JP's Blog

Q4

jithinpaul — Fri, 02 Oct 2009 06:08:03 +0000

Effect of adding a zero to a system

Consider the expression for time response for a second order closed loop transfer function.

Let a zero at s=-z be added to this transfer function.The multiplication term in the numerator of this expression has been adjusted so that steady state gain C/R(0) of the system is unity.

C(s)/R(s)=(s+z)(w_n²/z)/(s²+2zw_ns+w_n²)

This gives the steady state value of output Css=1 when input is unit step.Thus the system will track the step input with zero steady state error.

We have:

C(s)/R(s)=w_n²/(s²+2zw_ns+w_n²)+ (s/z)(w_n²)/(s²+2zw_ns+w_n²)

Let C_z(t) be the response of the system with a zero at s=-z.

Therefore

C_z(t)=c(t)+1/z*d(c(t))/dt

Where c(t) is the response .

The effect of added derivative term can be understood from the figure where a case for a typical value of ζ (less than 1) is considered.

The effect of the zero is to contribute a pronounced early peak to the system’s response whereby the peak overshoot may increase appreciably.The smaller the value of z,the closer the zero to origin,the more pronounced is the peaking phenomenon.Thus ,the zeros on the real axis near the origin are generally avoided in design.However in a sluggish system the introduction of a zero at proper position can improve the transient response.

As z increases(the zero moves farther into the left half of s-plane),its effect becomes less pronounced ie,the effect of zero on transient response may become negligible.

Reference:

Control System engineering -Nagrath and Gopal

Q3

jithinpaul — Fri, 02 Oct 2009 06:06:35 +0000

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]

References:

Q2

jithinpaul — Fri, 02 Oct 2009 06:03:58 +0000

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.

Its applications include computer mouse, CNC machines and robot arm. Incremental encoder produces a series of pulses according to the shaft rotation. By tracking these pulses we get the speed, direction and position of the motor drive.

References:

1.http://mechatronics.mech.northwestern.edu/

Q1

jithinpaul — Fri, 02 Oct 2009 05:49:54 +0000

Synchro

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). U.S. Naval terminology used the term “synchro” exclusively (possible exception: steering gear — info. needed).[1]

The rotors may be stationary. If one rotor is moved through an angle θ, the other selsyn shaft will move through an angle θ. If drag is applied to one selsyn, this will be felt when attempting to rotate the other shaft. While multi-horsepower (multi-kilowatt) selsyns exist, the main appplication is small units of a few watts for instrumentation applications– remote position indication.

Instrumentation selsyns have no use for starting resistors. They are not intended to be self rotating. Since the rotors are not shorted out nor resistor loaded, no starting torque is developed. However, manual rotation of one shaft will produce an unbalance in the rotor currents until the parallel unit’s shaft follows. Though we show three phase rotors above, a single phase rotor is sufficient as shown below. Note that a common source of three phase power is applied to both stators above.[2]

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.

References:

1.http://en.wikipedia.org/wiki/

2.http://www.vias.org/

Cincinnati Milacron Robotic T3 Robotic Arm

jithinpaul — Thu, 01 Oct 2009 07:53:05 +0000

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_arm-c1974-102640478-lg2 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. block1 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 picture1 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.

water borne diseases

jithinpaul — Thu, 20 Aug 2009 05:53:17 +0000

Have u ever had any water-borne diseases in ur area?..

SERVO MECHANISM

jithinpaul — Thu, 06 Aug 2009 06:24:47 +0000

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