A temperature-controlled HT (high-temperature) circulating system is a good example of a control system that can be enhanced by the inclusion of cascade control. The system involves two controllers in cascade, each equipped with its own temperature sensor.

• The first controller (outer loop) regulates the temperature of the water outlet and utilizes a PI (proportional-integral) controller.
• The control valve is located far from the outlet, where it accurately measures the temperature.
• The error term of this first PI controller is the difference between the desired HT temperature and the measured temperature at the outlet.

Instead of directly controlling the valve, the first PI controller sets the input for the second P (proportional) controller.

• The second controller (inner loop) compares the inlet temperature of the system with the output from the first controller.
• The second controller sends a signal to the control valve based on this comparison.
• The proportional and integral terms of the two controllers are designed to be different. The outer PI controller has a longer time constant, considering the entire system's thermal mass, while the inner loop responds more quickly.

This cascade control configuration allows each controller to be tuned to match the specific characteristics of the part of the system it controls, optimizing the overall system response. The outer loop addresses slower changes in the system, while the inner loop provides rapid adjustments, resulting in a more robust and efficient temperature control system.