Control Systems Fundamentals

Feedback Mechanisms

• Definition: A feedback mechanism is a control system component that monitors the system's output and compares it to the desired output, generating an error signal that drives the system towards the desired state.
• Types of Feedback:
  • Negative Feedback: Reduces the error between the actual and desired output, stabilizing the system.
  • Positive Feedback: Amplifies the error, often leading to instability.
• Feedback Loop Components:
  • Sensor: Measures the system's output.
  • Comparator: Compares the measured output to the desired output.
  • Error Signal: The difference between the measured and desired output.
  • Actuator: Adjusts the system's input based on the error signal.

Controller Tuning

• Definition: Controller tuning involves adjusting the control system's parameters to achieve optimal performance, stability, and response.
• Tuning Methods:
  • Trial and Error: Iterative process of adjusting parameters based on system response.
  • Ziegler-Nichols Method: A heuristic approach for tuning PID controllers.
  • Frequency Response Analysis: Analyzing the system's frequency response to determine optimal gains.
• Controller Tuning Parameters:
  • Gain: Amplifies the error signal.
  • Integral Time: Determines the rate of change of the error signal.
  • Derivative Time: Determines the rate of change of the error signal's derivative.

State-Space Control

• Definition: State-space control is a mathematical approach to control systems, representing the system's dynamics using state variables and linear algebra.
• State-Space Equations:
  • State Equation: Describes the evolution of the system's state variables over time.
  • Output Equation: Relates the system's output to the state variables.
• State-Space Control Systems:
  • Controllability: The ability to drive the system to a desired state using an input signal.
  • Observability: The ability to determine the system's state from the output signal.
• State-Space Control Techniques:
  • Pole Placement: Placing the system's poles to achieve desired stability and response.
  • Linear Quadratic Regulator (LQR): Optimal control technique for minimizing a performance index.