ans4:effect of adding zero

EFFECTS OF ADDING A ZERO ON THE ROOT LOCUS FOR A SECOND-ORDER SYSTEM

the effect of changing the gain K on the position of closed-loop poles

and type of responses.

(a) The zero s = –z1 is not present.

For different values of K, the system can have two real poles or a pair of complex

conjugate poles. 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.

In this case, the system can have only real poles and hence we can only find a value

for K to make the system 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 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 jaxis) lying further from the j

axis than the dominant pole in (b).

(d) The zero s = –z1 is located to the left of s = –p2.

This is the most interesting case. Note that 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, we can

now change the damping ratio and the natural frequency (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.

We can see that the resulting closed-loop pole positions are considerably influenced by

the position of this zero. Since there is a relationship between the position of closed-loop

poles and the system time domain performance, we can therefore modify the behaviour of

closed-loop system by introducing appropriate zeros in the controller.

Reference:

Web.mit.edu

www.wikipedia.com

ans3:poles and zeros

POLES AND ZEROS
POLES AND ZEROS OF A TRANSFER FUNCTION ARE THE FREQUENCIES FOR WHICH THE VALUE OF THE TRANSFER FUNCTION BECOMES INFINITY OR ZERO RESPECTIVELY. 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 MOST SIMPLE SENSE, CAN BE DESIGNED SIMPLY BY ASSIGNING SPECIFIC VALUES TO THE POLES AND ZEROS OF THE SYSTEM.
PHYSICALLY REALIZABLE CONTROL SYSTEMS MUST HAVE A NUMBER OF POLES GREATER THAN OR EQUAL TO THE NUMBER OF ZEROS. SYSTEMS THAT SATISFY THIS RELATIONSHIP ARE CALLED PROPER. WE WILL ELABORATE ON THIS BELOW.
LET'S SAY WE HAVE A TRANSFER FUNCTION DEFINED AS A RATIO OF TWO POLYNOMIALS:
H(s):N(s)/D(s)

WHERE N(S) AND D(S) ARE SIMPLE POLYNOMIALS. 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. BECAUSE OF OUR RESTRICTION ABOVE, THAT A TRANSFER FUNCTION MUST NOT HAVE MORE ZEROS THEN POLES, WE CAN STATE THAT THE POLYNOMIAL ORDER OF D(S) MUST BE GREATER THEN OR EQUAL TO THE POLYNOMIAL ORDER OF N(S).

EFFECTS OF POLES AND ZEROS
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. AN OUTPUT VALUE OF INFINITY SHOULD RAISE AN ALARM BELL FOR PEOPLE WHO ARE FAMILIAR WITH BIBO STABILITY. TTHE LOCATIONS OF THE POLES, AND THE VALUES OF THE REAL AND IMAGINARY PARTS OF THE POLE DETERMINE THE RESPONSE OF THE SYSTEM. REAL PARTS CORRESPOND TO EXPONENTIALS, AND IMAGINARY PARTS CORRESPOND TO SINUSOIDAL VALUES.
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:
WEB.MIT.EDU

Incremental encoder

The incremental encoder, sometimes called a relative encoder, is simpler in design than the absolute encoder. It consists of two tracks and two sensors whose outputs are called channels A and B. 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. The code disk pattern and output signals A and B are illustrated in Figure 5. By counting the number of pulses and knowing the resolution of the disk, the angular motion can be measured. The A and B channels are used to determine the direction of rotation by assessing which channels "leads" the other. The signals from the 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. It is also useful as a reference to define a home base or zero position.


Figure 5 illustrates two separate tracks for the A and B channels, but a more common configuration uses a single track with the A and B sensors offset a 1/4 cycle on the track to yield the same signal pattern. A single-track code disk is simpler and cheaper to manufacture.

The quadrature signals A and B can be decoded to yield the direction of rotation as hown in Figure 6. Decoding transitions of A and B by using sequential logic circuits in different ways can provide three different resolutions of the output pulses: 1X, 2X, 4X. 1X resolution only provides a single pulse for each cycle in one of the signals A or B, 4X resolution provides a pulse at every edge transition in the two signals A and B providing four times the 1X resolution. The direction of rotation(clockwise or counter-clockwise) is determined by the level of one signal during an edge transition of the second signal. For example, in the 1X mode, A= with B =1 implies a clockwise pulse, and B=with A=1 implies a counter-clockwise pulse. If we only had a single output channel A or B, it would be impossible to determine the direction of rotation. Furthermore, shaft jitter around an edge transition in the single signal woudl result in erroneous pulses..



reference
mechatronics.mech.northwestern.edu/design

A synchro or "selsyn" is a type of rotary electrical transformer that is used for measuring the angle of a rotating machine such as an antenna platform. In its general physical construction, it is much like an electric motor (See below.) The primary winding of the transformer, fixed to the rotor, is excited by a sinusoidal electric current (AC), which by electromagnetic induction causes currents to flow in three star-connected secondary windings fixed at 120 degrees to each other on the stator. The relative magnitudes of secondary currents are measured and used to determine the angle of the rotor relative to the stator, or the currents can be used to directly drive a receiver synchro that will rotate in unison with the synchro transmitter. In the latter case, the whole device (in some applications) is also called a selsyn (a portmanteau of self and synchronizing).



Schematic of Synchro Transducer: The complete circle represents the rotor. The solid bars represent the cores of the windings next to them. Power to the rotor is connected by slip rings and brushes, represented by the circles at the ends of the rotor winding. As shown, the rotor induces equal voltages in the 120° and 240° windings, and no voltage in the 0° winding. [Vex] does not necessarily need to be connected to the common lead of the stator star windings.


On a practical level, synchros resemble motors, in that there is a rotor, stator, and a shaft. Ordinarily, slip rings and brushes connect the rotor to external power. A synchro transmitter's shaft is rotated by the mechanism that sends information, while the synchro receiver's shaft rotates a dial, or operates a light mechanical load. Single and three-phase units are common in use, and will follow the other's rotation when connected properly. One transmitter can turn several receivers; if torque is a factor, the transmitter must be physically larger to source the additional current. In a motion picture interlock system, a large motor-driven distributor can drive as many as 20 machines, sound dubbers, footage counters, and projectors.

1) Synchro systems were first used in the control system of the Panama Canal, to transmit lock gate and valve stem positions, and water levels, to the control desks.2)Fire-control system designs developed during World War II used synchros extensively, to transmit angular information from guns and sights to an analog fire control computer, and to transmit the desired gun position back to the gun location.3)Smaller synchros are still used to remotely drive indicator gauges and as rotary position sensors for aircraft control surfaces, where the reliability of these rugged devices is needed. Digital devices such as the rotary encoder have replaced synchros in most other applications.

The relation between a synchro and stepper motor is that the stepper motor is just a special type of the synchro. A stepper motor is designed to rotate through a specific angle (called a step) for each electrical pulse received from its control unit.

CINCINATTI T3 ROBOT ARM

Definition

•A Robot is a Programmable, multi-function manipulator designed to move materials, parts, tools or specialized devices through variable programmed motions for the performance
of a variety of tasks.

The beginnings

•1920 Czech playwright Karel Capek introduces the word robotin the play R.U.R. -Rossum's Universal Robots.The word comes from the Czech robota, which means tedious labor.

•1938 The first programmable paint-spraying mechanism designed by Willard Pollard and Harold Roselund

•1942 Isaac Asimovpublishes Runaround, in which he defines the Three Laws of Robotics:
1. Robots must never harm human beings.
2. Robots must follow instructions from humans without violating rule 1.
3. Robots must protect themselves without violating the other rules.

•1951 In France, Raymond Goertz designs the first teleoperated articulated arm for the Atomic Energy Commission.The design is based entirely on mechanical coupling between the master and slave arms (using steel cables and pulleys).Derivatives of this design are still seen in places where handling of small nuclear samples is required.This is generally regarded as the major milestone in force feedback technology.

•1962 General Motors purchases the first industrial robot from Unimation and installs it on a production line. This manipulator is the first of many Unimates to be deployed.

•1965 Homogeneous transformations applied to robot kinematics -this remains the foundation of robotics theory today

•1976 Robot arms are used on Viking 1 and 2 space probes.Vicarm Inc. incorporates a microcomputer into the Vicarm design.

•1951 In France, Raymond Goertz designs the first teleoperated articulated arm for the Atomic Energy Commission.The design is based entirely on mechanical coupling between the master and slave arms (using steel cables and pulleys).Derivatives of this design are still seen in places where handling of small nuclear samples is required.This is generally regarded as the major milestone in force feedback technology.

•1962 General Motors purchases the first industrial robot from Unimation and installs it on a production line. This manipulator is the first of many Unimates to be deployed.

•1965 Homogeneous transformations applied to robot kinematics -this remains the foundation of robotics theory today

Two main types

•Mobility– Main goal is transport

•Manipulation – Main goal is to perform an action on the environment5 main parts

•For a machine to qualify as a robot, it usually needs these 5 parts:

•Mechanical linkage

•Actuators and transmissions

•Sensors

•Controllers

•User interface

•Power conversion unit

Cincinatti Milacron T3 Robot arm


At Cincinnati Milacron Corporation, Richard Hohn developed the robot called The Tomorrow Tool or T3. Released in 1973, the T3 was the first commercially available industrial robot controlled by a microcomputer as well as the first U.S. robot to use the revolute configuration

Cincinnati Milacron built large industrial robots primarily for welding industry. It was one of the first companies to change from hydraulic to electric robots. Milacron pioneered the first computerized numerical control (CNC) robot with improved wrists and the tool centre point (TCP) concepts. The first hydraulic machine, the T3 , was introduced in 1978. It closely resembled the General Electric Man-mate, ITT arm, and other predecessors (Sullivan 1971). Constructed of cast aluminium, it is available in two models of 6-axes revolute jointed arms. The largest, the T3-776, uses ballscrew electric drives to power the shoulder and elbow pitch. The ballscrews replaced the hydraulic cylinders originally used on the T3 robots. The elbow is a classical example of intermediate drive elbow. The same techniques, only upside down, appear in the shoulder. Shoulder yaw is provided by the standard bullgear on a base mounted motor drive. End users have discovered that ballscrews are not sufficiently reliable and are pressuring for an alternators. The eventual disappearance of ballscrews in industrial robots seems inevitable.

This robot is a more classically designed industrial robot. Designed as a healthy compromise between dexterity and strength this robot was one of the ground breakers, in terms of success, in factory environments. However, while this robot was a success in industry its inflexible interfacing system makes it difficult to use in research.


CONTROL SYSTEM




block diagram of T3-776 ROBOT ARM

The T3 robotic arms is controlled using a Hierarchical Control System.A Hierarchical control system is partitioned vertically into levels of control. The basic comand and control structure is a tree, configured such that each computational module has a single superior, and one or more subordinate modules. The top module is where the highest level decisions are made and the longest planning horizon exists. Goals and plans generated at this highest level are transmitted as commands to the next lower level where they are decomposed into sequences of subgoals. These subgoals are in turn transmitted to the next lower control decision level as sequences of less complex but more frequent commands. In general,the decisions and corresponding decompositions at each level take into account: (a) conrmands from the level above, (b) processed sensory feedback information appropriate to that control decision level, and (c) status reports from decision control modules at the next lower control level.

The hierarchical control structure serves as an overall guideline for the architecture and partitioning of a sensory interactive robot control system.

CMI T3-776 CONTROL SYSTEM BLOCK DIAGRAM




The figure shown above depicts the schematic block diagram of the integrated control structure as configured on the Cincinnati Milacron T3 Robot. The system is configured in the hierarchical manner and includes five major subsystems:
(1) The Real-Time Control System (RCS)
(2) The commercial. T3 Robot equipment
( 3 ) the End-Effector System
(4) The Vision System
(5) The Watchdog Safety System
The Real-Time Control System as shown in figure is composed of four levels:
(1) The Task Level
(2)The Elemental-Move Level
(3) The Primitive Level
(4)The T3 Level.
The Task, Elemental-Move and Primitive levels of the controller are considered to be Generic Control Levels. That is, these levels would remain essentially the same regardless of the particular robot (commercial or otherwise) being used. The T3 Level, however ,uses information and parameters particular to the T3 Robot and is, therefore, unique to the T3 Robot. The Joystick shown provides an alternate source of commands to the Primitive Level for manual control of the robot and is not used in conjunction with the higher control levels .The T3 Controller shown in figure is part of the T3 Robot equipment as purchased from Cincinnati Milacron. This controller is subordinate to the T3 Level of the RCS and communicates through a
special interface.
The End-Effector System consists of a two fingered gripper equipped with position and force sensing .The gripper is pneumatically actuated and servo controlled by a controller which is subordinate to the Primitive Level of the RCS. There are three sensory systems on the robot:
(1)The finger force and position sensors on the gripper which report data to the End
Effector Controller
(2)The 3 point Angle Acquisition System which reports data to the T3 Controller, the T3
Level of the RCS and to the Watchdog Safety System
(3)The Vision System which reports data to the Elemental-Move Level of the RCS.
Of the sensor systems, the vision system is obviously the most complex. It performs
sophisticated image processing which requires substantial computational time.
The Watchdog Safety System does not fit directly into the hierarchical control structure. It is an independent system which monitors robot motions and compares them to previously defined limits in position, velocity and acceleration. The Watchdog System has the power to stop the robot if any limits are exceeded and consequently monitors both the mechanical and
control systems of the robot.

PARTS THE REAL TIME CONTROL SYSTEM
(1)Task Level

The Task Level interfaces with the Workstation Level above it and the Elemental-Move Level below it. In the current configuration, the Task Level has no direct interfaces with sensory systems. The Task Level receives commands from the Workstation Level in terms of objects to be handled and named places in the workstation.
For example, the task might be to find a certain part on the tray at the load/unload station, pick
it up and put it in the fixture on the machine tool. This task could be issued as one command from the Workstation Level to the Task Level of the RCS.

(2)Elemental-Move Level

The E-Move Level interfaces with the Task Level above it and the Primitive Level below it. In addition, the E-Move Level interfaces with the Vision System from which it acquires part position and orientation data. The E-Move Level receives commands from the Task Level which are elemental segments of the Task Level command under execution. These are generally single moves from one named location to another. If a part acquisition is involved, data from the Vision System is requested to determine the exact location of the next goal point. The E-Move Level then develops a trajectory between the new goal point and its current position. A trajectory maybe simply a straight line move to the goal point or a more complex move, involving departure, intermediate and approach trajectories. These trajectories can be constructed using pre-stored trajectory segments or data acquired from the Vision System. If no pre-stored segments are found for the desired move and the use of vision data is not appropriate, then a straight line path to the new goal point is calculated.

(3)Primitive Level

The Primitive Level interfaces with the E-Move Level above it and the T3 Level and End-Effector Controller below it. The Primitive Level is the lowest level in the RCS
which is robot or device independent. Subsystems subordinate to the Primitive Level are considered to be at the device level in the control hierarchy. In this system, these subsystems or devices are the robot and the end-effector. T3 The Level shown in figure is not a true control decision level by itself and could be logically combined with the T3 Controller at the device level. The robot and end-effector are, therefore, at the same control decision level subordinate to the Primitive Level. Additionally, the Primitive Level interfaces with the Joystick. The Joystick is a peripheral device which is used for manual operation of the robot. Using the Joystick, the operator can control robot motion in several coordinate systems (world, tool or individual joint motions). Under Joystick control the human operator assumes the higher level planning and control duties normally handled by the E-Move and Task Levels when the robot is operating automatically. The actual Joystick unit has groups of small joysticks, rotory and rocker switches dedicated to each coordinate system. These are configured such t hat the robot will move basically the way the lever is pushed or the switch turned that the robot will move basically the way the lever is pushed or the switch turned, giving the operator a relatively feel for the motion produced ’The Primitive Level receives commands from the E-Move L e v e l in terms of goal points in Cartesian space.These points differ from those received by the E-Move Level from the Task Level in that they are not named locations and therefore assume no knowledge of the Workstation layout. These points are typically more closely spaced than those at the higher Levels although this is not necessarily the case.

(4) T3 Level
The T3 Level interfaces with the Primitive Level above it and the commercial Cincinnati Milacron T3
Robot Controller below it. In addition there is a sensory interface which supplies the six individual joint angles.
The T3 Level is so named because elements of it are peculiar to the T3 Robot. From a control hierarchy point of view the T3 Level does not constitute a logical control decision level but is infact a “gray box” necessary to transform command and feedback formats between the Primitive level and T3 con troller.

SERVOMECHANISM AND THEIR AREAS OF APPLICATION

INTRODUCTION

Servomechanism, or servo is an automatic device that uses error-sensing feedback to correct the performance of a mechanism. The term correctly applies only to systems where the feedback or error-correction signals help control mechanical position or other parameters. For example, an automotive power window control is not a servomechanism, as there is no automatic feedback which controls position—the operator does this by observation. By contrast the car's cruise control uses closed loop feedback, which classifies it as a servomechanism.

James Watt's steam engine governor is generally considered the first powered feedback system. The windmill fantail is an earlier example of automatic control, but since it does not have an amplifier or gain, it is not usually considered a servomechanism.

The first feedback position control device was the ship steering engine, used to position the rudder of large ships based on the position of ship's wheel. This technology was first used on the SS Great Eastern in 1866. Steam steering engines had the characteristics of a modern servomechanism: an input, an output, an error signal, and a means for amplifying the error signal used for negative feedback to drive the error towards zero.

Electrical servomechanisms require a power amplifier. World War II saw the development of electrical fire-control servomechanisms, using an amplidyne as the power amplifier. Vacuum tube amplifiers were used in the UNISERVO tape drive for the UNIVAC I computer.

Modern servomechanisms use solid state power amplifiers, usually built from MOSFET or thyristor devices. Small servos may use power transistors.

The origin of the word is believed to come from the French “Le Servomoteur” or the slavemotor, first used by J. J. L. Farcot in 1868 to describe hydraulic and steam engines for use in ship steering

BLOCK DIAGRAM - OF A SINLE-LOOP SERVOMECHANISM (SERVO-LOOP)

A servomechanism is unique from other control systems because it controls a parameter by commanding the time-based derivative of that parameter. For example a servomechanism controlling position must be capable of changing the velocity of the system because the time-based derivative (rate change) of position is velocity. A hydraulic actuator controlled by a spool valve and a position sensor is a good example because the velocity of the actuator is proportional to the error signal of the position sensor.

Servomechanism may or may not use a servomotor. For example a household furnace controlled by thermostat is a servomechanism, yet there is no motor being controlled directly by the servomechanism.

A common type of servo provides position control. Servos are commonly electrical or partially electronic in nature, using an electric motor as the primary means of creating mechanical force. Other types of servos use hydraulics, pneumatics, or magnetic principles. Usually, servos operate on the principle of negative feedback, where the control input is compared to the actual position of the mechanical system as measured by some sort of transducer at the output. Any difference between the actual and wanted values (an "error signal") is amplified and used to drive the system in the direction necessary to reduce or eliminate the error. An entire science known as control theory has been developed on this type of system.

OPEN LOOP AND CLOSED LOOP SERVOMECHANISMS

Servomechanisms are classified on the basis of whether they depend upon information sampled at the output of the system for comparison with the input instructions. The simplest servomechanisms are called open-loop servomechanisms and do not feed back the results of their output. Open-loop servomechanisms do not verify that input instructions have been satisfied and they do not automatically correct errors.

An example of an open-loop servomechanism is a simple motor used to rotate a television-antenna. The motor used to rotate the antenna in an open-loop configuration is energized for a measured time in the expectation that antenna will be repositioned correctly. There is no automatic check to verify that the desired action has been accomplished. An open-loop servomechanism design is very unsatisfactory as a basis for an antenna rotator, just as it is usually not the best choice for other applications.

When error feedback is included in the design the result is called a closed-loop servomechanism. The servo's output result is sampled continuously and this information is continuously compared with the input instructions. Any important difference between the feedback and the input signal is interpreted as an error that must corrected automatically. Closed-loop servo systems automatically null, or cancel, disagreements between input instructions and output results.

The key to understanding a closed-loop servomechanism is to recognize that it is designed to minimize disagreements between the input instructions and the output results by forcing an action that reduces the error.

AREAS OF APPLICATION.

v Servomechanisms were first used in military fire-control and marine navigation equipment.

v Today servomechanisms are used in- automatic machine tools,

v satellite-tracking antennas,

v remote control airplanes,

v automatic navigation systems on boats and planes,

v antiaircraft-gun control systems.

v fly-by-wire systems in aircraft which use servos to actuate the aircraft's control surfaces

v radio-controlled models which use RC servos for the same purpose.

v Many autofocus cameras also use a servomechanism to accurately move the lens, and thus adjust the focus.

v A modern hard disk drive has a magnetic servo system with sub-micrometre positioning accuracy.

v Typical servos give a rotary (angular) output. Linear types are common as well, using a screw thread or a linear motor to give linear motion.

v Another device commonly referred to as a servo is used in automobiles to amplify the steering or braking force applied by the driver. However, these devices are not true servos, but rather mechanical amplifiers. (See also Power steering or Vacuum servo.)

v In industrial machines, servos are used to perform complex motion.