question 4

The effect when described for a 2^nd order system:

Consider the second-order system

Poles are s = –p1 & s = –p2. When we add zero at s = –z1 to the controller, the open-loop transfer function will change to:

We can put zero at 3 different positions with respect to the poles:

1. To the right of s = –p1 Fig (b)

2. Between s = –p2 & s = –p1 Fig(c)

3. To the left of s = –p2 Fig (d)

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.

Over, critically or under damped

(b) The zero s = –z1 is located to the right of s = – p2 & s = –p1.

Over damped

(c) The zero s = –z1 is located between s = –p2 & s = –p1.

Over damped

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

Flexible configuration

Since there is a relationship between position of closed-loop poles and system time domain performance, we can modify the behaviour of closed-loop system by introducing appropriate zeros in the controller.

Reference:

ü Web.mit.edu

ü www.wikipedia.com

ü www.palgrave.com

ü Applied control theory- James r Leigh-1987

question 3

A system is characterized by its poles and zeros in the sense that they allow reconstruction of the (Input /output) differential equation. The terms zeros and poles are chosen, because the transfer function is zero at and infinite at . In general, the poles and zeros of a transfer function may be complex and 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. Such plots are known as pole-zero plots. It is usual to mark a zero location by a circle and a pole location, a cross. The location of the poles and zeros provide qualitative insights into the response characteristics of a system. A linear time-invariant systemwithout dead time is described completely by the distribution of its poles and zeros and the gain factor . Many computer programs are available to determine the poles and zeros of a system from either the transfer function or the system state equations.

Example of the pole and zero distribution of a rational transfer function in the complex plane

Real axis zeros tend to spread the loci faster and stabilize the system. Real-axis poles, on the other hand, tend to make the loci spread more slowly and curve toward instability. The root locus design method involves three steps: the closed loop function is determined, and then the open loop transfer function, and finally a compensation network are synthesized.

For stable systems, pole should be in right hand of S plane (negative real value) and if it is imaginary axis (non real), it indicates system is oscillatory.
If it is real and imaginary (a complex), then system response is damped oscillation. If poles are left in S plane then system is highly unstable.

synchro mechanism

Incremental encoders are position feedback devices that provide incremental counts. Incremental encoders have only a single band consisting of alternate transparent and opaque sectors. As the encoder turns, the photo sensor sends a quasi-sine wave to a Schmitt trigger, which transforms this into a sharp square wave, a series of pulses. These go to an UP/DOWN counter, whose count represents the encoder position. Commercially available incremental encoders typically give from 200 to high as 5000 pulses per turn.

Compared to coded pattern encoders, incremental encoders have four main advantages:

1. They are simpler and less expensive
2. They need no decoding circuits, only a counter.
3. Their range is only limited by the counter capacity. Additional encoder with step down gearing is used to increase the range that can be covered.
4. The measurement origin can be chosen at any point by resetting the counter (floating zero).

Drawback:

1. Incremental encoders do not measure absolute position, only incremental changes. Therefore, any mistake in the count is carried along to all subsequent counts.

Applications

• Precise angle measurement
• RPM or direction of rotation measurement
• X/Y positioning tables
• Positioning in handlings-systems
• I

incremental encoders

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 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..

(Materials taken from Introduction to Mechatronics and Measurement Systems, Histand & Alciatore, 1999 McGraw Hill)

SERVO MECHANISM

Servomechanism is an automatic device for the control of a large power output by means of a small power input or for maintaining correct operating conditions in a mechanism. It is a type of feedback control system. 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 machinery.

A servomechanism is unique from other control systems because it controls a parameter by commanding the time-based derivative of that parameter.

Servomechanism may or may not use a servomotor.

The 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.

Servo Wiring
All servos have three wires:
Black or Brown is for ground.
Red is for power (~4.8-6V).
Yellow, Orange, or White is the signal wire (3-5V).

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.

Thier only disadvantage is that these motors are much more costlier than stepper or dc motors.

Cincinati Milacron T3 Arm

The Cincinnati Milacron T3-776 robot is shown in .the picture. It is apparent that the
geometry of this manipulator is very similar to that of the Puma robot, i.e. the second
and third joint axes are parallel and the last three joint axes intersect at a point. The
detailed solution will therefore be very similar to that for the Puma robot. This solution
will be followed by a general discussion of a geometric solution that does not require that the hypothetical closure link be determined.

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.

The Cincinnati Milacron T3-786 robot was the workhorse of the robotics industry for many years. Almost indestructable, thousands of these machines are still in production in hostile, 24 hour manufacturing environments. Many manufacturers have come to depend on these machines, and are reluctant to give them up.

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.

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