a) Response Sketch:
Here’s the response sketch of a basic heater control showing temperature against time:
Key Points:
– Horizontal line: Desired temperature (setpoint).
– Sawtooth waveform: Actual temperature fluctuates around the setpoint.
– Peaks: Heater turns on, increasing temperature rapidly.
– Valleys: Heater turns off, temperature drops until the setpoint is reached and the cycle repeats.
– Hysteresis: Dead zone around the setpoint where the heater remains off (below) or on (above).
(b) Improving Accuracy/Speed of Response:
- Proportional Band Reduction: Decrease the hysteresis band to reduce the temperature swing and improve accuracy. However, too small a band can lead to frequent switching and increased wear on the heater.
- Rate Limiting: Limit the rate of temperature change by delaying heater activation or deactivation based on the rate of previous changes. This prevents large overshoots and improves stability.
- Pulse Width Modulation (PWM): Instead of full on/off cycles, rapidly switch the heater on and off at a high frequency. By varying the “on” time per cycle (duty cycle), the average power delivered can be controlled, providing more precise temperature control compared to simple on/off cycles.
- Feedback Controller: Introduce a simple feedback loop with a sensor measuring the actual temperature. The controller compares it to the setpoint and adjusts the heater state (on/off) based on the difference, aiming for a more continuous and accurate response.
Remember, each method has its advantages and limitations. Choosing the best approach depends on specific requirements for accuracy, speed, complexity, and cost.