I. Todić et al.Upravljanje položajem i brzinom elektromehaničkog aktuatora (EMA) za primjene u zračnom prostoru ISSN 1330-3651 (Print), ISSN 1848-6339 (Online) UDC/UDK 629.735.036.7-35:681.515.8]:519.876.5 POSITION AND SPEED CONTROL OF ELECTROMECHANICAL ACTUATOR FOR AEROSPACE APPLICATIONS Ivana Todić, Marko Miloš, Mirko Pavišić Original scientific paper Main focus of this paper is control of electromechanical actuator (EMA) for aerospace applications. Control of EMA done using position regulator and control which combine position and speed regulator is shown. The main guideline is to decrease power losses, heating and current consumption in the system. One of the important areas within the field of variable speed motor drives are the system’s operational boundaries. Presently, the operational boundaries of variable speed motor drives are set based on the operational boundaries of single speed motors, i.e. by limiting current and power to rated values. This results in under-utilization of the system, and places the motor at risk of excessive power losses. In this paper, the first part represents general concept of electromechanical actuators and mathematical modelling of the system; then the control of position and speed of electromechanical actuator (EMA) by using PID controller is presented. The second part shows simulations of our own design of control speed and position by PID controller using SIMULINK and MATLAB software. Keywords: brushless DC motor, electromechanical actuator (EMA), PID controller, position control, speed control, simulations Upravljanje položajem i brzinom elektromehaničkog aktuatora (EMA) za primjene u zračnom prostoru Izvorni znanstveni članak Težište ovog rada je upravljanje elektromehaničkim aktuatorom (EMA) za primjene u zračnom prostoru. Upravljanje EMA je ostvareno uporabom pozicijskog regulatora i upravljanja koje kombinira položaj i brzinu regulatora. Osnovna smjernica bila je smanjenje gubitaka snage, zagrijavanja i potrošnje struje u sustavu. Jedno od važnih područja u okviru pogona promjenljivim brzinama motora su operativne granice sustava. Danas se operativne granice pogona s promjenljivim brzinama motora postavljaju na osnovu operativnih granica pogona na bazi prosječnih vrijednosti, npr. ograničenjima struje i snage na preporučene vrijednosti. To dovodi do nedovoljne iskorištenosti sustava i velikih gubitaka korisne snage. U ovom radu, u prvom dijelu je predstavljen osnovni koncept elektromehaničkog aktuatora (EMA) i njegov matematički model, zatim je prikazano upravljanje položajem i brzinom elektromehaničkog actuatora uporabom PID regulatora. U drugom dijelu usporedo se daje prikaz simulacija vlastite konstrukcije upravljanja položajem i brzinom pomoću PID regulatora, uporabom SIMULINK-a u MATLAB-u. Ključne riječi: DC motor bez četkica, elektromehanički aktuator (EMA), PID regulator, pozicijsko upravljanje, brzinsko upravljanje, simulacije 1 Introduction operational boundaries of single speed motor drives, i.e. by limiting current and power to rated values. In reference to the literature ([1, 2] and many others The operational boundary of any motor drive must be not cited here), for the better part of 20th century most set based on the maximum possible power loss vs. speed motion control systems were designed to operate at a profile for the given motor. fixed speed. Also, all control strategies for a machine must be Many existing systems still operate based on a speed analysed and compared based on such an operational determined by the frequency of the power grid. However, boundary [3]. the most efficient operating speed for many applications, such as fans, blowers and centrifugal pumps, is different 2 General concept and mathematical model of EMA from that enforced by the grid frequency. Also, many high performance applications, such as robots, machine Linear actuator is a device that applies force in a tools and the hybrid vehicle, require variable speed linear manner, as opposed to rotationally like an electric operation to begin with. As a result, a major transition motor. Electro-mechanical actuators are similar to from single speed systems to variable speed systems is in mechanical actuators except that the control knob or progress. handle is replaced with an electric motor. Rotary motion The transition from single speed drives to variable of the motor is converted to linear displacement of the speed drives has been in effect since the 1970s when actuator. movements towards conservation of energy and The main equation used to describe electro- protection of the environment were initiated. About mechanical actuator is based on Euler equation and seventy percent of all electrical energy is converted into Faraday’s law: mechanical energy by motors in the industrialized world. This may be the most important factor behind today’s dω r high demand for more efficient motion control systems. A J = Te − Tm − F ⋅ ω r . (1) dt large body of research is available on variable speed drives due to the significant industrial and commercial The angular position may be obtained by integration interest in such systems. of the angular velocity: However, some areas of importance merit further investigation. One such area is the operational boundary of motor drives. The operational boundaries of variable θ r = ∫ ω r dt. (2) speed motor drives are being incorrectly set based on the Tehnički vjesnik 20, 5(2013), 853-860 853 Ca Φ'a = . −trap ≤ cosθ e ≤ trap f (cosθ e ) = . We will compare control of EMA based on position controller and 2 λ = Ka ⋅ . V Φ 'c = c . The transfer function for the motor: 3 854 Technical Gazette 20. dt dt dt Usually pulse-width modulation circuit is used for control of DC brushless motor in EMA applications. be used for calculation of electromotive force: It will be assumed that DC brushless motor can be presented by equivalent electric circuit [8. load torque and coulomb and viscous friction in electromotive force and rotor velocity [4. driving circuit applies different voltages to two ends of (4) the motor according to the input signal to rotate the motor shaft in different directions. cosθ e . 9. 2 π Cc = f cosθ e + . The bridge power Te = p ⋅ λ ⋅ (Φ ' a ⋅ia + Φ 'b ⋅ib + Φ ' c ⋅ic ) . V. trap V1 − Power supply. trap C a = f (cosθ e ). kg∙m2 Cb Ka − Torque constant. Input signal in pulse-width where [6. (6) 2p (as a major part of EMA) is to control its input current.1 Position controller and dynamic characteristics Ka The main guideline of control of DC brushless motor λ= . trap G − Gearbox ratio RA − Resistance in phase A. (11) Electrical angle is: Ka2 θ e = p ⋅θ r (8) J − Total inertia. J CM = .Position and speed control of electromechanical actuator for aerospace applications I. For calculation of suitable PID position controller we will DC motor which was under our consideration has need to determine transfer function of EMA system [ref. 10] (Fig 1). (N∙m)/A Φ 'b = . LA − Inductance in phase A. trapezoidal flux distribution. Next gearbox: equations are expressed in the phase reference frame (ABC frame): Tm = T f + TA + Tgf + Tgv . Figure 1 Schematic of motor model presented by equivalent electric 2 circuit where: where: flat − back EMF flat area [degrees]. (7) sgn (cosθ e ) trap. Ω 2 π Cb = f cosθ e − . 853-860 . All those equations are implemented in SIMULINK dt 3 model to simulate electromechanical actuator system.trapezoidal flux distribution 3. H 3 IA − Current in phase A. (3) dt 3 3 Control of EMA dic dia dib = − + . inertia of motor and its load. dib 1 Ls + Rs ⋅ ib = [− vab + vbc + p ⋅ λ ⋅ ωr (Φ 'a −2Φ 'b +Φ 'c )]. and beck of motor. Todić et al. We can use sinusoidal flux distribution if we set flat = 0 .sinusoidal flux distribution signal (position/deflection or desired speed). 5(2013). 7]: modulation circuit is the result of PID control of desired . voltage. Now we need to introduce equations to describe Load torque is calculated as sum of coulomb friction relationship between current. (5) combined controller which simultaneously control 3p position and speed. . 5]. cosθ e > trap flat π 1 − 180 trap = sin . (10) dia 1 Ls + Rs ⋅ ia = [2vab + vbc + p ⋅ λ ⋅ ωr (− 2Φ 'a +Φ 'b +Φ 'c )]. The Generated electromagnetic torque is given by: pulse-width modulation signals are generated according to polarity and intensity of input signals. The following equations will Chapter 4 of this paper]. A (9) C VA − Back EMF in phase A. (14) 1 + H PID ( s ) ⋅ H M ( s ) 4 .129 ⋅ s + 0 . Upravljanje položajem i brzinom elektromehaničkog aktuatora (EMA) za primjene u zračnom prostoru 1 3. (20) Kd 2 K p 0 . (17) I J ⋅G ⋅ s2 Ki + K p ⋅ s + K d ⋅ s 2 H PIDs ( s ) = A0 ⋅ .5418 ⋅ s 2 + 72 .5418 ⋅ s 2 + 72 . Position PID regulator will C⋅s stay unchanged. Todić et al. (18) s Figure 2 Block diagram of DC brushless motor and position PID H PID ( s ) ⋅ H M ( s ) regulator H s (s) = . Imposed component is output signal from ω 1 1 K (12) the speed controller.24 ⋅ s + 36 . (19) 1 + H PID ( s ) ⋅ H M ( s ) The transfer function for the actuator system can be written as [11]: Using MATLAB calculation we can obtain Hs(s) of our electromechanical actuator system: H PID ( s ) ⋅ H M ( s ) H (s) = . I Ka ⋅C ⋅ s K ⋅ J ⋅ s J ⋅ s the whole system like additional differential component a Ka2 so coefficients in speed controller need to be the same order like differential component in position controller.005787 ⋅ s 3 + 0 . Speed controller will take effect on ⇒ = = = a .005832 ⋅ s 2 + 1.7224 ⋅s + ⋅ s +1 Ki Ki H (s) = . position and speed controller θ= ⋅ ω. 5(2013).515 × 10 −5 ⋅ s 2 + 1.2 Combined regulator. (13) The general transfer function for PID regulator and s position controller is: θ Ka H Ms ( s ) = = . (16) 0 .12 H (s) = .I. G⋅s The main guideline is to impose some additional I ω ⋅ Kv = V = .7224 H s (s) = . control on the same system. I J ⋅G ⋅ s2 The transfers function for PID regulator: Figure 4 Block diagram of DC brushless motor and speed PID regulator Ki + K p ⋅ s + K d ⋅ s 2 H PID ( s ) = A0 ⋅ .12 Figure 5 Bode diagram of speed controller Figure 6 Block diagram of DC brushless motor and combined position and speed regulator Figure 3 Bode diagram of position controller Tehnički vjesnik 20.129 ⋅ s + 0 .24 ⋅ s + 36 . (15) G⋅J 3 Kd 2 K p ⋅s + ⋅s + ⋅ s +1 K i ⋅ A0 ⋅ K a ⋅ K Ki Ki Using MATLAB calculation we can obtain H(s) of our electromechanical actuator system: 0 . 853-860 855 . θ Ka ⇒ H M (s) = = . Gearhead (4) and DC 4 Model of EMA brushless motor (5).1 deg 6 Hz used to compare small signal bandwidth of both systems (Fig. used to compare response of both mechanical system (Fig. Simulation To illustrate the above mentioned. Lever mechanism (2). Todić et al. Dn – Nominal diameter.Position and speed control of electromechanical actuator for aerospace applications I. 8). 20). Main parts are: Object /Fin (1). Controller consists of driver and DSP. 5(2013). Jk – Inertia of control surface. L1 – Lever arm length. Figure 7 Rough schematic of EMA used in the simulations (nm. maximum requirements (Fig. Fig. θk – Deflection of control surface. several series of results on two different input signals based on guidance results follow as well as Simulink schematic of electro. 12). Combined regulator will be based on sum of Model of EMA used in simulations is presented in responses of both position and speed regulators. Simulation results on input signal 6 deg 3 controller for both position and velocity controller of Hz used to compare response of both systems on EMA and for modelling of EMA system. Mm – Rated speed and torque of motor. 853-860 . system in realistic conditions (Fig. Sv – Lead. algorithm and autopilot. In this paper. 16). 7. 13 to Fig. nv. Mv – Rated speed and torque of planetary roller screw. Planetary roller screw (3). Figure 8 SIMULINK schematic of EMA 856 Technical Gazette 20. 17 to Fig. SIMULINK is used for design of PID 9 to Fig. Mmax – Maximum output torque) 5 Results Simulation results on input signal 0. 5(2013). Upravljanje položajem i brzinom elektromehaničkog aktuatora (EMA) za primjene u zračnom prostoru Figure 9 Angle responses of position controller and combined position + speed controller Figure 10 Angular speed of position controller and combined position + speed controller Figure 11 Current consumption from battery in case of position controller combined position + speed controller Figure 12 Heating in DC brushless motor in case of position controller and combined position + speed controller Tehnički vjesnik 20. 853-860 857 .I. Todić et al. 853-860 .Position and speed control of electromechanical actuator for aerospace applications I. 5(2013). Figure 13 Angular speed of position controller and combined position + speed controller Figure 14 Current consumption from battery in case of position controller and combined position + speed controller Figure 15 Heating in DC brushless motor in case of position controller and combined position + speed controller Figure 16 Angle response of position controller and combined position + speed controller 858 Technical Gazette 20. Todić et al. Todić et al. 853-860 859 . 5(2013). Upravljanje položajem i brzinom elektromehaničkog aktuatora (EMA) za primjene u zračnom prostoru Figure 17 Angle response of position controller and combined position + speed controller Figure 18 Current consumption from battery in case of position controller and combined position + speed controller Figure 19 Heating in DC brushless motor in case of position controller and combined position + speed controller Figure 20 Angular speed of position controller and combined position + speed controller Tehnički vjesnik 20.I. rs that type of signal will never be used in real situation. R. 44. Blagojević. Miloš. Myers. N. J. 7 References [1] Cowan. 52. 5(1997). D. New Zealand. Duke. Marinković. 1991. Serbia produce more overshoot. New York. Z. [4] Grenier... Ivana Todić. 717-725. L. A. Development and Test of Electromechanical Actuators for Thrust Vector Control // 29th Joint Propulsion Conference / Monterey.Sc. G. 2005. 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[5] Trounce. but in aerospace application E-mail: mmilos@mas. D.