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static speed control system for triaxial telescope scanning axis SUBBOTIN DMITRII Department of Electrotechnics and Precision Electromechanical Systems University ITMO 197101, Saint Petersburg, Kronverkskiy pr., 49 RUSSIAN FEDERATION e- mail: Subb-Dm@yandex.ru SERGEY LOVLIN Department of Electrotechnics and Precision Electromechanical Systems University ITMO 197101, Saint Petersburg,Kronverkskiy pr., 49 RUSSIAN FEDERATION e- mail: seri l@yandex.ru MADINA CVETKOVA Department of Electrotechnics and Precision Electromechanical Systems University ITMO 197101, Saint Petersburg,Kronverkskiy pr., 49 RUSSIAN FEDERATION e- mail: madina1986@bk.ru Abstract nowdays, besides systems based on continuous rotation engines, different scanning systems are used. Such systems often are based on drives with limited rotation a ngle, which shaft can do quite complex reciprocating linear or rotational motions. One of the basic requirements for scanning system is speed maintaining high accuracy in different work modes. In this article is presented astatic two loop speed control sys tem for triaxial telescope scanning axis. The structural scheme, the synthesis method and vector matrix mathematical model is proposed. The proposed struct ure and synthesis method allow to increase the speed maintain accuracy in working modes. Key words : Infrared Telescope, magneto electric converter, scanning diagram, speed control system, synthesis method, the mathematical model. 1 Introduction Basis of the guidance system of the modern telescope is support- rotating device (SRD) and tracking electric drives. For example, infrared telescope guidance system is based on triaxial SRD with azi muth, elevation and scanning axe s. On each axis is located an electrounit, containing an electric motor and sensor s of angular position and engine speed tightly coupled with shafts. A lot of works are devoted to the synthesis of precision gearless servo drive control systems of azimuth and elevation axes , based on the valve motors [1]. Specific are requirements for t he scanning axes electric drives. In many cases, they must ensure the movement of the axis within small range of angles in accordance with the timing diagram shown by curve 1 in Figure.1. Fig. 1. Electric drive scanning diagram On Figure: 1 and 2 - cu rves corresponding to the drive scan diagram by angle and speed, respectively. Full scan cycle sc contains two working stroke plot ( and ) with duration and two nonworking stroke ( and ) with duration nw . At working stroke sections angle should vary linearly within the range of gr XSWR gr with an DFFHSWDEOHVSHHGPDLQWDLQHUURUUDWH$QJOH change principle in nonworking stroke areas is not Advances in Automatic Control ISBN: 978-960-474-383-4 175

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limited. Duration of nonworking stroke is measured between the end of one working stroke and the beginning of the next. Diagram options and its reproduction accuracy requirements depend on the selected scanning mode. In this article we will focus on the diagram properties shown in Table 1. Parameters gr ,' sc s , s nw , s 30 2,4 0,2 10 Table 1. Scanning diagram parameters In view of a sufficiently small range of scanning axis rotation angle variation for the drive implementation is not necessary to use traditional electric motors with an unlimited rotation angle. Promising for these purposes is to use contactless magneto electric converters (MEC) of electrical input signal (voltage) to the proportional angular displacement of its rotor [2]. Carried out mathematical modeling of scanning process with given MEC characteristics, diagram scanning parameters, MEC control winding negligible inductance and small moments of static load torque on the axis confirmed the possibility of realizing the desired movement of the executive axis in the trapezoidal reference signa l (curve 1 in Fig.1.) tracking mode. Scanning drive test on real SRD showed the need to consider in the control system synthesis both the large values of the MEC control winding inductance and the coulomb friction in the bearings of the axis. Under these conditions, the desired motion of the axis is not possible to provide in any one scanning mode. Adjusting the effect of these factors is possible in speed closed loop structures, using the speed curve diagram 2 shown in Fig.1 as the reference signal. During the scanning mode simulation were established minimally implemented errors for which the voltage surge on the MEC control winding does not exceed the maximum allowable value of 48 V. 2 Block diagram Block diagram of the studied system is shown in Fig. 2 , where the dashed lines are highlighted elements and connections forming a block diagram of the actual MEC, grounded in the work [ ]. P1 - PD controller, compensates MEC electrical time constant , where and - respectively the resistance and inductance of the control winding [ ]. The necessity of such compensation occurs when the inductance reaches high values. P2 - control system external loop regulator, designed to increase input and load torque astatism. Fig . 2. Control system block diagram On Figure: is MEC control winding resistance, is MEC control winding inductance, e is the slope of the back EMF coefficient, is the total scanning axis inertial torque, is the inner damping coefficient, is the coulomb friction torque, dM is the stiffness of mechanical characteristic or «magnetic spring» stiffness, dI dM is the stiffness of traction characteristic or electric circuit sensitivity, DS speed loop feedback gain, DQG are external and internal control loop errors, z2 and 1 are external and internal control loop reference signals, is voltage on the MEC control winding, is MEC control ZLQGLQJFXUUHQWLVWKHURWDWLRQDQJOH dt : is the rotation speed. According to the developer of the DB600-100- D3043 converter [ ], which will be XVHGLQUHDOVFDQQLQJV\VWHP0( mechanism" system has the following parameters: = 4500 N·m/rad; = 85 N·m/A; = 0; = 1.5 V·s/rad.; = 0.6 H; = 14 Ohm; = 236 kg·m ; = 25 N·m; y_max = 48 V (maximum voltage of the control winding which is Advances in Automatic Control ISBN: 978-960-474-383-4 176

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equal to the maximum value of the output voltage of the inverter.). 3 Internal loop description Consider the dynamic properties of the internal speed loop. The transfer function of PD controller has the form: )1( )( pT pTK pW DP (1) where transfer coefficient, differentiation time constant and v additional inertial element time constant. Fig. 3 shows regulator de tailed block diagram, where : DSz KU 11 . Fig . 3. PD -regulator detailed block diagram. Using given block diagram, form the expression for the MEC control winding voltage as: )( DP vDP DSDP TK TTK KTK : , (2) where PD regulator state variable. Introduce the following notation ,/ JK (3) JR KKK DSPi (4) and implementing the control winding electrical time constant compensation by selection D = and , without great error internal loop transfer functions on input z1 and disturbance operation, when DS >> can be presented as: 1p1p (p z1 (p) 21 DS TT pK (5) 1p1p (p) (p) 21 TT . (6) Time constants are defined by: (7) (8) After selection from the condition transfer coefficient P1 can be found from the expression (4). Analysis of the transfer functions (5) and (6) shows that at constant voltage reference and load torque, regardless of their size , steady state speed value is zero. This fact determines the specificity of MEC speed control system synthesis - providing a given accuracy of speed maintaining in the work area of scan diagram under conditions of essentially appro aching zero velocity. Diagrams, presented on Figure 4, correspond to the internal speed control loop with MEC parameters given above, synthesized from condition of providing speed PDLQWDLQHUURU $VUHIHUHQFHVLJQDOZDVXVHG the scanning diagram speed varying curve 2, Figure 1. Scanning diagram parameters are shown in Table 1. Fig . 4. Diagram of scan mode simulation. On Figure: 1 LQSXWVSHHGFXUYH (t) in scale 1:1, 2 URWDWLRQVSHHGFXUYHWLQVFDOH - scanning axis rotation angle (t) in scale 1:1, 4 - MEC control winding current (t) in scale 1:2, 5 voltage on the MEC control winding (t) in scale 1:50. The simulation of scanning process for electric drive based on MEC with described control system was held using Simulink. As see n from Figure 4 , during scan diagram tracking mode voltage surge occur on the winding control, when scanning mode changes from nonwork to work stroke areas . Analysis showed that the amplitude of these surges is related with the value of the transfer coeffi cient . Reducing the error in the work area associated with increase of , [grad/s] >JUDGV@ >JUDG@ >@ , [V] 2.0 2.5 3.0 3.5 4.0 0.5 0.5 sec Advances in Automatic Control ISBN: 978-960-474-383-4 177

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regulator transfer coefficient . However, the increase of 1 leads to an increase of the surge amplitude . By reducing the allowable error to a value less than 5% amplitude of the surge peaks can be much higher than the maximum permissible value. 4 External loop tuning 4.1 External loop description One way to improve accuracy while ensuring maximum allowable voltage at the MEC control winding is the introduction of the second (external) speed control loop with regulator providing increasing order of input signal and load torque astatism. The transfer function of the outer loop controller P2 has the form )1( )( 22 pT pTK pW IP (9) This regulator provides first order astatism of input signal , second order of the load torque and allows to setup control loop to the technical optimum in which the closed loop setpoint transfer function can be expressed as: )122( )( )( )( DS KpTpT pU pW (10) where uncompensated time constant, which determines the estimated time of transition in the system ; the step res ponse of the voltage reference is PR = 4.7 T (11) Considering the small effect of coefficient on the dynamic processes in the system and eliminating the appropriate feedback in t he block diagram, presented on Figure 2, it is easy to find the transfer function of the system disturbance (load torque) in the form of an expression: )( )()( )1( )( )( )( 21 PP pW pWpW pTR pM pW Which, considering (1), (9) and (10), can be presented as : )1 )( 1( )1 )( 1( )( 221 pTpTKKK pTpTpT pW IIPP evI (12) Expression (12) leads to the conclusion of the second order of the disturbance astatism of the contro l loop. 4.2 External loop optimization For loop optimization use block diagram (Fig. 5), where controller with transfer function (9) represented as detailed block diagram, internal loop RIWKHV\VWHPDVWUDQVIHUIXQFWLRQDQG - DS – outer loop controller input error. Fig 5. Block diagram of external speed control loop. Reference signal for internal loop is: 231 Ppz KyU (13) Get the expression for calculating voltage on MEC control winding for observed structure after substitution (13) in (2) as (14), where and block diagram integrators output signals. 21 21 )( DPP PD vDP DSDP TKK KT TTK KTK : , (14) Loop tuning consists in selecting such controller parameter s, at which transfer function of open loop is matched to the reference expression: )1(2 )( pTpT pW re PP (15) Because , time constant should be compensated for selection , and n on- compensable time constant form as T , (16) where << 2 is internal loop PD -controller additional inertial time constant, which is unaccounted in (5). Then open outer loop transfer function is: )1( )( pTpT pW (17) Comparing transfer function (17) with reference transfer function (15) get condition for transfer coefficient as: 01 KT (18) Now can be formulated a control system synthesis technique from the condition of providing a given transient time ( PR ) with known MEC parameters: Advances in Automatic Control ISBN: 978-960-474-383-4 178

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- calculate time constant ( ) by formula (11) from providing given performance condition, and then calculate by formula (16). - calculate coefficient from expression (8) as: 02 (19) - calculate from expression (4) as: DSi KK JR (20) - using expression (7) calculate required value of time constant and integrator time constant . Figure 6 shows process modeling results for scan mode of electric drive with two loop control system, synthesized according to the procedure described above from conditions of minimal transition process time in reaction to reference variable . System parameters are: =1 ms, = 57 ms, =4 ms, = 3 ms, =333. 4, =18.5 sec , =364.6, =125, = 25 Nm . Fig. 6. S can process in two loop MEC control system On Figure : 1 speed reference signal DS [1/s] in scale 1000:1, corresponding to the scan diagram, 2 real speed value >V@LQVFDOH 1000:1, 3 rotor angle >UDG@LQVFDOH MEC control winding voltage u [V] in scale 10:1 formed by expression (14), 5 – winding current >@ in scale 10:1. Comparison of scan modeling results for single loop system (Fig. 4) and for two- loop system, shows that in two -loop system speed value in the working area of scan diagram is kept constant and equal to reference speed signal, with no voltage spikes on MEC control winding in moments when scanning mode changes from nonwork to work areas. Accuracy speed deviation from the nominal value is 4.5% percent for two- loop control system. Additional voltage surge on MEC control winding, in amplitude values attaining 46 V, in moments of speed value transition by 0 due to the high rate of current change in the control winding and , hence, voltage surge on control winding inductance, when the coulomb friction torque change its sign. 5 Conclusion To improve the accuracy of trapezoidal scan diagram reproduction on its working areas by electric drive, constructed on the basis of t he DC electromechanical converter voltage to proportional angle, was proposed two loop speed control system with regulator, with provide enhance of astatism order by reference signal and by disturbance as a load torque . The accuracy of speed deviation from the nominal value for two loop speed control system is 4.5% percent (the simple control system with one control loop had speed error =7.5%) Method of parametric control system synthesis for two -loop speed maintain system is represented. References 1. Vasiliev V.N., Thomasov V.S., Shargorodskii V.D. Status and prospects of high precision observation electric complexes / / Math. universities. Instrument. 2008. vol.51, N6. pp.5 12. 2. Reshetnikov E.M., Sablin Ju.A. Elektromehanicheskie preobrazovateli gidrav licheskih i gazovyh privodov [Electromechanical actuators of gas and hydraulic converters] M.: Mashinostroenie [ Mechanical engineering], 1982. – 144 s. 3. Tolmachev V.A., Demidova G.L. Matematicheskie modeli i dinamicheskie harakteristiki jelektromehaniches kih preobrazovatelej s ogranichennym uglom povorota [Mathematical models and dynamic characteristics of a Turning Angle Limited Electromechanical Converter] // Izvestia vuzov. Priborostroenie [News of universities. Instrument engineering.]. 2008. T. 5 1. S. 18 –23. 4. Tolmachev V.A., Subbotin D.A. Odnokonturnaja sistema upravlenija osi skanirovanija infrakrasnogo teleskopa s proporcional'no differencial'nym reguljatorom skorosti [Infrared telescope with a proportional differential speed regulator single loop scanning axis control system] // Nauchno - tehnicheskij vestnik informacionnyh tehnologij, mehaniki i optiki [Scientific and Technical Journal ITMO] 2012. – S. 73–78. 5. Lviv Polytechnic National University. http://www.lp.edu.ua/ http://teplovizors.ru/ , 23.01.2014. , [grad/s] >JUDGV@ >JUDG@ >@ , [V 0.5 0.5 1.5 2 2.5 3 3.5 4 sec Advances in Automatic Control ISBN: 978-960-474-383-4 179

49 RUSSIAN FEDERATION e mail SubbDmyandexru SERGEY LOVLIN Department of Electrotechnics and Precision Electromechanical Systems University ITMO 197101 Saint PetersburgKronverkskiy pr 49 RUSSIAN FEDERATION e mail seri lyandexru MADINA CVETKOVA Depart ID: 22287

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static speed control system for triaxial telescope scanning axis SUBBOTIN DMITRII Department of Electrotechnics and Precision Electromechanical Systems University ITMO 197101, Saint Petersburg, Kronverkskiy pr., 49 RUSSIAN FEDERATION e- mail: Subb-Dm@yandex.ru SERGEY LOVLIN Department of Electrotechnics and Precision Electromechanical Systems University ITMO 197101, Saint Petersburg,Kronverkskiy pr., 49 RUSSIAN FEDERATION e- mail: seri l@yandex.ru MADINA CVETKOVA Department of Electrotechnics and Precision Electromechanical Systems University ITMO 197101, Saint Petersburg,Kronverkskiy pr., 49 RUSSIAN FEDERATION e- mail: madina1986@bk.ru Abstract nowdays, besides systems based on continuous rotation engines, different scanning systems are used. Such systems often are based on drives with limited rotation a ngle, which shaft can do quite complex reciprocating linear or rotational motions. One of the basic requirements for scanning system is speed maintaining high accuracy in different work modes. In this article is presented astatic two loop speed control sys tem for triaxial telescope scanning axis. The structural scheme, the synthesis method and vector matrix mathematical model is proposed. The proposed struct ure and synthesis method allow to increase the speed maintain accuracy in working modes. Key words : Infrared Telescope, magneto electric converter, scanning diagram, speed control system, synthesis method, the mathematical model. 1 Introduction Basis of the guidance system of the modern telescope is support- rotating device (SRD) and tracking electric drives. For example, infrared telescope guidance system is based on triaxial SRD with azi muth, elevation and scanning axe s. On each axis is located an electrounit, containing an electric motor and sensor s of angular position and engine speed tightly coupled with shafts. A lot of works are devoted to the synthesis of precision gearless servo drive control systems of azimuth and elevation axes , based on the valve motors [1]. Specific are requirements for t he scanning axes electric drives. In many cases, they must ensure the movement of the axis within small range of angles in accordance with the timing diagram shown by curve 1 in Figure.1. Fig. 1. Electric drive scanning diagram On Figure: 1 and 2 - cu rves corresponding to the drive scan diagram by angle and speed, respectively. Full scan cycle sc contains two working stroke plot ( and ) with duration and two nonworking stroke ( and ) with duration nw . At working stroke sections angle should vary linearly within the range of gr XSWR gr with an DFFHSWDEOHVSHHGPDLQWDLQHUURUUDWH$QJOH change principle in nonworking stroke areas is not Advances in Automatic Control ISBN: 978-960-474-383-4 175

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limited. Duration of nonworking stroke is measured between the end of one working stroke and the beginning of the next. Diagram options and its reproduction accuracy requirements depend on the selected scanning mode. In this article we will focus on the diagram properties shown in Table 1. Parameters gr ,' sc s , s nw , s 30 2,4 0,2 10 Table 1. Scanning diagram parameters In view of a sufficiently small range of scanning axis rotation angle variation for the drive implementation is not necessary to use traditional electric motors with an unlimited rotation angle. Promising for these purposes is to use contactless magneto electric converters (MEC) of electrical input signal (voltage) to the proportional angular displacement of its rotor [2]. Carried out mathematical modeling of scanning process with given MEC characteristics, diagram scanning parameters, MEC control winding negligible inductance and small moments of static load torque on the axis confirmed the possibility of realizing the desired movement of the executive axis in the trapezoidal reference signa l (curve 1 in Fig.1.) tracking mode. Scanning drive test on real SRD showed the need to consider in the control system synthesis both the large values of the MEC control winding inductance and the coulomb friction in the bearings of the axis. Under these conditions, the desired motion of the axis is not possible to provide in any one scanning mode. Adjusting the effect of these factors is possible in speed closed loop structures, using the speed curve diagram 2 shown in Fig.1 as the reference signal. During the scanning mode simulation were established minimally implemented errors for which the voltage surge on the MEC control winding does not exceed the maximum allowable value of 48 V. 2 Block diagram Block diagram of the studied system is shown in Fig. 2 , where the dashed lines are highlighted elements and connections forming a block diagram of the actual MEC, grounded in the work [ ]. P1 - PD controller, compensates MEC electrical time constant , where and - respectively the resistance and inductance of the control winding [ ]. The necessity of such compensation occurs when the inductance reaches high values. P2 - control system external loop regulator, designed to increase input and load torque astatism. Fig . 2. Control system block diagram On Figure: is MEC control winding resistance, is MEC control winding inductance, e is the slope of the back EMF coefficient, is the total scanning axis inertial torque, is the inner damping coefficient, is the coulomb friction torque, dM is the stiffness of mechanical characteristic or «magnetic spring» stiffness, dI dM is the stiffness of traction characteristic or electric circuit sensitivity, DS speed loop feedback gain, DQG are external and internal control loop errors, z2 and 1 are external and internal control loop reference signals, is voltage on the MEC control winding, is MEC control ZLQGLQJFXUUHQWLVWKHURWDWLRQDQJOH dt : is the rotation speed. According to the developer of the DB600-100- D3043 converter [ ], which will be XVHGLQUHDOVFDQQLQJV\VWHP0( mechanism" system has the following parameters: = 4500 N·m/rad; = 85 N·m/A; = 0; = 1.5 V·s/rad.; = 0.6 H; = 14 Ohm; = 236 kg·m ; = 25 N·m; y_max = 48 V (maximum voltage of the control winding which is Advances in Automatic Control ISBN: 978-960-474-383-4 176

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equal to the maximum value of the output voltage of the inverter.). 3 Internal loop description Consider the dynamic properties of the internal speed loop. The transfer function of PD controller has the form: )1( )( pT pTK pW DP (1) where transfer coefficient, differentiation time constant and v additional inertial element time constant. Fig. 3 shows regulator de tailed block diagram, where : DSz KU 11 . Fig . 3. PD -regulator detailed block diagram. Using given block diagram, form the expression for the MEC control winding voltage as: )( DP vDP DSDP TK TTK KTK : , (2) where PD regulator state variable. Introduce the following notation ,/ JK (3) JR KKK DSPi (4) and implementing the control winding electrical time constant compensation by selection D = and , without great error internal loop transfer functions on input z1 and disturbance operation, when DS >> can be presented as: 1p1p (p z1 (p) 21 DS TT pK (5) 1p1p (p) (p) 21 TT . (6) Time constants are defined by: (7) (8) After selection from the condition transfer coefficient P1 can be found from the expression (4). Analysis of the transfer functions (5) and (6) shows that at constant voltage reference and load torque, regardless of their size , steady state speed value is zero. This fact determines the specificity of MEC speed control system synthesis - providing a given accuracy of speed maintaining in the work area of scan diagram under conditions of essentially appro aching zero velocity. Diagrams, presented on Figure 4, correspond to the internal speed control loop with MEC parameters given above, synthesized from condition of providing speed PDLQWDLQHUURU $VUHIHUHQFHVLJQDOZDVXVHG the scanning diagram speed varying curve 2, Figure 1. Scanning diagram parameters are shown in Table 1. Fig . 4. Diagram of scan mode simulation. On Figure: 1 LQSXWVSHHGFXUYH (t) in scale 1:1, 2 URWDWLRQVSHHGFXUYHWLQVFDOH - scanning axis rotation angle (t) in scale 1:1, 4 - MEC control winding current (t) in scale 1:2, 5 voltage on the MEC control winding (t) in scale 1:50. The simulation of scanning process for electric drive based on MEC with described control system was held using Simulink. As see n from Figure 4 , during scan diagram tracking mode voltage surge occur on the winding control, when scanning mode changes from nonwork to work stroke areas . Analysis showed that the amplitude of these surges is related with the value of the transfer coeffi cient . Reducing the error in the work area associated with increase of , [grad/s] >JUDGV@ >JUDG@ >@ , [V] 2.0 2.5 3.0 3.5 4.0 0.5 0.5 sec Advances in Automatic Control ISBN: 978-960-474-383-4 177

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regulator transfer coefficient . However, the increase of 1 leads to an increase of the surge amplitude . By reducing the allowable error to a value less than 5% amplitude of the surge peaks can be much higher than the maximum permissible value. 4 External loop tuning 4.1 External loop description One way to improve accuracy while ensuring maximum allowable voltage at the MEC control winding is the introduction of the second (external) speed control loop with regulator providing increasing order of input signal and load torque astatism. The transfer function of the outer loop controller P2 has the form )1( )( 22 pT pTK pW IP (9) This regulator provides first order astatism of input signal , second order of the load torque and allows to setup control loop to the technical optimum in which the closed loop setpoint transfer function can be expressed as: )122( )( )( )( DS KpTpT pU pW (10) where uncompensated time constant, which determines the estimated time of transition in the system ; the step res ponse of the voltage reference is PR = 4.7 T (11) Considering the small effect of coefficient on the dynamic processes in the system and eliminating the appropriate feedback in t he block diagram, presented on Figure 2, it is easy to find the transfer function of the system disturbance (load torque) in the form of an expression: )( )()( )1( )( )( )( 21 PP pW pWpW pTR pM pW Which, considering (1), (9) and (10), can be presented as : )1 )( 1( )1 )( 1( )( 221 pTpTKKK pTpTpT pW IIPP evI (12) Expression (12) leads to the conclusion of the second order of the disturbance astatism of the contro l loop. 4.2 External loop optimization For loop optimization use block diagram (Fig. 5), where controller with transfer function (9) represented as detailed block diagram, internal loop RIWKHV\VWHPDVWUDQVIHUIXQFWLRQDQG - DS – outer loop controller input error. Fig 5. Block diagram of external speed control loop. Reference signal for internal loop is: 231 Ppz KyU (13) Get the expression for calculating voltage on MEC control winding for observed structure after substitution (13) in (2) as (14), where and block diagram integrators output signals. 21 21 )( DPP PD vDP DSDP TKK KT TTK KTK : , (14) Loop tuning consists in selecting such controller parameter s, at which transfer function of open loop is matched to the reference expression: )1(2 )( pTpT pW re PP (15) Because , time constant should be compensated for selection , and n on- compensable time constant form as T , (16) where << 2 is internal loop PD -controller additional inertial time constant, which is unaccounted in (5). Then open outer loop transfer function is: )1( )( pTpT pW (17) Comparing transfer function (17) with reference transfer function (15) get condition for transfer coefficient as: 01 KT (18) Now can be formulated a control system synthesis technique from the condition of providing a given transient time ( PR ) with known MEC parameters: Advances in Automatic Control ISBN: 978-960-474-383-4 178

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- calculate time constant ( ) by formula (11) from providing given performance condition, and then calculate by formula (16). - calculate coefficient from expression (8) as: 02 (19) - calculate from expression (4) as: DSi KK JR (20) - using expression (7) calculate required value of time constant and integrator time constant . Figure 6 shows process modeling results for scan mode of electric drive with two loop control system, synthesized according to the procedure described above from conditions of minimal transition process time in reaction to reference variable . System parameters are: =1 ms, = 57 ms, =4 ms, = 3 ms, =333. 4, =18.5 sec , =364.6, =125, = 25 Nm . Fig. 6. S can process in two loop MEC control system On Figure : 1 speed reference signal DS [1/s] in scale 1000:1, corresponding to the scan diagram, 2 real speed value >V@LQVFDOH 1000:1, 3 rotor angle >UDG@LQVFDOH MEC control winding voltage u [V] in scale 10:1 formed by expression (14), 5 – winding current >@ in scale 10:1. Comparison of scan modeling results for single loop system (Fig. 4) and for two- loop system, shows that in two -loop system speed value in the working area of scan diagram is kept constant and equal to reference speed signal, with no voltage spikes on MEC control winding in moments when scanning mode changes from nonwork to work areas. Accuracy speed deviation from the nominal value is 4.5% percent for two- loop control system. Additional voltage surge on MEC control winding, in amplitude values attaining 46 V, in moments of speed value transition by 0 due to the high rate of current change in the control winding and , hence, voltage surge on control winding inductance, when the coulomb friction torque change its sign. 5 Conclusion To improve the accuracy of trapezoidal scan diagram reproduction on its working areas by electric drive, constructed on the basis of t he DC electromechanical converter voltage to proportional angle, was proposed two loop speed control system with regulator, with provide enhance of astatism order by reference signal and by disturbance as a load torque . The accuracy of speed deviation from the nominal value for two loop speed control system is 4.5% percent (the simple control system with one control loop had speed error =7.5%) Method of parametric control system synthesis for two -loop speed maintain system is represented. References 1. Vasiliev V.N., Thomasov V.S., Shargorodskii V.D. Status and prospects of high precision observation electric complexes / / Math. universities. Instrument. 2008. vol.51, N6. pp.5 12. 2. Reshetnikov E.M., Sablin Ju.A. Elektromehanicheskie preobrazovateli gidrav licheskih i gazovyh privodov [Electromechanical actuators of gas and hydraulic converters] M.: Mashinostroenie [ Mechanical engineering], 1982. – 144 s. 3. Tolmachev V.A., Demidova G.L. Matematicheskie modeli i dinamicheskie harakteristiki jelektromehaniches kih preobrazovatelej s ogranichennym uglom povorota [Mathematical models and dynamic characteristics of a Turning Angle Limited Electromechanical Converter] // Izvestia vuzov. Priborostroenie [News of universities. Instrument engineering.]. 2008. T. 5 1. S. 18 –23. 4. Tolmachev V.A., Subbotin D.A. Odnokonturnaja sistema upravlenija osi skanirovanija infrakrasnogo teleskopa s proporcional'no differencial'nym reguljatorom skorosti [Infrared telescope with a proportional differential speed regulator single loop scanning axis control system] // Nauchno - tehnicheskij vestnik informacionnyh tehnologij, mehaniki i optiki [Scientific and Technical Journal ITMO] 2012. – S. 73–78. 5. Lviv Polytechnic National University. http://www.lp.edu.ua/ http://teplovizors.ru/ , 23.01.2014. , [grad/s] >JUDGV@ >JUDG@ >@ , [V 0.5 0.5 1.5 2 2.5 3 3.5 4 sec Advances in Automatic Control ISBN: 978-960-474-383-4 179

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