Fundamentals of electrical drive controls_Deur_Pavković_2012

Deur, J., Pavković, D., “Fundamentals of Electrical Drive Controls”, UNESCO Encyclopedia of Life Support Systems, Chap 6.39.21, 2012 FUNDAMENTALS OF ELECTRICAL DRIVE CONTROLS Joško Deur and Danijel Pavković University of Zagreb, Faculty of Mechanical Engineering and Naval Architecture, I Lučića 5, HR10002 Zagreb, Croatia Keywords: Electrical drives, control, modeling, DC motor, permanent-magnet synchronous motor, cascade control, chopper, sensors, speed control, position control, pointing, tracking, friction, compliance, backlash, state control, nonlinear compensation Contents Introduction Elements of controlled electrical drive 2.1 Separately-excited DC motor 2.1.1 Dynamic model 2.1.2 Steady-state curve 2.2 Electronic power converters 2.3 Sensors 2.4 Electronic control unit and control algorithms Adjustment of DC motor speed 3.1 Speed adjustment by armature resistance control 3.2 Speed adjustment by armature voltage and field control Design of DC drive cascade control system 4.1 Cascade control structure 4.2 Damping optimum criterion 4.3 Armature current control 4.4 Speed control 4.5 Position control 4.5.1 Small-signal operating mode 4.5.2 Large-signal operating mode Design of tracking system 5.1 Tracking of a-priori known reference 5.2 Tracking of a-priori unknown reference Control of permanent-magnet synchronous motor 6.1 Modeling of motor 6.2 Control Compensation of transmission compliance, friction, and backlash effects 7.1 Model of two-mass elastic system with friction and backlash 7.2 Compliance compensation 7.3 Friction compensation 7.4 Backlash compensation Conclusion Summary Controlled electrical drives can be regarded as the most flexible and efficient source of controlled mechanical power Understanding and developing the controlled electrical drive systems require a multi-disciplinary knowledge, starting from electrical machine theory, through electronic power converter technology to control system design techniques This article gives a systematic overview of elements of a controlled electrical drive with emphasis on the control system design The basic procedure of feedback and feedforward cascade control system design is presented for the separately-excited DC motor It is then demonstrated that the basic principle of current/torque control can be applied to AC machines modeled in the rotational field coordinate frame, while the superimposed speed and position controller structure remains the same as with the DC motor Finally, a notable attention is paid to analysis of transmission compliance, friction, and backlash effects, and their compensation by means of advanced control algorithms Introduction Electrical drives represent a dominant source of mechanical power in various applications in production, material handling, and process industries Applying the feedback control techniques to electrical drives substantially improves their performance in terms of achieving precise and fast motion control (servo-control) with a high efficiency Traditionally, the controlled electrical drives were based on direct-current (DC) motors and analog controllers However, the rapid development of power electronics and microprocessor technology in the last three decades has propelled application of servo-control to brush-less, alternating-current (AC) drives, and provided implementation of advanced motion control algorithms including compensation of transmission compliance, friction, and backlash effects The overall control performance, efficiency, reliability, and availability of the controlled electrical drives have been substantially improved, thus accelerating their penetration into various engineering applications This article presents an overview of controlled electrical drive technology with emphasis on control system design The presentation is based on the separately-excited DC motor, since control of this motor can be easily understood and readily extended to AC motors First, the elements of a controlled electrical drive are described (Section 2), which include DC motor and its mathematical model, electronic power converters, sensors, and electronic control units including the basic control algorithms Next, the steady-state form of DC motor model is used to describe the motor speed adjustment (or open-loop control) in the regions below and above the rated speed, as well as the controlled starting and regenerative braking of the motor (Section 3) This serves as a basis for presenting a cascade structure of motor feedback control, including optimal tuning of current, speed, and position controllers (Section 4) For tracking applications, the feedback system is extended by feedforward paths or a feedforward compensator, in order to reduce the dynamic tracking error (Section 5) Section shows, on an example of permanent-magnet synchronous motor (PMSM), how the naturally decoupled armature and field control of DC motor can be applied to the coupled dynamics of three-phase AC motors Finally, Section analyzes influences of transmission insufficiencies related to compliance, friction and backlash effects on the static and dynamic behavior of a servodrive, and presents control algorithms for compensating these effects The theoretical discussions are illustrated by a number of computer simulation results Elements of Controlled Electrical Drive Figure shows the structural block diagram of a controlled electrical drive An electrical motor is coupled to a working mechanism in order to provide a transfer of mechanical power The main additional features of controlled electrical drives compared to their conventional counterparts are: (i) the power transfer is made time variant/controllable using an electronic power converter , and (ii) the drive motion can be controlled in a precise manner based on the use of feedback paths containing sensors and electronic control unit The control tasks can be different, starting from current control (corresponding to open-loop torque/force control), through speed and position control, and towards force control Normally, the controlled power flows from the electrical grid to the working mechanism However, during transients or occasional continuous braking intervals, the motor switches to a generator mode and the power flows back to the grid If the power converter does not support the regenerative braking feature (typically in low-power drives), the braking power is dissipated on a braking resistor Figure Structural block diagram of controlled electrical drive 2.1 Separately-Excited DC Motor Direct-current (DC) motor (see cross-section schematic in Fig 2a) consists of a magnetic field flux (excitation) circuit (placed on the stator), armature circuit (placed on the rotor), and a commutator which inverts the current in an armature coil whenever it passes through the neutral zone that is perpendicular to the stator field axis The power is transferred to the armature through brushes that are fixed in the neutral zone and leaned to the commutator The excitation and armature circuits can be connected separately from each other, or a series or parallel connection can be utilized instead The separately-excited DC motors are mostly used in controlled drives, owing to the possibility of independent field and armature current control and related superior control features in a wide speed range Figure Simplified cross-section schematic (a) and equivalent scheme of separately-excited DC motor 2.1.1 Dynamic Model Figure 2b shows an equivalent scheme of the separately-excited DC motor The stator magnetic flux  acts upon the armature current ia , thus producing the motor torque On the other hand, when the rotor rotates, the voltage e (back electromotive force, EMF) is induced in the armature winding The motor dynamics are described by the following set of differential equations (see Nomenclature), given in both time ( t ) and Laplace ( s ) domain: ua (t )  Ra ia (t )  La dia (t )  e(t )  ua ( s )  Ra ia ( s)  La sia ( s)  e( s ) dt e(t )  K e  (t ) (t ) J (1b) d (t )  mm (t )  ml (t )  Js ( s )  mm ( s )  ml ( s ) dt mm (t )  K m  (t )ia (t ) uM (t )  RM iM (t )  N M (1a) (1c) (1d) d (iM (t ))  uM ( s)  RM iM ( s)  N M s ( s) dt d (t )   (t )  s ( s)   ( s ) dt (1e) (1f) where (iM ) is the nonlinear static magnetizing curve The armature circuit, Eq (1a), can be described by the following transfer function ia ( s ) Ka   , ua ( s )  e( s ) La s  Ra Ta s  (2) where K a  Ra and Ta  La Ra are the armature gain and armature time constant, respectively Based on Eqs (1) and (2), a block diagram of the motor model can be created, as shown in Figure 3a In the basic case of constant excitation circuit voltage (uM  const    const.) or permanentmagnet excitation, the block diagram reduces to the one shown in Figure 3b based on the following substitutions: K t  K m  and K v  K e  Figure Block diagram of DC motor: (a) general case and (b) constant-flux case 2.1.2 Steady-State Curve Under the steady-state conditions, the time-derivatives of motor dynamic variables vanish (e.g dia dt  0; s  ) After rearranging the steady-state forms of motor equations (1), the following expression for the motor steady-state curve is obtained:  ua Ra mm  Ke Ke K m      0  (mm ) (3) The steady-state curve is shown in Figure Since the armature resistance Ra is relatively small (particularly for high-power machines), the steady-state curve is rather stiff, i.e the motor speed drop  due to the increase of load ml  mm is small compared with the idle speed 0 The drive operating point is determined as the cross-section point of the motor and load static curves (Fig 4; note that mm  ml is valid for the steady-state conditions according to Eq (1c)) If the motor speed is lower than the idle speed:   0  e  ua  ia  , the motor operates in the driving mode (1st quadrant of the coordinate system in Fig 4) Otherwise, for the case when   0 ( e  ua and ia  ), the machine operates in the generator braking mode, thereby producing the electric energy and transmitting it to the grid (2nd quadrant in Fig 4) For the reverse motion (   ), the driving and braking modes relate to the 3rd and 4th quadrants, respectively (see also Section 3) Figure Steady-state curve of DC motor and construction of operating point 2.2 Electronic Power Converters The electronic power converters transform the grid power system with constant parameters (e.g voltage, frequency) into the motor power system with variable parameters and potentially different voltage waveform They can be divided into several characteristic groups, as shown in Figure A rectifier is connected to AC grid and it provides variable-voltage power supply for DC motors Inverters are utilized when variable-frequency AC motors are supplied from a DC grid (e.g in transport applications) When a power converter allows for both power directions to cover the driving and generator braking modes, it is called regenerative converter Other power converter types include DC/DC converters and AC/AC converters Figure Basic types of electronic power converters Unless very low-power drives are considered (e.g up to 50W), power converters are designed as switching devices This is because of a great efficiency of electronic valves when used in switching (on/off) mode Historically, thyristors were the first semiconductor switching components Their main advantage is that they are able to withstand extremely large currents (typically up to 10,000 A), while their main disadvantage is that they are actually semi-controllable semiconductor switches (i.e they cannot be turned off actively) Thyristors have conveniently been used in linecommutated power converters (rectifiers and regenerative converters, see left part of Fig 5) aimed at supplying the DC motors directly from AC grid However, the response time of these converters is relatively slow, as it closely relates to the inverse of AC grid frequency, and the produced voltage waveform is characterized by a significant ripple In order to overcome these disadvantages, which become more relevant when supplying AC machines, pulse width-modulated (PWM) voltagesource transistor converters can conveniently be used In the low power range (e.g up to several kW) fast and efficient MOSFET components are used, while power converters with larger power ratings (up to 1MW) rely on insulated gate bipolar transistor (IGBT) components The switching frequency is typically significantly larger than kHz (more than 20 kHz for MOSFET converters), so that the response time is a fraction of millisecond Figure shows the voltage-source transistor converter used in DC drives, which is usually called four-quadrant (4Q) chopper or H-bridge converter The corresponding "idealized" voltage and current waveforms for the 1st-quadrant operation are shown in Figure The full-bridge three-phase rectifier converts the AC grid voltage to DC link voltage One of the diagonal pairs of chopper transistors is switched on at any time, thus bringing the positive or negative DC link voltage UD to the motor Since the (constant) switching frequency f c  T1  T2  is very high (typically kHz), the motor speed relates to the average motor voltage, which reads (Fig 7): ua  ua (t )  T1  T2 T1 T2  ua (t )dt  T1  T2 U D   2T1 f c  1 U D  (2  1)U D , T1  T2 (4) where   T1 f c  T1 / T1  T2  is the output square-wave voltage duty cycle Moreover, since f c  1/ Ta is usually satisfied, the armature current ia , and thus the torque mm , is effectively smoothed by the lag (low-pass) nature of the armature dynamic model (2) Thus, for the square-wave (AC) armature voltage signal ua  t  the armature current ia has a DC form, while opposite is valid for the DC link voltage U D and current iD (Fig 7) According to Eq (4), the armature voltage can be arbitrarily varied in the range [U D ,U D ] by changing the duty cycle  (pulse width modulation, PWM) During the interval T1 of the 1st-quadrant converter operation, the current is conducted through the transistors Q1  Q1 , while for the interval T2 the still positive motor current flows through the freewheeling diodes D  D2 Since T1  T2 , more power flows from the DC link to the motor than vice versa, and the energy spent is covered by the power grid through the rectifier This could be expected since the motor operates in the 1st quadrant Figure Electrical scheme of H-bridge transistor converter Figure "Idealized" waveforms of H-bridge converter Table outlines the converter operation in all four quadrants of the speed vs torque coordinate system in Figure For instance, in the 2nd quadrant, T1  T2 is still valid since the motor speed  and the armature voltage ua are larger than zero (cf Fig 4) However, the armature current ia is negative (for the negative motor torque mm ), which means that the current flows through freewheeling diodes D1  D1 during the interval T1 and through transistors Q2  Q2 during the interval T2 Thus, since T1  T2 the average motor power is negative, i.e it flows to the DC link and increases the DC link (capacitor) voltage Since the simple rectifier topology cannot provide the power flow to the grid, the braking resistor is switched on by the transistor Qb (Fig 7) when the capacitor voltage exceeds the upper threshold, thus dissipating the motor braking power When the DC link voltage drops below the lower threshold (indicating the driving operation and the power flow from the grid), the transistor Qb is again turned off Table Description of four-quadrant chopper operation Quadrant: st nd (motor) (generator) 3rd (motor) 4th (generator) ua and  >0 >0