Archive for October, 2009

ASSIGNMENT:2 question1

October 2, 2009

What is a Synchro? Is it related in any way to a stepper motor?

The term synchro is a generic name for a family of inductive devices which work on the principle of a rotating transformer. A synchro is an electromagnetic transducer commonly used to angular position of a shaft into an electrical signal. It is commercially known as a selsyn or an autosyn.

The basic synchro unit is usually called a synchro transmitter. Its construction is similar to that of a three phase alternator. The stator is of laminated silicon steel and is slotted to accommodate a balanced three-phase winding which is usually of concentric coil type that is, three identical coils are placed in the stator with their axis 120° apart and is star connected. The rotor is of dumbbell construction and is wound with a concentric coil. An ac voltage is applied to the rotor winding through slip rings. This voltage causes a flow of magnetizing current in the rotor coil which produces a sinusoidally time varying flux directed along its axis and distributed sinusoidally in the air gap along the stator periphery. The synchro transmitter acts like a single phase transformer in which the rotor coil is the primary and stator coils form the three secondary’s.

The stepper motor is a special type of synchronous motor which is designed to rotate through a specific angle ,called a step, for each electrical pulse received from its control unit. Typical step sizes are 7.5°, 15° or larger. The stepper motor is used in digitally controlled position control systems in open loop mode. The input command is in the form of a train of pulses to turn a shaft through a specified angle.

The advantages of using stepper motors are:

  1. Their compatibility with digital systems.
  2. No sensors are needed for position and speed sensing as these are directly obtained by counting input pulses and periodic counting if speed information is needed.

Since stepper motors are essentially digital actuators, there is no need to use analog to digital or digital to analog converters in digital control systems. They are used in paper feed motors in type writers and printers, positioning of print heads, pens in X-Y plotters and recording heads in computer disk drives.

Reference: control systems.(nagrath and gopal)

ASSIGNMENT:2 question2

October 2, 2009

What are incremental encoders? Are they useful to us in any way?

  • A rotary encoder or shaft encoder is an electro-mechanical device that converts the angular position of a shaft or axle to an analog or digital code, making it an angle transducer.
  • There are two main types: absolute and incremental (relative).
  • An incremental rotary encoder (quadrature encoder) consists of two tracks and two sensors whose outputs are called channels A and B.
  • Outputs are either mechanical or optical.
  • As the shaft rotates, pulse trains occur on these channels at a frequency proportional to the shaft speed, and the phase relationship between the signals yields the direction of rotation.
  • By counting the number of pulses and knowing the resolution of the disk, the angular motion can be measured.
  • The channels are used to determine the direction of rotation by assessing which channel “leads” the other.
  • The signals from two channels are a 1/4 cycle out of phase with each other and are known as quadrature signals.
  • Often a third output channel, called INDEX, yields one pulse per revolution, which is useful in counting full revolutions.

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  • They are used to track motion and can be used to determine position and velocity,  track the position of the motor shaft on permanent magnet brushless motors.

ASSIGNMENT:2 question 4

October 2, 2009

What would the effect of adding a zero to a control system? Consider the second-order system, G(s) = 1/((s+p1)*(s+p2)) , p1>0 , p2>0 The poles are s = –p1 and s = –p2 and the simple root locus plot for this system is shown in (a). When we add a zero at s = –z1 to the controller, the open-loop transfer function will be: G1(s)= K(s+z1)/((s+p1)*(s+p2)) , z1>0graph We can put the zero at three different positions with respect to the poles: 1. To the right of s = –p1 (b) 2. Between s = –p2 and s = –p1 (c) 3. To the left of s = –p2 (d) (a) The zero s = –z1 is not present. the system can have two real poles or a pair of complex conjugate poles ,may be overdamped, critically damped or underdamped. This means that we can choose K for the system to be overdamped , critically damped or underdamped. (b) The zero s = –z1 is located to the right of both poles, s = – p2 and s = –p1.System can have only real poles and system is overdamped. Thus the pole–zero configuration is even more restricted than in case (a). Therefore this may not be a good location for our zero, since the time response will become slower. (c) The zero s = –z1 is located between s = –p2 and s = –p1. This case provides a root locus on the real axis. The system is overdamped. The responses are therefore limited to overdamped responses. It is a slightly better location than (b), since faster responses are possible due to the dominant pole (pole nearest to jw axis) lying further from the jw axis than the dominant pole in (b). d) The zero s = –z1 is located to the left of s = –p2. By placing the zero to the left of both poles, the vertical branches of case (a) are bent backward and one end approaches the zero and the other moves to infinity on the real axis. With this configuration, the damping ratio and the natural frequency can be changed to some extent. The closed-loop pole locations can lie further to the left than s = –p2, which will provide faster time responses. This structure therefore gives a more flexible configuration for control design. Since there is a relationship between the position of closed-loop poles and the system time domain performance, the behavior of closed-loop system can be modified by introducing appropriate zeros in the controller.

ASSIGNMENT:2 question3

October 2, 2009

POLES AND ZEROS The transfer function provides a basis for determining important system response characteristics without solving the complete differential equation. A transfer function is defined as a ratio of two polynomials: H(S)= N(S)/D(S) Where N(s) and D(s) are simple polynomials These can be written as: N(s)=(s − z1)(s − z2) . . . (s − zm−1)(s − zm) D(s)=(s − p1)(s − p2) . . . (s − pn−1)(s − pn) , Zeros are the roots of N(s) (the numerator of the transfer function) obtained by setting N(s) = 0 and solving for s. Poles are the roots of D(s) (the denominator of the transfer function), obtained by setting D(s) = 0 and solving for s. All of the coefficients of polynomials N(s) and D(s) are real, therefore the poles and zeros must be either purely real, or appear in complex conjugate pairs. Poles and Zeros of a transfer function are the frequencies for which the value of the transfer function becomes infinity or zero respectively.As s approaches a zero, the numerator of the transfer function (and therefore the transfer function itself) approaches the value 0. When s approaches a pole, the denominator of the transfer function approaches zero, and the value of the transfer function approaches infinity.The values of the poles and the zeros of a system determine whether the system is stable, and how well the system performs. Control systems, in the simplest sense, can be designed simply by assigning specific values to the poles and zeros of the system. A system is characterized by its poles and zeros .Because the transfer function completely represents a system differential equation, its poles and zeros effectively define the system response. In particular the system poles directly define the components in the homogeneous response. The locations of the poles, and the values of the real and imaginary parts of the pole helps to determine the response of the system. The stability of a linear system may be determined directly from its transfer function. An nth order linear system is asymptotically stable only if all of the components in the homogeneous response from a finite set of initial conditions decay to zero as time increases.In order for a linear system to be stable, all of its poles must have negative real parts. Reference: http://en.wikibooks.org/wiki/Control_Systems/Poles_and_Zeros