Basic Concepts of Control Systems

Basic Concepts of Control Systems

• Control Engineering is concerned with techniques to solve six problems: identification, representation, solution, stability, design, and optimization.
• Conventional Approach: Electrical oriented, based on complex function theory.
• Modern Approach: Mechanical oriented, based on state variable theory.
• Control engineering is applicable to various engineering disciplines such as aeronautical, chemical, mechanical, environmental, civil and electrical engineering.

Basic Terminologies in Control Systems

• System: A combined unit of physical components designed to achieve a specific task.
• Control: The action of directing or managing a system.
• Plant or Process: The component of a system that needs to be controlled.
• Input: Signal or excitation applied to a control system.
• Output: Actual response of a control system.
• Controller: Component that regulates the plant.
• Disturbances: Signals that negatively affect the performance of a control system.
• Control System: A system that manages itself or another system to reach a specific goal.
• Automation: Automatic control of a process.
• Actuator: Device that provides motive power for the output of a system.
• Design: Planning the form, parts, and details of a system to meet a desired purpose.
• Simulation: A model used to analyze a system's behavior using real input signals.
• Optimization: Adjusting system parameters for the most favorable design outcome.
• Feedback Signal: A measure of the system's output, used for feedback control.
• Negative Feedback: Output signal is subtracted from the input signal for feedback control.
• Block Diagrams: Unidirectional blocks representing transfer functions of system elements.
• Signal Flow Graph (SFG): A diagram with nodes and directed branches that graphically represent a set of linear relations.
• Specifications: Detailed statements about the intended function and performance of a system.
• Open-loop Control System: A system that controls the process without using feedback. The output does not influence the input to the process.
• Closed-loop Feedback Control System: Measures the output and compares it to the desired output, utilizing feedback in controlling the process.
• Regulator: A control system that mainly focuses on rejecting disturbances while aiming to maintain a fixed value for the controlled outputs.
• Servo System: A control system where the controlled outputs are mechanical quantities like position, velocity, or acceleration.
• Stability: Describes whether the system remains under control or increases without bound.
• Multivariable Control System: A system with more than one input or output variable.
• Trade-off: A compromise between conflicting criteria in design considerations.

Classification of Control Systems

Natural and Man-made Control Systems

• Natural Control System: A system created by nature (e.g., solar system, digestive systems).
• Man-made Control System: A system created by humans (e.g., automobiles, power plants).

Automatic and Combinational Control Systems

• Automatic Control System: Uses mathematical and engineering principles, commonly incorporating sensors, actuators, and responders.
• Combinational Control System: Blends natural and man-made elements (e.g., driving a car).

Time-variant and Time-invariant Control Systems

• Time-variant Control System: At least one parameter changes over time (e.g., driving a vehicle).
• Time-invariant Control System: No parameters change over time (e.g., a system with only inductors, capacitors, and resistors).

Linear and Non-linear Control Systems

• Linear Control System: Satisfies homogeneity and additive properties (e.g., f(x+y) = f(x) + f(y) and f(?x) = ?f(x)).
• Non-linear Control System: Does not satisfy homogeneity and additive properties (e.g., f(x) = x^3 ).

Continuous-Time and Discrete-Time Control Systems

• Continuous-Time Control System: All parameters are functions of continuous time (e.g., armature type speed control of a motor).
• Discrete-Time Control System: All parameters are functions of discrete time (e.g., microprocessor type speed control of a motor).

Deterministic and Stochastic Control Systems

• Deterministic Control System: Predictable, repetitive output for a specific input or disturbance.
• Stochastic Control System: Unpredictable, non-repetitive output for a given input or disturbance.

Lumped-parameter and Distributed-parameter Control Systems

• Lumped-parameter Control System: Mathematical model represented by ordinary differential equations.
• Distributed-parameter Control System: Mathematical model represented by an electrical network (combination of resistors, inductors, and capacitors).

Single-input-single-output (SISO) and Multi-input-multi-output (MIMO) Control Systems

• SISO Control System: One input and one output.
• MIMO Control System: More than one input and one output.

Open-loop and Closed-loop Control Systems

Open-loop Control System

• Control action depends only on the input signal, independent of the output response.
• Advantages: Simple design, easy construction, economical, easy maintenance, highly stable operation.
• Disadvantages: Not accurate or reliable when input or system parameters change, requires recalibration.

Closed-loop Control System

• Control action depends on both input signal and output response.
• Advantages: More accurate operation, efficient under changing parameters, less nonlinearity effect on output, high bandwidth, automation capability, no need for frequent recalibration.
• Disadvantages: Complex design, difficult construction, expensive, complex maintenance, less stable operation.

Servo-mechanisms

• A feedback unit in a control system where the control variable is a mechanical signal (position, velocity, or acceleration).
• Output signal directly fed to the comparator as feedback in closed-loop systems.
• Used in systems with both command and output signals that are mechanical in nature.
• Examples: Missile launchers, machine tool position control, power steering, roll stabilization in ships.

Mathematical Modeling and Representation of Physical Systems

• An idealized physical system is called a physical model.
• The process of creating a block diagram to analyze performance and determine transfer functions is called mathematical modeling.
• Mechanical Systems:
  • Translational or Linear Systems: Motion along a straight line.
    • Inertia Force: F(t) = Ma(t)
    • Damping Force: FD(t) = Bv(t)
    • Spring Force: FK(t)=Kx(t)
  • Rotational Systems: Motion around a fixed axis.
    • Inertia Torque: T1(t) = J?(t)
    • Damping Torque: TD(t) = B?(t)
    • Spring Torque: T?(t) = K?(t)
• Electrical Systems:
  • Analogous system components:
    • Force <=> Voltage
    • Mass <=> Inductance
    • Stiffness <=> Reciprocal of Capacitance
    • Damping Coefficient <=> Resistance
    • Displacement <=> Charge

Effect of Feedback on Sensitivity

• The transfer function with feedback is T(s) = C(s) / R(s) = G / 1 + GH, where:
  • T(s) is the transfer function
  • C(s) is the output
  • R(s) is the input
  • G is the open-loop gain
  • H is the feedback gain
• Sensitivity is defined as the percentage change in the transfer function to the percentage change in gain: S = %change in T(s) / %change in G(s)
  • This can be expressed as: SGT = dT/dG * G/T
• When H increases, (1 + GH) increases, leading to a decrease in sensitivity.
• When H decreases, (1 + GH) decreases, leading to an increase in sensitivity.
• Sensitivity and feedback gain are reciprocally related.

Effect of Feedback on Noise

• Feedback reduces the impact of noise and affects physical activity.
• Feedback influences performance parameters like bandwidth, impedance, transient response, and frequency response.
• The transfer function for noise disturbance is C(s)/Td(s)=1/(G(s).H(s)) = C(s)=Td(s)/G(s).H(s) where:
  • C(s) is the output
  • Td(s) is the external noise or disturbance
  • G(s) is the open-loop gain
  • H(s) is the feedback gain
• To decrease noise influence on output, increase G(s).H(s) by increasing either G(s) or H(s).

Advantages of Feedback in Control Systems

• Reduces unwanted external distractions and noise.
• Improves system performance through mitigation.
• Minimizes system error.
• Allows manipulation of the transient behavior.
• Provides a reference point for comparison.

Disadvantages of Feedback in Control Systems

• Increases system complexity.
• Reduces the overall gain of the system, requiring adjustments.
• Requires additional components for implementation.
• May lead to instability, potential oscillation, or deviation from desired output.
• Introduces a reliance on error parameters.
• Changes in output influence the system's input.

Applications of Feedback in Control Systems

• Manufacturing and production processes
• Building and home automation
• Transportation systems
• Power generation and distribution
• Medical equipment
• Agricultural and farming processes
• Military and defense systems
• Robotics