What would be the effect of adding a zero to a control system?

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 the figure(a).


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

We can put the zero at different positions and see the effects.

(a) The zero s = –z1 is not present.

Here, we can choose K for the system to be over damped, critically damped or under damped.

(b) The zero s = –z1 is located to the right of both poles, s = – p2 and s = –p1.

Here we can only find a value for K to make the system over damped.

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

The responses here are limited to over damped responses but, with faster responses.

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

Here, we can change the damping ratio and the natural frequency. This structure gives a more flexible configuration for control design.

Hence we conclude that there is a relationship between the positions of closed-loop poles and the system time domain performance. We can therefore modify the behavior of closed-loop system by introducing appropriate zeros in the controller.

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.


Control Systems Engineering, Nagrath & Gopal



What do the poles and zeros contribute to in the control system?

A system can be characterized by its poles and zeros since they allow reconstruction of the input/output differential equation. 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 provide a complete description of the system.

If you take a transfer function in terms of time G(t) = O(t) / I(t), and do a Laplace transform on it, you’ll get G(s) = O(s) / I(s), where s is a complex variable.
Now instead of solving partial differential equations in time, you can solve algebraic equations in terms of s, and then convert back to time. If you factor numerator and denominator, there will be a value for each factor that make it 0

Consider G(s) = (s-2) (s+3) / [(s-1) (s+4)].
Any value of s that makes the numerator 0, is called a zero, so in the above, you get zeros when s=+2, and s=-3.
Likewise, any value of s that makes the denominator 0, is called a pole. So in the above, s=+1 and s=-3 are poles.

The stability of a linear system may be determined directly from its transfer function. In a stable system, all components of the homogeneous response must decay to zero as time increases. If any pole has a positive real part, there is a component in the output that increases without bound, causing the system to be unstable.

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 location of the poles and zeros provide qualitative insights into the response characteristics of a system.

By carefully choosing or plotting poles and zeros, you can control how fast a system oscillates, if the oscillations grow or disappear, and other such related stability issues.



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

Incremental encoders are a type of Optical encoders which are used in control systems to convert linear or rotary displacement into digital code or pulse signals. The speciality of incremental encoders is that their output is a pulse for each increment of resolution but these makes no distinction between increments as compared to Absolute encoders( the other type of optical encoder), whose output is a digitally coded signal with distinct digital code indicative of each particular least significant increment of resolution.

The incremental encoder consists of

  • a rotary disc having alternate opaque and transparent sectors
  • a light source (LED)
  • a stationary mask
  • a sensor (photo diode)


As the disc rotates, during half of the increment cycle the transparent sectors of rotating and stationary discs come in alignment permitting the light from the LED to reach the sensor thereby generating an electrical pulse.

Rotary encoders are used to track the position of the motor shaft on permanent magnet brushless motors, which are commonly used on CNC machines, robots, and other industrial equipment. In these applications, the encoder (feedback device) plays a vital role in ensuring that the equipment operates properly.

Control Systems Engineering, Nagrath & Gopal

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

The term “synchro” is an abbreviation of the word “synchronous.” It is the name given to a variety of rotary, electromechanical, position-sensing devices.

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.

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. It is commercially known as a selsyn or an autosyn.


Synchros can be thought of as “variable transformers” .When an AC voltage applied to the rotor shaft winding, it causes a change in the synchro’s Stator output voltage. In its general physical construction, it is much like an electric motor. 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 the 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 (self and synchronizing). When several synchros are correctly connected, all of the rotors will align themselves in the same angular position. This is useful, since when the angular position of one synchro is forced to change, it can drive another synchro to indicate the angular change.

With their rugged construction and high reliability, Synchros have been used since World War II as the “angle” transducer of choice for Military, Space and Aviation applications, where only the best will do.

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.





Cincinnati Milacron T3 Robot Arm

MVC-003F An industrial robot is officially defined by ISO as an automatically controlled, reprogrammable, multipurpose manipulator programmable in three or more axes.

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.

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 robot is an example of jointed arm robot which most closely resembles the human arm. This type of arm consists of several rigid members connected by rotary joints. In some robots, these members are analogous to the human upper arm, forearm and hand; the joints are analogous to the human shoulder, elbow and wrist.

The T3 robot arm is mounted on a rotary joint whose major axis is perpendicular to the robot mounting plate. This axis is known as the base or waist. Three axes are required to emulate the movement of the wrist and they are called: pitch, yaw and roll.



The T3 robotic arms are controlled using a Hierarchical Control System. A Hierarchical control system is partitioned vertically into levels of control.

The basic command 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 sub goals. These sub goals are in then transmitted to the next lower control decision level as sequences of less complex but more frequent commands.



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

hirarchyThe 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 which 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 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.

(1) Task Level

The Task Level interfaces with the Workstation Level above it and the Elemental-Move Level below it. 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.

(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. 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).

(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.


Hydraulically actuated, the T3 is used in applications such as welding automobile bodies, transferring automobile bumpers and loading machine tools. In 1975, the T3 was introduced for drilling operations and in the same year T3 became the first robot to be used in the aerospace industry.



Servomechanisms and their application areas

A servomechanism is an automatic device used to correct the performance of a mechanism by  means of an error-sensing feedback. 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.

In many applications, servomechanisms allow high-powered devices to be controlled by signals from devices of  much lower power. The operation of the high-powered device results from a signal (called the error, or difference,  signal) generated from a comparison of the desired position of the high-powered device with its actual position. The  ratio between the power of the control signal and that of the device controlled can be on the order of billions to one.

All servomechanisms have at least these basic components:

  • a controlled device,
  • a command device,
  • an error detector,
  • a comparator,
  • a device to perform any necessary error corrections (the servomotor).


In the controlled device, that which is being regulated is usually the position. This device must, therefore, have some means of generating a signal (such as a voltage), that represents its current position, which is send to the feedback elements. These elements generate a signal called the feedback signal, which is in a form which is comparable with the input. Now, the comparator compares the two signals and sends the change in the two values as the error to the error detector. Now, this error detector sends a signal to the command device which on the nature of the signal drives the servo motor, which repositions the controlled device.


Servomechanisms were first used in gun laying (aiming), military fire-control and marine-navigation equipment. Today, applications of servomechanisms include their use in

  • Automatic machine tools
  • Satellite-tracking antennas
  • Celestial-tracking systems on telescopes
  • Automatic navigation systems
  • Antiaircraft-gun control systems
  • Roll stabilization of ships
  • Radar servo tracking systems

Radar Servo Tracking System

The purpose of a tracking system is to determine the location or direction of a target on a near-continuous basis. An ideal tracking system would maintain contact and constantly update the target’s bearing (azimuth), range and elevation. The output of the tracking system can be sent to a fire control system, which stores the information and derives the target’s motion and therefore its future position.

In a servo tracking system, the radar antenna is initially trained on a target after which it automatically remains pointed at the target as it follows its motion. Furthermore, the system provides continuous position information to the operator and possibly to a fire control system. The antenna is rotated by a motor which provides a negative position feedback signal to a controller.

The commanded input signal is the desired azimuth of the antenna. The error signal drives the motor to reposition the antenna until the position feedback indicates the antenna is at the desired azimuth, at which point the error signal is zero and the motor stops. This servo-mechanism can be combined with a tracker, which determines the azimuth as the target, which the system now uses as the input.


Here, the input comes from the tracker. The combination is called a radar servo-tracking system. The tracker takes the return signal and position information and determines the location of the target.