Control Systems Engineering

• Control System presented by Dr. Vilas H Gaidhane from BITS Pilani, Dubai Campus.

Course Objectives

• Understand the basics of feedback in control systems.
• Study the classification of control systems.
• Study mathematical modeling of electromechanical systems.
• Learn block diagram reduction techniques.
• Study Signal Flow Graph, Mason's Gain formula to calculate the system transfer function.
• Study the properties and advantages of feedback systems.
• Analyze time response of dynamic systems.
• Apply Routh Test to study closed-loop system stability.
• Draw root locus, Bode plot, Polar plot for systems to study stability.
• Study PID controller design.
• Explore concepts of State, State Variables, and State Models.

Textbooks

• Nagrath I. J. and M. Gopal, "Control Systems Engineering", New Age Publishers.

References

• Kuo, B. C., and Golnaraghi, F., "Automatic Control Systems", John Wiley & Sons, 8th Ed, 2003.
• K. Ogata, "Modern Control Systems", Pearson Education, 4th Ed., 2002.

Introduction to Control Systems

• A system is a collection of components performing a particular task.
• A control system is a system where the output is controlled by varying the input.
• A physical system comprises interconnected physical objects serving an objective.
• Idealized physical systems are called physical models.
• Physical models can be mathematical models that are linear-time varying or linear-time invariant.
• James Watt's centrifugal governor appeared in the 18th century for engine speed control.
• Minorsky worked on automatic ship steering controllers in the 1920s.
• Nyquist developed a method for analyzing the stability of controlled systems in the 1930s.
• Frequency response methods were used in the 1940s to design linear closed-loop control systems.
• The root-locus method by Evans fully developed in the 1950s.
• State space methods, optimal control, and adaptive control emerged in the 1960s.
• Learning controls began being investigated in the 1980s.
• Current research involves applications like biological, biomedical, economic, and socio-economic context.

Classification Of Control Systems

• Depending on the presence of a human-being, control systems are classified as:
  • Manually Controlled System
  • Automatic Control System
• Depending on feedback, control systems can be:
  • Open-loop control
  • Closed-loop control
• Depending on purpose, control systems include:
  • Position Control System
  • Velocity Control System
  • Process Control System
  • Temperature Control System

Open-Loop Control Systems

• In an open-loop control system, the output is not measured or "fed back" for comparison with the input.
• The system expected to faithfully follow commands regardless of the result.
• Systems operating on a time basis are open-loop systems.
• Examples using a washing machine, traffic control systems and a room heater.
• Clothes dryer example: The timer stops after 30 minutes even if clothes are wet.

Closed-Loop Control Systems

• Feedback control systems maintain a predefined output-input relationship.
• They use the difference between output and input to control the system.
• The closed-loop control utilizes feedback to reduce system error.
• Air Conditioner example: Comparison of temperature is done with the help of the thermostat, thermostats turn on or off the compressor depending on the difference between the set and the room temperatures.

Open-Loop Vs Closed-Loop Systems

• Open-Loop System:
  • Simple and economical
  • Consumes less power
  • Easier to construct
  • Not as reliable or accruate, however, they are more stable
  • External disturbances are not corrected automatically
  • More sensitive to noise
• Closed-Loop System:
  • Complex and costlier
  • Consumes more power
  • More difficult to construct
  • More reliable and accurate, yet potentially unstable
  • External disturbances are corrected automatically
  • Less sensitive to noise

Types Of Control Systems

• Linear Control System, follows the principle of superposition
  • Analytical and graphical design techniques are available.
  • They can be mathematically represented.
• Nonlinear Control System, Occurs when signal magnitude extends beyond the range of operations.
  • Nonlinear systems occur because of saturation, backlash, dead zone.
  • These systems difficult to model mathematically, and there are no general methods for analysis and design.
• Time-Invariant Control System, parameters are stationary over time.
• Time-Variant Control System, parameters vary over time.
  • Time-varying system design is more complex than invariant one.
• Lumped Parameters system, components are concentrated.
  • This involves solving a set of ordinary differential equations.
• Distributed parameters system, (R, L, C) are distributed.
  • Requires solving partial differential equations.
• Analog Control System
  • Variables are a function of a continuous time t.
• Digital Control System
  • Variables are known only at discrete time intervals.

Requirements of a good Control System

• Accuracy
  • A control system must be highly accurate
  • Open loop systems are generally less accurate
• Sensitivity
  • A system must be insensitive to the environment
• External Disturbances and noise
  • A system must be insensitive to the external disturbances and noise but sensitive to the input commands.
• Stability
  • System should be more stable. The output of the system must follow the input.

Feedback

• Refers to returning some of the output to the input for classification as:
• Positive feedback
• Negative Feedback
• Formulas:
  • T is the transfer function or overall gain
  • G is the open loop gain
  • H is the gain of the feedback path

An introductory course on feedback and control systems. Topics include mathematical modeling of electromechanical systems, block diagram reduction, time response analysis, and PID controller design. Stability analysis using Routh Test, root locus, Bode plot, and polar plot are also covered.