Coulomb friction by adding an adequate compensation voltage Ucomp to the normal control action U (see Fig. 10). Different methods such as dithering, feed-forward compensation and adaptive friction compensation will be described.

In general, the success of each compensation depends on the quality of U~o,w, but also on the frequency response of the energy transducer Gpl. However, an overcompensation may destabilize the position control loop (Maron, 1991).

Dithering. Dynamic linearization, or so-called dithering, is the classical way of analog and even digital friction compensation. By adding a high frequent, periodic signal to the control action U, the friction is compensated during half the period, whereas during the second half it is undercompensated. The method is quite robust with regard to the amplitude and frequency of the dither signal. A little overcompensation results only in a small armature dither. However, if the amplitude is too large, the control performance deteriorates. Another dis- advantage is a slower motion, which is caused by the second half of the dither signal stopping or even accelerating the mass in the wrong direction (Maron, 1991).

Feedforward compensation. This approach is from the theoretical point of view the ideal control strategy for friction compensation (see e.g. Wallenborg, 1987; Southward et al., 1991). By adding the compensation value

Fc~ Uomp(k) = - Kp---~ sign Jew(k)] (20)

to the controller action U, an optimal inverse function of the Coulomb relay characteristic is obtained. Note that instead of the unknown velocity dY/dt the control error ew is used for the sign of Ucomp.


In practical applications, the accurate values of the Coulomb friction Fc and energy transducer gain KpI are not exactly known and have to be approximated by the measured/ estimated static behavior (hysteresis characteristic) (see e.g. Maron and Raab, 1989) or the measured/estimated dynamic friction relation in equation (2) (Maron, 1991). To avoid an overcompensation, a safety factor o: < 1 can be introduced

Fc:~ U~omp(k) = -or .~p j . sign [e~(k)] (21)

allowing 100- (1 - t r )% compensation of the effective friction value. The remaining offset is then controlled by the integral part of the position controller.

Adaptive friction compensation. In the preced- ing methods, the friction compensation was realized by a feedforward control strategy. Better results may be expected, if the actual friction value can be adapted in an additional feedback 'friction control loop'. Therefore an adaptive friction compensation was developed, which interprets the abbreviation

eM(k ) = y(k ) - yM(k ) (22)

between the measured output Y(k) and a linear reference model YM(k) as frictional effect. Using a nonlinear friction controller as described in Maron et al. (1990) and Maron (1991), an inherent adaptation of the compensation value Ucomp to slowly time-varying frictional forces is performed. Due to the fact that external loads FL act in the same way as frictional forces (see Fig. 10), transient load changes in particular may affect a transient overcompensation for several sampling instants (compare also Canudas de Wit et al., 1987).

Varying process parameters and adaptive position control

During normal operation, most of the actuating systems change their parameters in a significant way. This is caused by several environmental conditions, wear or imminent physical principles such as position-dependent forces or dampings. Hence, fixed and robust algorithms are usually not suitable. An improved control performance over the whole range of operation as well as lifetime may be obtained by adaptive control techniques for the whole actuator.

For the considered actuating systems, parameter scheduling and model identification adaptive control systems are especially suitable. Both concepts are described in e.g. Astr6m and Wittenmark (1989), and Isermann et al. (1992).

7

FIG. 11. Adaptive control with parameter scheduling.

Parameter scheduling. Parameter scheduling based on the measurement of varying operation conditions is an effective method to deal with known and approximately time-invariant process nonlinearities. Supposing measurable auxiliary variables V, that correlate well with the process changes, the adaptation of the controller parameters r is performed as functions of V (parameter schedule) (see Fig. 11).

Parameter scheduling offers the specific advantages of a simple microcontroller implementation and a fast reaction to modelled process changes, providing an adaptation even during transient operations. Typical applications therefore are the feedforward adaptation to a varying supporting energy behavior such as for example the electric voltage in automotive applications (e.g. Raab, 1993), or the compensation of position dependencies in pneumatic/ hydraulic systems (e.g. Anders, 1986).

Parameter adaptive control systems. Parameter adaptive control systems for the closed-loop position control of actuators are characterized by using identification methods for parametric process models. The overall structure, performing online parameter estimation, controller design, supervision and coordination are shown in Fig. 12.

Depending on typical sampling frequencies from 40Hz up to lkHz and more, the implementation requires adequate microcontrollers or microcomputers or even digital signal processors. The practical application of parameter-adaptive control techniques is determined by the identification of the dynamic actuating system in a closed loop. The objective is to get good estimates of varying process

supervision and coordination level I

FIG. 12. Parameter adaptive control structure.


parameters under the given constraints of 150 transient load changes and several nonlinearities such as frictional forces or hysteresis. This can 125 usually (only) be realized for the mentioned ~" large sampling frequencies if the dominant ~ ~0o process changes are described by low-order ~ actuator models (Raab, 1993). Practical applica- ~ 7s tions, including additional identification condi- ~ 50

t~

tions as discussed in Section 3, show that E actuator models with integral or first-order are 25 good enough for this purpose (see Raab, 1990; K6ckemann et al., 1991; Glotzbach, 1991). 0

i I i I

5 IO 15 20 26

position Y [ mm ]

5. EXPERIMENTAL RESULTS WITH MODEL- BASED ACTUATOR CONTROL

The proposed methodology for process identification and nonlinear model-based control techniques was tested on different actuator types. Experimental results which show some disadvantages of the actuator behavior are presented in this section. Because the actuator design remains unchanged, the results show the development of high performance systems by using only a more sophisticated control software and intensified digital signal processing. An implementation of the presented algorithms has been tested on a standard 8-bit microcontroller (Siemens 80535). A transfer to similar actuating systems is possible.

Electromagnetic actuators Electromagnetic actuators play an important

role as linear motion elements in e.g. hydraulic/pneumatic valves, Back6 (1990) or fuel injection pumps (H~ifner and Noreikat, 1985). A precise position control is a challenging task as there are severe nonlinearities in the system. These include friction forces, magnetic hysteresis and nonlinear force-current characteristics (e.g. Lee, 1981; Lu, 1984), which limit the closed-loop control performance in terms of accuracy and dynamics.

Solenoid drive. The specified d.c. solenoid drive (Fig. 13) has a positioning range of 25 mm and shows a nonlinear force characteristic as

u_~L T .~i y

I

position sensor coil spring armature

FIG. 13. Scheme of the investigated d.c. solenoid drive (Binder Magnet GmbH).

FlG. 14. Position-dependent nonlinear force-current characteristic of the solenoid drive. The dotted line represents the

linear spring characteristic.

depicted in Fig. 14. The displacement of the armature works against a spring and can be measured by an inductive position sensor. Process input is thereby a pulse width modulated (PWM) and amplified voltage U, which manipu- lates the coil current 1.

The objective is to design a robust position control loop, which includes the correction of the nonlinear static characteristic in Fig. 14 and compensation of dominant frictional forces. The low cost solenoid, which usually performs simple mechanical switching tasks, then offers similar features to a sophisticated magnet with proportional I/O-behavior.

Therefore the static force-current-position dependency has to be linearized by a nonlinear correction as shown in Fig. 9. An appropriate function, describing the nonlinear characteristic of Fig. 14 is obtained by a polynomial approximation

f ( I , Y) = I . 22~=o (Yo- y) i with I1o = 26 mm (23)

(Raab, 1992). The resulting statics of the linearized actuator are shown in Fig. 15, where a typical hysteresis characteristic becomes obvious. Its gradient represents the local gain Kp of the actuator, which can be assumed now as constant. The position-dependent width of the hysteresis characteristic is a measure for frictional forces and magnetic hysteresis (see e.g. Maron and Raab, 1989).

According to the 'linearized' system and the equations for the inner current loop

T~i(t) + l(t) = K, . U(t) (24)

and the mechanical subsystem

m}'(t) + di'(t) + cY(t) = KMagl(t) - Fc sign (I?) + FL(t) (25)


10 ' ' ' l ' ' ' l ' ' ' l ' ' ' l ' ' ' l ' ' ' l ' ' ' l ' , , i , , , 1 , , ,

E E 8 Kp.M

i i i

4 )-

0

0 0 1 2 3 4 5 6 7 8 9 10

input U [Vl

2O

3E la,. > .

2 ~, - i5

FIG. 15. Hysteresis characteristic and position dependent local gain of the 'linearized' solenoid drive.

the I /O behavior of the actuator can be modelled as a third-order system in the form of equations (3) and (4) (e.g. Raab, 1993). The unknown parameters are obtained during a pre-identification phase, exciting the actuator with the shown input signal (Fig. 8) and sampling at 400 Hz. Considering the effect of Coulomb friction as discussed in Section 3, the nonlinear output error parameter estimation leads to the following 'direction-dependent transfer functions'

r(s) C+(s) = - - U(s )

382400 e -'~zSs (26)

(s + 116.4)(s 2 + 40.4s + 3329.4)

r(s) C_(s)- U(s)

220100 e -'25s. (27)

= (s + 47.9)(s z + 47.9s + 3444.5)

Index +/ - denotes the direction of the armature motion and the additional deadtime describes the effect of an asynchronous PWM-generation.

Figure 16 shows the obtained control performance, using a numerical optimized position controller

u(k) 2.231 - 4.204q -l + 2.000q -2 Gc(q-l) = ew(k) - (1 - q-~)(1 - 0.616q -~)

(28)

(PIDTl-type, To = 2.5 msec) where q- i is a shift operator for one sampling time [u(k)q -1= u(k -1 ) ] . Although there is a change in the actuators' dynamic behavior, the controller designed for the slower negative motion (worst case) is robust enough for positive motions. The dynamic features are suitable and stability is obtained even in the positioning range (17 mm < Y


pQ~t~n sensor ./

valve 1 ~e 2 U1 2

a~nosphere N pressure .. 1000 mber

lexible nembrane

,! FIG. 18. Scheme of the low pressure membrane drive

(Pieburg GmbH).

automatic generated 'dither signal', which adapts its amplitude and frequency with regard to the control performance.

Similar experimental results could be obtained, using a proportional magnet drive in a diesel fuel injection pump (Raab, 1993).

Pneumatic actuator The chosen pneumatic actuator is charac-

terized by a rugged and temperature resistant design, which offers in general a high reliability (Fig. 18). Designed for actuating tasks in modern vehicle carburators, the membrane drive has a positioning range of 20 mm (Baumgartner, 1982; Schiirfeld, 1984). The supporting energy is low air pressure from the manifold, varying in automotive applications from 100 mbar to nearly atmosphere. A positioning control is obtained by manipulating the internal pressure potential with two pulse width modulated on/off valves.

The present system incorporates some typical drawbacks of low-cost membrane drives. Accor- ding to a changing low-pressure support, the dynamics of the system vary over wide ranges (Fig. 19). In addition, nonlinear process dynamics are coupled with the shaft and membrane position. They depend on the motion direction as well as on the external load.

Hence a fixed, robust designed closed-loop position controller cannot give a good control performance. Therefore the control performance of the actuator was improved by using adaptive control techniques. The developed methods are based on a discrete time actuator model, which is obtained by theoretical modelling. Under the given constraints, the dynamics for each direction can be described by an integral behavior

Y(k ) = Y (k - 1) + K,I " To" U,(k - 1)

for

Y(k ) < Y (k - 1)(down ~) (29)

Y(k ) = Y (k - 1) + K,2. To. U2(k - 1)

for

Y(A) > Y (k - 1)(up T)

where Kn/i2 represent integration constants with the physical dimension of a velocity (mm/sec) (Raab, 1992). In comparison to the sampling time To= 20msec, the model parameters are supposed to be constant or slowly time-varying.

For closed-loop position control, a digital P-algorithm with motion dependent parameters,

Ul(k) = qolew(k) , ew(k) < 0 (30)

U2(k) = qo2ew(k), ew(k) > 0

is used. According to an estimated process parameter range from KI = 10. . . 80 (mm/sec), the design of the controller gain qo by a numerical minimization of a quadratic cost function delivers the adequate values presented in Fig. 20.

Due to the fact that the process parameters Kn and especially K~2 are highly dependent on the low pressure PL, an additional measurement (and sensor) of PL enables the design of a parameter scheduled control strategy

I" = [qo,, qo2] =f[Kn(PL) , KI2(PL)] (31)

Vl open V2 open V2 dosed V2 dosed Vl closed Vl open

/ / \/oo

0 . . . . , I 0.5 1 1,5 2 2.5 3

time [secl

FIG. 19. Varying dynamics of the pneumatic actuator for different low pressure potentials within the manifold.

o 5 o"

3

p~ 2

6 i f ' i , i , l - , i '

W - 5 mm

~ t s(with fixed qo) ~ . t

%,=o. .

10 20 30 40 50 60 70 80

process parameter K, [ mm I aac ]

14

12

O8 .."

06 ~

o , ~ O2

FIG. 20. Parameters and closed-loop settling times for a fixed and scheduled adaptive position controller.


for both operation directions. The obtained control performance, evaluated by the settling time ts for a closed-loop step response is presented in Fig. 20. Compared to a fixed, robust tuned position controller, which is designed for the worst case of the integration constant K~, a considerable improvement in the range of low pressures is achieved (the shaded area in Fig. 20).

A more sophisticated approach is the application of a parameter adaptive control structure, which performs the tasks shown in Fig. 12. For online/realtime identification of the unknown process parameters K . and KI2 , the recursive DSFI-algorithm with the forgetting factor ~, = 0.975 is applied. Estimation is started by the supervision level, if appropriate exciting conditions are fulfilled. A valid estimate is already obtained after 3-4 sampling instants. Hence the actual system parameters are obtained during small setpoint changes.

Process identification and controller tuning have to be coordinated during real time application. The algorithm used depends on monitored process I/O signals, an online comparison with a reference model and an evaluation of the time varying eigenvalue of the

2O

E E is

0

P L " 200 mbar I P L "700 mbar : W- F L - 10 N

, , , I . . . . i , , , , , L , , 5 i0 15 20

5

g

,],

U2

io 15

time [ sec ]

~ 75

5o E

~-- 25

E

o . I

N I r E "~ 75L

q 02 , ~

^ K 12 -' ^

KI1

N

q 01

Io ~5

. ~ 12 ~ L o "

o6

i 0

-06 "~

2O

time [ see I

FK;. 21. Time history of the parameter adaptive position control for different pressures of the air supply and load Fl,

T o = 20 msec.

a~laptive

p ...... I

process paramete K I - 12,,, ,,

04 . . . . : ': '

: i ' 1. C

frequency [ Hz ]

FIG. 22. Measured frequency response of the closed loop for the parameter adaptive and conventional fixed controller,

recursive estimator

z, = 1 - ~pT. 7(k) (32)

(see Kofahl, 1988; Isermann et al., 1992). The time history of the parameter adaptive

position control is shown in Fig. 21 for different supporting pressures and external load changes. Adaptation is performed during appropriate process excitation phases. This guarantees a good estimation result and leads to a well-tuned control algorithm. An accuracy up to 15-20 ttm even when using the maximal system dynamics can be obtained over the whole range of supporting energy changes and external loads.

Compared to the positioning accuracy and dynamics of the fixed controller, an improved control performance is obtained. An evaluation of closed-loop performance for sinusoidal reference, values is shown in Fig. 22. The bandwidth with the adaptive controller is increased to about 6 Hz for all cases, compared to 1-6Hz with the fixed controller. Process parameter K~ varies thereby between 12 and 50 mm/sec, which represents a low air pressure range from PL = 800--400 mbar.

6. MODEL-BASED FAULT DETECTION, DIAGNOSIS AND SUPERVISION OF ACTUATORS

An important feature of an intelligent actuator is the automatic supervision and fault diagnosis of its components. Figure 23 shows an actuator influenced by faults. External faults are caused, for example, by the power supply, contamina- tion or collision; internal faults by wear, missing lubrication, sensor faults or other malfunctions of components like springs, bearings or gears.

If the faults influence direct measurable output variables they may be detected by an appropriate signal evaluation. The corresponding functions are called monitoring, if the measured variables are checked with regard to a certain tolerance of the normal values and alarms are triggered if the tolerances are exceeded. For


U

internal & external ~ faults

y+~,, process ~=lm

~0+ A~ o Xo+ AXo

FIG. 23. Scheme of an actuator influenced by faults.

actuators, the current of the input supply or the control deviation, for example, can be monitored. In the cases where the limit value violation signifies a dangerous state, an appropriate action can be indicated automatically. This is called automatic protection. An example is the actuator switch-off at the end of the positioning range.

The classical ways of limit value checking of some few important measurable variables are appropriate for overall supervision. However, developing actuator faults are only detected at a rather late stage and the available information does not allow an in-depth fault diagnosis. Research efforts have shown that the use of process models allows an early fault detection in connection with normal measured variables (Isermann, 1984b, 1991b). Nonmeasurable quantities like state variables and parameters may then be estimated. With this improved knowledge a supervision with fault diagnosis becomes possible.

Fault diagnosis with parameter estimation The electromagnetic actuator shown in Fig. 13

is now considered for the 'linearized' operation range from 0 to 25 mm. From the equations for the current circuit equation (24) and the mechanical subsystem equation (25), a third- order differential equation follows:

Y(3)(t) + a~'(t) + a~'(t) + a~Y(t)

=b~U(t) + C~c(t). (33)

The parameters of the continuous time representation

O r = [a~, a~', ao, b0, C~c] (34)

depend thereby on the physical process coefficients

pT = IT,, o , co0, Kp, Cf, c] (35)

with e.g.

D - 2VC~--~, w0 = . (36)

These process coefficients can be expressed in terms of the parameter estimates O (Raab,

normal condition F1 F2 F3 F4

i o - d.e. velue ~o I.,-,*.,,,~,,.'~. I -2

-3 - -4 -

-5 I

10 20 30 40 50

~'-60 ~ I ~ '~ I z 0 5 0 ~-r ......... \ naturedli ......... d l~'n ping I ~ ,~ I i ......... fr~luerl~%~~e~l^a)o [ Hz ]1106 -~ L /damping D ~,. .=~,] ~ ~

:-~ 20 I / time constant T I [ msec ] ] ~.~.~.,~,,.~.,~ 02

0 I0 20 30 ~0 50

number of evalua~ons

FIG. 24. Parameter estimates for an electromechanical drive with different faults (positive motion direction).

1993). Hence after estimation of the model parameters O by measuring the voltage U and the position Y, all process coefficients P can be calculated.

In the following some experimental results are shown for artificially generated actuator faults: FI: too large pretension of the spring F2: decrease of the spring constant (by break or

aging spring change from c= 1650- 1200 N/m)

F3: increase of friction (increase of surface roughness and jamming)

F4: fault in the current circuit (weak controller gain).

The parameters were estimated by the proposed output error minimization using specific excitation signals (see Section 3). Sampling time was To = 2.5 msec. Figure 24 and Table 2 show the results for different faults. Based on the deviations (symptoms), all faults can be identified. This can be performed by a pattern recognition or a systematic treatment of fault-symptom-trees (Freyermuth, 1991). In all

TABLE 2. CHANGES OF PROCESS COEFFICIENTS FOR AN ELECTROMECHANICAL DRIVE IN DEPENDENCE ON DIFFERENT

FAULTS

Static coefficients Dynamic coefficients Fault type Kr,+ Co+ tOo+ D+ TI+

F1 0 - - 0 0 0 F2 ++ - - - O O F3 0 + 0 ++ 0 F4 O O + + + +

+ = Increase, - = decrease, O = no change. Estimates for positive motion direction, co = C~c/a~.

AUTO 29:5-L


cases, different patterns of coefficient changes result. This enables an unique diagnosis of the four faults.

Fault detection with state estimation. With the basic equations (24) and (25), the continuous time state representation of the electrochemical actuator

i(t) = A'x(/) + h* U(t) Y(t) = c* rx(t) (37)

can be obtained with

x(t) = [-rl (t)22(t)23(t)Yc4(t)]

=- [Y(t) ~'(t)l(t)c~c(t)]

0 1 0 0 c d KMag 1 m m m m

A* = (38) 1

0 0 0 T, 0 0 0 0

b* = K= e* = .

If the process coefficients are known, the state variables x(t) can be estimated by a disturbance observer based on the measurement of U(t) and Y(t) (see e.g. Bakri et al., 1988).

Now only the static behavior is considered, resulting in

Y(t) : Kp U(t) + ro + x4(t). (39)

This equation is depicted for the nominal state in Fig. 25. It describes the left and right hysteresis characteristics with two different steady state values x4, and x4,- in relation to the nominal actuator statics without hysteresis Kp U + Yo-

Now a discrete time state observer is used

xa(k + 1) = Axa(k) + bu(k) + he,(k) (40)

;4F ~ w

~ 3 5

25

4

X 3

-~ o

, _ _ . ~ ._:. ~ ~. . J

i

o

'~:' 5 i : 5 :

time [ sac I

FIG. 26. Measured actuator signals and disturbance observer signals for the actuator without faults, T O = 2.5 msec.

with the residual

ea(k) = y(k) - eTxB(k). (41)

The representation is obtained by discretization of equation (40) for the sampling time T0. xB(k) describes thereby the continuous time state variables x(t) at the sampling instants kT0, k=0, 1, 2 , . . . . The observer feedback is designed by pole placement resulting in

hT=[0.5459 47.485 0 1.017]. (42)

Figure 26 shows the measured signals of the residuals and two observed state variables of the actuator without faults.

Now XB4(k) is monitored for the case where the observer is adapted for motion in one direction, indicated by a small residual

leB(k)l = eB (43)

As indicated in Fig. 27 by black areas, equation (39) then gives values of the nominal hysteresis characteristic.

Figure 28 shows the corresponding measured and observed signals if the actuator friction increases continuously from la, lb to 2a, 2b.

Y

Yo/

Kp 'U +Yo

U

FIG. 25. Simplified hysteresis curve of the electromagnetic actuator in the nominal state (index.).

' i r I ' I ' ~ ' I k" = ' I '

>_4 >.3 R

2 ~ . ~ ~ Kp 'U(k )+Yo+ XB4(k)

1

1 2 3 4 5 6 7

input U [V]

FIG. 27. Measured hysteresis characteristic for the actuator without faults and trajectories of equation (39).


6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

5 U. -7 "~

I I g . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0 4

~2 g

-4

-6 0 ~. 2 3

time [sec]

FIG. 28. Measured actuator signals and disturbance observer signals for the actuator with increasing friction T to '2' with

fault, T O = 2.5 msec.

The position control variable Y(k) does not change, and only U(k) shows larger values. This shows that a closed loop compensates this fault. The observed state Xa4(k), however, indicates significant changes from the nominal values (shaded ranges) for the adapted observer [equation (43)] such that xa4+ x4,-. Compare also Fig. 29 with Fig. 27. These deviations are now the symptoms for fault detection with state estimation.

A comparison of both methods of fault detection shows:

Parameter estimation: --less a priori knowledge of the process model

required (only model structure) --parameter deviations allow an in-depth fault

diagnosis of different faults, especially for multiplicative faults

---extensive computations required. State estimation: --more a priori knowledge required as process

model parameters must be known ---state estimates show fast response to sudden

faults, especially for additive faults

3

2 1 Kp.U(k) +Y0 + XB4lkl

L I , t I , I ,

o 1 2 3 4 5 6 7

input U [V]

FIG. 29. Measured characteristic hysteresis for the actuator without faults and trajectories of equation (39) for increasing

friction (with fault).

- -no in-depth fault diagnosis --less computations required. Hence parameter estimation gives more information on the type of faults which may develop slowly, and the used state estimation approach gives fast information for suddenly-appearing faults, with less computations.

7. IMPLEMENTATION ON MICROCONTROLLERS

Due to the rapidly advancing microcomputer technology the implementation of sophisticated digital control algorithms is possible even on low-cost hardware devices (see e.g. F~irber, 1989). In the field of actuator control the microcontroller is therefore the dedicated processor type, which performs the embedded control, including process interfacing and signal processing.

Before discussing the implementation, the proposed algorithms should be evaluated in terms of their arithmetic properties and related hardware requirements. As considered in e.g. Raab (1993), the most commonly applied type of algorithm is the discrete time controller as formulated by equation (14). Because only limited ranges of variables and limited quantization of coefficients and variables are required, fixed point numbers and arithmetics are usually sufficient, if dealt with appropriately (Hansel- mann, 1987). Common 8- or 16-bit microcontrollers then offer an efficient realtime computation, even with nonlinear model-based control algorithms. Problems usually arise when state controllers [equation (15)], parameter and state estimators have to be implemented on a microcontroller, performing fast and precise computing. With respect to the wide number ranges and required precision, only floating point numbers and related arithmetics are considered as appropriate (Hanselmann, 1987; Kofahl, 1986). Although the floating point environment is easy to achieve through sub- routine libraries, the increasing computational effort usually limits realtime applications to 'low order' algorithms, or requires that a more sophisticated hardware has to be used (for example 32-bit microcontrollers with custom VLSI designs).

For the algorithms presented in Sections 3, 4 and 6, we have focused on the implementation using only a low-cost hardware. The chosen microcontroller Siemens 80535, 12 MHz system clock, performs 8-bit arithmetics under the given constraints of storage and register capacity (see e.g. Feger, 1987). Using self-defined data formats and a speed-optimized assembler code, computation times and sampling frequencies


TABLE 3. COMPUTING TIME AND OBTAINED SAMPLING FREQUENCIES WITH A LOW-COST 8-BIT MICROCONTROLLER

Algorithm

Electromagnet Closed-loop position control

PIDTI PIDT1 + feed-forward friction control PIDTI + adaptive friction control

Fault diagnosis and supervision via state estimation via parameter estimation

Membrane drive Closed-loop position control

Parameter scheduling Parameteradaptive control

Computation Max. sampling time (msec) frequency (Hz)

0.48(0.53)* 1200(1000) 0.55 (0.60)* 820(600) 2.11 (2.16)t 430(400)

2.73t

0.42t 1200# 7.68t 120t

The values in brackets denote the position control algorithm with nonlinear correction.

* 16-bit fixed-point data format. t 24-bit floating-point data format. $ Implementation requires a sophisticated floating-point hardware.

were obtained as presented in Table 3. The values are given for the tested and embedded realtime software including process interfacing (AD-conversion, PWM-generation).

Nonlinear closed-loop position control can be performed with sampling frequencies from 400 Hz (with adaptive friction compensation) up to 1 kHz. The maximal value is limited by the computational and interfacing delay. In the case of adaptive control the implementation requires 24-bit floating point numbers, which result in decreased sampling rates. Fault detection with state estimation is possible with sampling time 2.7 msec. Hence, nonlinear position control and this fault detection requires a sampling time of about 5msec, or a sampling frequency of 200Hz. For fault diagnosis using parameter estimation, more sophisticated microcontroller hardware including an extended storage capacity has to be used, which is no problem for e.g. quality control after actuator manufacturing or maintenance computers.

siderably be improved by adaptive control techniques by which the controllers 'learn' about the process. Model-based methods are then used for supervision and fault diagnosis of the actuator. Hence the microcomputer controlled actuators observe their own faults and 'reason', close to realtime, about the causes. They may also make decisions with regard to the reached control performance and especially for the diagnosed faults. The decision may be a fail-safe-operation or a reconfiguration if other actuators can take over the task.

In the future the design of an actuator may be not limited to the mechanical side and a simple position controller, because the added microelectronics influence the static and dynamic behavior considerably and allow them to perform new tasks. Hence an integrated design takes place, both on the mechanical and the electronic side, on the hardware and the software side. These are typical features of a mechatronic design.

8. CONCLUSIONS AND FURTHER DEVELOPMENT

This paper has tried to show how actuators can perform more intelligent functions if they are governed by microcontrollers. We concen- trate primarily on 'low degree intelligence' which aims to make the actuator a more autonomous system. One important basis is the theoretically derived mathematical model which includes nonlinear behavior with friction and hysteresis. Another basis involves parameter and state estimators which are driven by few measurable signals. It could be shown theoretically and experimentally for three actuator types that the positioning accuracy and dynamics could con-

Acknowledgements--The research on actuators was supported by the Forschungsvereinigung Verbren- nungskraftmaschinen e.V (FVV), Frankfurt, and the Bundesministerium fiir Forschung und Technologie (BMFF). The authors are grateful for the financial support and discussions with the sponsoring committee under the chair of Dipl.-Ing. J. Gloger, VW AG, Wolfsburg.

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