Effect of Adding a Zero

Consider the second-order system given by:

G(s) =1 / ((s+p₁)(s+p₂)) p1 > 0, p2 > 0

The poles are given by s = –p1 and s = –p2 and the simple root locus plot for this system is shown in Figure . When we add a zero at s = –z1 to the controller, the open-loop transfer function will change to:

G₁(s) =K(s+z₁) / ((s+p₁)(s+p₂)) , z₁>0

Effect of adding a zero to a second-order system root locus.

We can put the zero at three different positions with respect to the poles:

1. To the right of s = –p1 Figure (b)

2. Between s = –p2 and s = –p1 Figure (c)

3. To the left of s = –p2 Figure (d)

(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. Thus K for the system can be overdamped, critically damped or underdamped.

(b) The zero s = –z₁ is located to the right of both poles, s = – p₂and s = –p₁.

Here, the system can have only real poles. Hence only one value for Kto make the system overdamped exists. 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 jω-axis) lying further from the jω-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, we can now change the damping ratio and the natural frequency . 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

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. 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. [1]

The poles and zeros are properties of the transfer function, and therefore of the differential equation describing the input-output system dynamics. Together with the gain constant K they completely characterize the differential equation, and provide a complete description of the system. A system is characterized by its poles and zeros in the sense that they allow reconstruction of the input/output differential equation. In general the system dynamics may be represented graphically by plotting their locations on the complex s-plane, whose axes represent the real and imaginary parts of the complex variable s (pole-zero plots). For the stability of a linear system, all of its poles must have negative real parts,that is they must all lie within the left-half of the s-plane. A system having one or more poles lying on the imaginary axis of the s-plane has non-decaying oscillatory components in its homogeneous response, and is defined to be marginally stable. [2]

Incremental encoders !!!!!!!!!

Incremental encoders are position feedback devices that provides incremental counts. Thus, incremental encodersprovide relative position, where the feedback signal is always referenced to a start or home position. Forincrementalencoders, each mechanical position is uniquely defined. The current position sensed is only incremental from the last position sensed. Incremental encoders are also non-contacting optical, rotary, quadrature output device. •Theseincremental encodersare also called optical encoders or optical incremental encoders because they utilizes optical technology. Optical incremental encoders are highly sort after as position feedback devices due to its durability and ability to achieve high resolution. Avago’s optical incremental encoders are exceptionally recognized for its reliability and accuracy.

Synchro?? how is it Related to stepper motor!!!!!

A SYNCHRO is a motor like device containing a rotor and a stator and capable of converting an angular position into an electrical signal, or an electrical signal into an angular position. A Synchro can provide an electrical output (at the Stator) representing its shaft position or it can provide a mechanical indication of shaft position in response to an applied electrical input to its stator winding.

STEPPER MOTOR

A stepper motor is a “digital” version of the electric motor. The rotor moves in discrete steps as commanded, rather than rotating continuously like a conventional motor. When stopped but energized, a stepper (short for stepper motor) holds its load steady with a holding torque. Wide spread acceptance of the stepper motor within the last two decades was driven by the ascendancy of digital electronics. Modern solid state driver electronics was a key to its success. And, microprocessors readily interface to stepper motor driver circuits.

Cincinnati Milacron T3 type robotic arm

CINCINNATI MILACRON T3 ROBOT ARM

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 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.

CINCINNATI MILACRON T3-776

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

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.

Hierarchical Control System Block Diagram

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

Block Diagram of T3-776 Arm

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.
4. 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 OF 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 controller

SERVO MECHANISM

"A feedback system that consists of a sensing element, amplifier, and servomotor, used in the automatic control of a mechanical device."


INTRODUCTION
A system for the automatic control of motion by means of feedback. The term servomechanism, or servo for short, is sometimes used interchangeably with feedback control system (servosystem). In a narrower sense, servomechanism refers to the feedback control of a single variable (feedback loop or servo loop)In the strictest sense, the term servomechanism is restricted to a feedback loop in which the controlled quantity or output is mechanical position or one of its derivatives (velocity and acceleration).

The purpose of a servomechanism

• Accurate control of motion without the need for human attendants (automatic control)



• Maintenance of accuracy with mechanical load variations, changes in the environment, power supply fluctuations, and aging deterioration of components (regulation and self-calibration)



• control of a high-power load from a low-power command signal (power amplification)



• control of an output from a remotely located input, without the use of mechanical linkages (remote control, shaft repeater).

BLOCK DIAGRAM

IMPORTANT FIELDS
Servomechanisms were first used in speed governing of engines, automatic steering of ships, automatic control of guns, and electromechanical analog computers. Today, servomechanisms are employed in almost every industrial field. Among the applications are cutting tools for discrete parts manufacturing, rollers in sheet and web processes, elevators, automobile and aircraft engines, robots, remote manipulators and teleoperators, telescopes, antennas, space vehicles, mechanical knee and prostheses, and tape, disk, and film drives
A BRIEF NOTE
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. Servomechanisms were first used in military fire-control and marine navigation equipment. Today servomechanisms are used in automatic machine tools, satellite-tracking antennas, remote control airplanes, automatic navigation systems on boats and planes, and antiaircraft-gun control systems. Other examples are fly-by-wire systems in aircraft which use servos to actuate the aircraft's control surfaces, and radio-controlled models which use RC servos for the same purpose. Many autofocus cameras also use a servomechanism to accurately move the lens, and thus adjust the focus. A modern hard disk drive has a magnetic servo system with sub-micrometre positioning accuracy. 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.

History

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 make use of 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.

Applications

Servomechanisms are useful to control motion without human attendants, or to maintain the accuracy of an environment like a power plant, and to control action from a remote isolated station. The controller typically uses (and has) much less power than that of what is being controlled. Almost always it is the position or velocity which is being controlled.

Servomechanisms are used to control mechanical things such as motors, steering mechanisms, and robots. Servomechanisms are used extensively in robotics. A robot controller can tell a servomechanism to move in certain ways that depend on the inputs from sensors. Multiple servomechanisms, when interconnected and controlled by a sophisticated computer, can do complex tasks such as cook a meal. A set of servomechanisms, including associated circuits and hardware, and intended for a specific task, constitutes a servo system.Servo systems do precise, often repetitive, mechanical chores. A computer can control a servo system made up of many servomechanisms. For example, an unmanned robotic warplane (also known as a drone) can be programmed to take off, fly a mission, return, and land. Servo systems can be programmed to do assembly-line work and other tasks that involve repetitive movement, precision, and endurance.

A servo robot is a robot whose movement is programmed into a computer. The robot follows the instructions given by the program, and carries out precise motions on that basis. Servo robots can be categorized according to the way they move. In continuous-path motion, the robot mechanism can stop anywhere along its path. In point-to-point motion, it can stop only at specific points in its path. Servo robots can be easily programmed and reprogrammed. This might be done by exchanging diskettes, by manual data entry, or by more exotic methods such as a teach box. When a robot arm must perform repetitive, precise, complex motions, the movements can be entered into the robot controller’s memory. Then,when the memory is accessed, the robot arm goes through all the appropriate movements. A teach box is a device that detects and memorizes motions or processes for later recall.

The constant speed control system of a DC motor is a servomechanism that monitors any variations in the motor’s speed so that it can quickly and automatically return the speed to its correct value. Servomechanisms are also used for the control systems of guided missiles, aircraft, and manufacturing.

The power steering system in an automobile is an example of a servomechanism. The direction of the front wheels is controlled by the angle of the steering wheel. Should the motion of the car turn the front wheels away from the desired direction, the servomechanism, consisting of a mechanical and hydraulic system, automatically brings the wheels back to the desired direction. Another example of a servomechanism is the automatic control system by which a THERMOSTAT, (q.v.) in one of the rooms of a house controls the heat output of the heating furnace. Other examples include automatic pilots used on ships, aircraft, and space vehicles, in which the direction of motion of the vehicle is controlled by a compass setting. Unmanned spacecraft are automatically turned to point their cameras, radio antennae, and solar panels in the desired directions by servomechanisms. The input in that case is the sensing of the direction of the sun and stars, and the output is the control of small jets that turn and orient the spacecraft.
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.

Servomechanisms were first used in military fire-control and marine navigation equipment. They were also used in military applications, such as an antiaircraft gun that tracks a plane via radar. As the plane moves the radar gives the plane’s position information to the gun, which computes the new position of the plane and realigns. This process can go indefinitely. Some other applications are satellite tracking and satellite antenna alignment systems, automatic machine tools, star-tracking systems on telescopes (since the stars’ position changes as the earth rotates), and navigation systems.

RC servos are hobbyist remote control devices servos typically employed in radio-controlled models, where they are used to provide actuation for various mechanical systems such as the steering of a car, the flaps on a plane, or the rudder of a boat.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. RC servos are composed of an electric motor mechanically linked to a potentiometer. Pulse-width modulation (PWM) signals sent to the servo are translated into position commands by electronics inside the servo. When the servo is commanded to rotate, the motor is powered until the potentiometer reaches the value corresponding to the commanded position. Due to their affordability, reliability, and simplicity of control by microprocessors, RC servos are often used in small-scale robotics applications.The servo is controlled by three wires: ground (usually black/orange), power (red) and control (brown/other colour). This wiring sequence is not true for all servos, for example the S03NXF Std. Servo is wired as brown(negative), red (positive) and orange (signal). The servo will move based on the pulses sent over the control wire, which set the angle of the actuator arm. The servo expects a pulse every 20 ms in order to gain correct information about the angle. The width of the servo pulse dictates the range of the servo’s angular motion. A servo pulse of 1.5 ms width will set the servo to its “neutral” position, or 90°. For example a servo pulse of 1.25 ms could set the servo to 0° and a pulse of 1.75 ms could set the servo to 180°. The physical limits and timings of the servo hardware varies between brands and models, but a general servo’s angular motion will travel somewhere in the range of 180° – 210° and the neutral position is almost always at 1.5 ms.RC Servos are usually powered from either NiCd or NiMH packs common to most RC devices. More recently these systems are powered by Lithium Polymer (LiPo) packs. Voltage ratings vary from product to product, but most servos are operated at 4.8 V or 6 V DC from a 4 or 5 cell NiCd or NiMH battery, or a regulated LiPo pack.

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.

Today servomechanisms are used in automatic machine tools, satellite-tracking antennas, remote control airplanes, automatic navigation systems on boats and planes, and antiaircraft-gun control systems. Other examples are fly-by-wire systems in aircraft which use servos to actuate the aircraft’s control surfaces, and radio-controlled models which use RC servos for the same purpose. Many autofocus cameras also use a servomechanism to accurately move the lens, and thus adjust the focus. A modern hard disk drive has a magnetic servo system with sub-micrometre positioning accuracy