Comparison of Different Actuator Concepts forApplications in Rotating Machinery

Considerable improvements of machines can be expected in the near future through the use ofelectronics in combination with 
control techniques. A key position will be held by the actuator systems that finally have to accomplish the controlled energy 
transfer according to the objectives. For rotating machine parts this is usually done via the bearings. Basically, there are two 
possibilities to transmit the controlled forces; contact free via magnetic fields (magnetic bearings) or the traditional way via 
conventional bearings. To realize the regulating actions multiple physical effects can be employed. In this paper some of the 
promising types of actuators and their advantages and disadvantages will be discussed, as well as how effectively to use these 
active elements under different objectives. Questions concerning the practical realizations will be given high priority.

The heart of such new applications are the actuators.Depending on the objectives, they control the energy center of the system.In order to achieve this, some promising actu- ator concepts will be introduced and their strong and weak points will be discussed with regard to their industrial ap- plications.The procedure of integrating the actuators into the whole system, the steering, and the design of an effi- cient control will be laid out.The objective of this paper is to give hints to help practically oriented engineers choose the appropriate actuators for their specific application.

POSSIBLE ACTUATORS
In the future, the dynamics of machines will be specifically and purposely adapted to the requirements of the particu- lar technical task by the use of electronics in combination with control techniques.A key position will thereby be held by the actuators, which will perform the energy trans- fer, depending on the objective.The actuators have the task of transforming the information about the systemn supplied by the sensors--into the desired physical actions.
To realize these regulating actions, multiple and also very different physical effects can be used.With regard to in- dustrial applications, the following demandsmas well as the costsmshould be given high priority: compactness, because usually the available space is quite limited large forces, which has to be seen in relation to the masses to be moved and the necessary regulating dis- tances, as well as the regulating frequencies to be re- alized regulating frequencies at least as high as the highest vibration to be controlled simple actuator transfer characteristics to avoid addi- tional dynamic problems due to the actuator dynamic light weight, which is a major criterion for applications in aeronautics and the space industry In what follows some actuator concepts will be dis- cussed and commented upon regarding their advantages and disadvantages.

Piezo Actuators
Piezo actuators have been commonly used for some time.They are especially well suited when dealing with vi- brations with small amplitudes or to adjust mirror systems or other components in high-precision constructions within the/zm-range (Haidenwanger and Klose [1992]; Goto 1992]).They have also been investigated theoreti- cally and experimentally for their ability to influence ro- tors via conventional bearings (Palazzolo 1989], 1992]; Santos and Ulbrich [1992]) and mechanisms in general (Liao and Sung [1990]).Piezo actuators' special merits are their high stiffness kp and their performance in high- frequency ranges.The realizable control forces can be calculated by fp(t) IpCpkpu(t) kps(t) () where Ip is the piled height of the crystal wafers, Cp is the electrostatic capacity (each crystal wafer is a capacitor), and kp is the stiffness of the actuator (see Figure 1).The regulating distance is called s(t), the control voltage u(t).
The crucial disadvantages that limit the application range are the small, realizable, regulating distances (Ip/lO00) and the very low material damping of the actuators (impacts are transfered almost undamped).Due to the dependency of the regulating distance on the to- tal height, the size of piezoelectric actuators can be quite large.Also the permissable compressive load is very small so usually the control forces can only be applied through additional transfer elements (Palazzolo 1989]).A typical transfer function of a piezo actuator is shown in Figure 2.
It can be seen that a strong reduction of amplitude begins at 200 Hz and the phase lag progresses linearly with the frequency.At 1000 Hz the phase lag is already -180.

Hydraulic Actuators
Figure 3 shows a sectional view of a newly developed hy- draulic actuator.The operating part consists of two cylindrical chambers which are closed in the working direction (in Figure 3 the vertical direction) by elastic membranes.The pressure difference Ap between the two chambers and 2, necessary to create the regulating operation, is supplied by the servo valve.
The special design of the actuator yields a high radial stiffness and ensures a corresponding safety against tilting effects (depending on the distance between the two mem- branes as well as on their thickness).Through this arrange- ment the regulating movements can be applied completely without friction.
The length IH of the hydraulic actuator is changed by the length s(t) due to the regulating action.The control force can be expressed by an equation similar to that of the piezo system: fH(t) A*Ap(t) kMs(t) (2) where A* is the characteristic membrane area, kM 2CL the effective membrane stiffness, CL the membrane stiff- ness, and s(t) the regulating distance in the direction of the force.The regulating force is generated by the pressure difference Ap and not (different from the piezo ac- tuator system) proportional to the control voltage.Unfor- tunately, the regulating pressure strongly depends on all fluidmechanical losses of the hydraulic and the dynamic of the servo valve.Thus the realizable regulating frequencies are mainly determined by the cut-off frequency of the used servo valve and some hydrodynamic influences (pipes, fluid).Due to these hydrodynamic influences the actuator has basically an integrating transfer character- istics, as can be seen in Figure 4 (Althaus and Ulbrich  [1992]).
Due to the choice of membranes (diameter, thickness) a multitude of static characteristic curves can be real- ized.Also, the maximum control forces and regulating distances can be adapted in wide ranges with an adequate choice of the membranes.The given design limit is al- Amplitude [m/v] 200 500 1000 [Hz] Phase [degree] 440 1000 [Hz] FIGURE 2 Measured transfer function of the investigated piezo actuator (ratio regulating distance s(t) over input voltage u(t)) (Santos [1993]).
ways the maximum material stress in the membranes.The thicker the membranes at a given diameter, the larger the stiffness of the actuator and the smaller the maximum regulating distance.For practical purposes this is not a problem because the generally high stiffnesses of the sys- tems under consideration allow only small deformations and thus require only small regulations.In this context it should also be noted that the physics comply with the reg- ulating actions since in the deflected state the controller generally has to apply resilient forces in opposite direction to the deflection s(t).This means the term kHs(t) from eq. (2) will be superimposed by the control force A* Ap(t).
A typical transfer function of a hydraulic actuator is shown in Figure 5.When using these actuators to control rotor vibra- tions, two actuators with radial working directions can be positioned perpendicular to each other if necessary (Ulbrich 1992]).

Magnetic Actuators
Magnetic actuators can be classified into two types.One type are the magnetic bearings that permit a non-contact force transfer.The other type are the electromagnetic ac- tuator systems where the regulating actions--as with the other presented actuator concepts--are applied indirectly, usually via conventional bearings.In both types the mag- netic forces can be controlled by either current or voltage.In the case of control by current (the power amplifiers are working as a current source) the relationship between the realizable force f (t), the control current i(t) and the reg- ulating distance s(t) is strongly nonlinear.The resulting force can be expressed by where so is the air gap in neutral position, i0 is the con- stant premagnetizing current, and ki, ks, kw and kM are constants depending mainly on the geometry of the actu- ator design, the used magnetic material and the employed electrical components.Under the assumptions of small control currents (t) << i0 and small regulating distances s(t) << so the following linear correlation between the control current and the resulting force can be obtained: f (t) kii(t) 4-(ks kM)s(t) (4) The constants ki (force-current coefficient), ks (force- displacement coefficient) and kM 2CL (stiffness factor of the assembly in working direction, CL stiffness of the membranes) permit large varieties in layout and construc- tion of the actuators.Equation 4shows the destabilizing effect of such a magnetic actuator system due to a negative stiffness indicated by the 4-ks factor.The most severe case of this destabilizing effect occurs in non-contact magnetic bearings (kM 0!).
Figure 6 shows two types of magnetic actuator systems that are currently being developed.The difference between both types is basically the realization of the premagnetizing.In type I, the necessary premagnetizing is realized electrically (indirectly) and in type II, it is realized by spe- cial permanent magnets (directly).The magnetic potential is realized in type I through the product iow (io is the pre- magnetizing current, to is the number of windings in the premagnetizing coil) and in type II the circulation ioto with FIGURE 5 Measured transfer characteristic of an investigated hydraulic actuator (ratio regulating distance s(t) over input voltage to servo valve u(t)) (Althaus and Ulbrich [1992]).
H. ULBRICH electromagnetic actuator (type I) (pre-rnagnetizing with electromagnet) electromagnetic actuator (type II) (pre-magnetizing with permanent magnet) li i---i_.iI:-(R)--; ill  COMPARISON OF ACTUATOR CONCEPTS 67 respect to the premagnetizing is realized by the integrated permanent magnets (magnetic potential (R)pm A iow).Fig- ure 7 shows the control force as a function of the control current for both types.Tuning of both systems with the objective of maximizing the control forces at a constant actuator size shows that using permanent magnets for the premagnetizing results into a control force about 2.5 times as high as in the case of indirect premagnetizing.
Figure 8 shows the measured control force frequency curve for type I up to a frequency of 300.Hz.It turns out that the phase lag at 300 Hz is already -60.Sub- stantial improvements can be expected here by the use of new soft-magnetic materials.These experimental investi- gations have not yet been finished.

SUMMARY
Figure 9 gives an overview of the discussed actuator systems with regard to their realizable regulating distances and frequencies.Table I shows a rating of some character- istics of the different actuator systems with regard to their specific requirements.This should just be understood as a rough classification, but it already allows to make out the typical applications of all the discussed actuator systems.New developments in the field of magnetic materials let us expect an even stronger shifting of their attributes toward magnetic actuators (Meeks [1992]; O'Connor [1992]).

INCLUDING THE ACTUATORS INTO THE SYSTEM TO BE CONTROLLED
An efficient use of actuators requires a mathematical de- scription of the open-loop system that has been adapted to the problem and where the actuators, which are also represented by their mathematical models, have been in- tegrated.The resulting model is able to describe the physi- cal relations ofthe complete dynamic interactions between the open-loop system and the actuators.

Mathematical Description of the System
General movements of systems consisting of rigid, elastic, and fluid components can be mathematically described by a system of differential equations (Bremer [1989]): M(q, t)ij + f(q, (1, t) jT (q)hcontroller(t) b(q, t) (5) Vector q(t) represents the generalized coordinates that describe the movements of the system.The mass matrix M(q, t) generally depends on q and explicitly the time t.Vector f(q, 1, t) considers all the forces involved in the en- ergy household (except the control forces).Vector b(q, t) contains the forces resulting from the steering and control whose components act in the direction of the generalized coordinates (this results immediately from the multiplica- tion of h(t) with the Jacobian matrix jT).Closed kine- matic loops can be treated with this method as well as elastic components (e.g., in actively controlled four-bar linkages; Ulbrich and Ahlemeyer [1994]).For the design of the control it is important whether the geometrical pa- rameters (e.g., the distance s(t) may be given as a forced condition) or the forces (an additional degree of freedom will be introduced if not already included) are controlled.
In general, a reference movement, for example, the rigid body motion of a function-generating mechanism or a flight maneuver of an airplane turbine--is given by the vector q(t).The nonlinear equation of motion for this ref- erence movement can be gained from eq. 5: Mr(qr)ir qg(qr, qr) br(t) Ur(t) With a given qr(t), tr(t) and lr(t) the steering vector Ur(t) to realize this reference movement can now directly be calculated.Given the case that undesired small su- perimposed deviations appearmrepresented by the vector e(t)mthat are composed ofsmall rigid body movements or also possibly elastic deformations of the structure, a con- trol can be added.The starting point for the design of such a control is the linearized system (linearized around the reference movement, i.e. q(t) qr(t) + e(t), lel << Iqrl, eq.4): Me(t)(t) -+-Pe(t)(t) + Qe(t)e(t) be(t) Ue(t) (7)   Comments on the Control The realization of an efficient control will be decisively in- fluenced by the choice of the actuator-and sensor systems and their positioning within the whole system as well as the choice of the control concepts including the optimiza- tion of the controller.The optimization of the controller strongly depends on the chosen objectives.In any case the controller will be optimized with respect to a criterion for the quality of the employed control.Discussions of differ- ent quality criteria and some remarks on the further procedure can be found in Bremer [1990] and Ulbrich [1992].
For the optimization of controllers there are already a multitude of computer programs available that usually re- sult into a parameter optimization, that is, tuning of the  poor +++ + controller amplifications to optimize the quality criterion to obtain an optimal system performance according to the objectives.
The realization of the control can be analog, digital, or "hybrid".An analog control will, in most cases, not be flexible enough and is only employed in so-called constant controllers.When system changes during the operation are considered or nonlinear controllers are realized then usually the advantages of a digital control can be exploited.
The only problem that can arise in digital controllers is the limited cycle time, but that depends on the particular task to be solved.Also, new developments in the field of parallel computer design (transputer) will further reduce the cycle times and can as such constitute a solution.If cycle times are still not fast enough it can sometimes be useful to employ a "hybrid control" in order to separate the time-critical components, for example, the rotorfrequent vibrations of high-speed rotors (Ulbrich [1982]), and to combine a fast analog control with a digital adaptation of the control parameters.

CONCLUSION
The advance of electronics in combination with automatic control technology will continue.Through constantly in- creasing the speed of computers as well as improving the precision of analog elements, more and more com- plicated calculations and simulations, embedded into the information circuits of controlled systems, will contribute to improve further the dynamics of these systems.It is just a matter of time before active bearings will be regularly employed in machine tools, gas turbines, terrestrial turbines, engine suspensions, valve control, and various other mechanisms.To account for these future require- ments a practically oriented development of actuators that are specifically adapted to the particular problem with a simultaneous integration of the necessary sensors is of high importance.To realize this, some concepts that are partially still under development have been presented and discussed and the task of how to come to an efficient use of such active components to improve machines in their dynamic characteristics, has been explained.Nomenclature b(q, t) br(t) e(t) f(q, 1, t) fH(t) fM(t) fp(t) g(qr, r) vector of generalized control forces control vector for realizing the reference motion error vector considering the deviation from reference motion vector of generalized forces control force of hydraulic actuator [N] control force of magnetic actuator [N] control force of piezo actuator [N] generalized control forces for reference motion control pressure [Pa]  vector of generalized coordinates vector of generalized coordinates of the lineadzed coordinates regulating distance [m] input voltage of the piezo actuator [V] control vector to minimize the error e(t) [N] effective membrane area [m2] capacity of the piezo actuator [F] Jacobian matrix mass matrix mass matrix of error system mass matrix of reference system damping matrix of error system stiffness matrix of error system FIGURE 3 Hydraulic actuator.

COMPARISON
FIGURE 4 Force--distance relations for the hydraulic actuator.