Closed Loop Control

🚗 Control Systems Lectures - Closed Loop Control

🎯 Introduction

This lecture covers open-loop vs closed-loop control systems.

A control system is a mechanism that alters the future behavior or state of a system. For it to be considered a control system (not just a mechanism that changes a state), the output must tend toward a desired state.

Control theory is the mathematical strategy used to select appropriate inputs to achieve desired outputs. Without it, engineers would rely solely on trial and error.

⚙️ Components of a Control System

Every control system consists of two basic parts:

• The Plant: the system to be controlled
• The Input: acts on the plant and generates the system output

🔓 Open-Loop Control

In open-loop systems, the input does not depend on the output. These are used for simple, predictable processes.

✅ Examples:

• Dishwasher: Runs for a preset time regardless of how clean the dishes actually are.
• Sprinkler System: Waters the lawn based on a timer, not soil moisture level.
• Car Without Cruise Control: Pedal is fixed, so speed varies with hills or valleys.

Main Drawback: Open-loop systems cannot adjust for disturbances or changes in the system.

🔁 Closed-Loop (Feedback) Control

In closed-loop systems, the output is measured and fed back to adjust the input.

Also known as:

• Feedback Control
• Negative Feedback
• Automatic Control

🧠 How It Works:

1. Measure output using a sensor.
2. Compare output to the reference (desired) value.
3. Generate an error term.
4. Feed error into the controller.
5. Controller adjusts the input to reduce the error.

This creates a feedback loop where the system continually tries to drive the error to zero.

✅ Examples:

• Dishwasher with Cleanliness Sensor: Stops when dishes are actually clean.
• Sprinkler with Moisture Sensor: Runs only until soil moisture reaches a set level.
• Car with Cruise Control:
  • Sensor = speedometer
  • Reference = desired speed (e.g., 100 mph)
  • If car slows on a hill, controller increases gas.
  • If car speeds up downhill, controller decreases gas.

📐 Block Diagram Abstraction

Let’s define abstract labels in a block diagram:

• V : Reference Signal
• D : Controller
• G : Plant
• Y : Output
• H : Sensor
• E : Error Term

From the diagram, we get the equation:

E = V - H * Y
Y = E * D * G

Solve these to find Y in terms of V:

Y = (D * G / (1 + D * G * H)) * V

This is the transfer function of the closed-loop system.

🎯 Insight: The feedback path alters the behavior of the original plant. The resulting system behaves like an open-loop system with a modified plant that now tracks the input better.

❓ Final Thought

Can any plant G be made to behave however we want just by adding a controller D and sensor H?

For instance, in the car example:

• Can we turn a Pinto into a Ferrari just by applying more gas and using feedback?

We’ll discuss that in the next lecture!