Digital Control And State Variable Methods By M Gopal Pdf 11

5.10 Taking outputs of integrators as state variables (x1 and x2are outputs of top two integrators from left to right; x3 and x4are corresponding variables for other integrators): & & x1= 4x4 + 3u1; x 2 = x1 3x2 + u1 + 2u2; & & x 3 = x2 + 3u2; x4 = 4x4 + x3;

Digital Control And State Variable Methods By M Gopal Pdf 11

The given state model is in controllable companion form. Sincethere is a pole-zero cancellation, the model is unobservable. 5.41(a) lI A = (l 1) (l + 2) (l + 1) The system is unstable. (b) G(s)= c(sI A)1 b =

Choosing e(k 1) as controller state variable, xc(k), we obtain,xc(k + 1) = e(k), u(k) = 41xc(k) + 50e(k) as the state model of thecontroller. The plant difference equations are given by (solutionto Problem 6.16) x(k + 1) =

(c) Since there is a pole-zero cancellation, the system iseither uncontrollable or unobservable or both. Given state model isin controllable canonical form. Therefore, the model iscontrollable but not observable.

A variable-frequency drive (VFD) is a type of motor drive used in electro-mechanical drive systems to control AC motor speed and torque by varying motor input frequency and, depending on topology, to control associated voltage or current variation.[1][2][3][4][5] VFDs may also be known as 'AFDs' (adjustable-frequency drives), 'ASDs' (adjustable-speed drives), 'VSDs' (variable-speed drives), 'AC drives', 'micro drives', 'inverter drives' or, simply, 'drives'.

The VFD controller is a solid-state power electronics conversion system consisting of three distinct sub-systems: a rectifier bridge converter, a direct current (DC) link, and an inverter. Voltage-source inverter (VSI) drives (see 'Generic topologies' sub-section below) are by far the most common type of drives. Most drives are AC-AC drives in that they convert AC line input to AC inverter output. However, in some applications such as common DC bus or solar applications, drives are configured as DC-AC drives. The most basic rectifier converter for the VSI drive is configured as a three-phase, six-pulse, full-wave diode bridge. In a VSI drive, the DC link consists of a capacitor which smooths out the converter's DC output ripple and provides a stiff input to the inverter. This filtered DC voltage is converted to quasi-sinusoidal AC voltage output using the inverter's active switching elements. VSI drives provide higher power factor and lower harmonic distortion than phase-controlled current-source inverter (CSI) and load-commutated inverter (LCI) drives (see 'Generic topologies' sub-section below). The drive controller can also be configured as a phase converter having single-phase converter input and three-phase inverter output.[9]

In variable-torque applications suited for Volts-per-Hertz (V/Hz) drive control, AC motor characteristics require that the voltage magnitude of the inverter's output to the motor be adjusted to match the required load torque in a linear V/Hz relationship. For example, for 460 V, 60 Hz motors, this linear V/Hz relationship is 460/60 = 7.67 V/Hz. While suitable in wide-ranging applications, V/Hz control is sub-optimal in high-performance applications involving low speed or demanding, dynamic speed regulation, positioning, and reversing load requirements. Some V/Hz control drives can also operate in quadratic V/Hz mode or can even be programmed to suit special multi-point V/Hz paths.[14][15]

Although space vector pulse-width modulation (SVPWM) is becoming increasingly popular,[17] sinusoidal PWM (SPWM) is the most straightforward method used to vary drives' motor voltage (or current) and frequency. With SPWM control (see Fig. 1), quasi-sinusoidal, variable-pulse-width output is constructed from intersections of a saw-toothed carrier signal with a modulating sinusoidal signal which is variable in operating frequency as well as in voltage (or current).[11][18][19]

An embedded microprocessor governs the overall operation of the VFD controller. Basic programming of the microprocessor is provided as user-inaccessible firmware. User programming of display, variable, and function block parameters is provided to control, protect, and monitor the VFD, motor, and driven equipment.[11][21]

Depending on the model a VFD's operating parameters can be programmed via: dedicated programming software, internal keypad, external keypad, or SD card. VFDs will often block out most programming changes while running. Typical parameters that need to be set include: motor nameplate information, speed reference source, on/off control source and braking control. It is also common for VFDs to provide debugging information such as fault codes and the states of the input signals. 350c69d7ab