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Consider a temperature control loop composed of a voltage-controlled power source (gain coefficient of 2 kW/V), a furnace, a compensator (which acts as a controller), and an electrical thermometer to obtain a measurement of the room temperature. This system can be represented by the following block diagram, with all units shown: Controller Heater R'(s) Volts 8(s + 1.6) 2 kW/V S+ 0.2 Volts kW Furnace 500 (s + 0.1)(s +25) Thermometer T'(s) T'm(s) 0.01 V/°C Volts °C Note that our system's setpoint is in volts rather than °C. a) Determine the closed-loop transfer function for measured temperature setpoint changes, Tm(s) R'(s)' b) Create Bode plots of this system using controller gains of Kc = {1, 10, 100}. c) If the compensator is replaced by a PID-controller, determine the initial controller parameters for this system under PID control using the Ziegler-Nichols initial tuning method. d) Model both the original system and the system under PID control obtained in Part (c) in Simulink. Simulating a step change of 0.01 V in R'(s), obtain time-domain plots for both models showing the actual temperature, T', and the measured temperature, T responses. e) Lastly, we will simulate some unwanted cooling effects to our system. Modify your simulation from part d) to apply a -100 kW step disturbance to the input of the furnace, while R'(s) = 0. Compare each model's ability to reject disturbances.

Consider a temperature control loop composed of a voltage-controlled power source (gain coefficient of 2 kW/V), a furnace, a compensator (which acts as a controller), and an electrical thermometer to obtain a measurement of the room temperature. This system can be represented by the following block diagram, with all units shown: Controller Heater R'(s) Volts 8(s + 1.6) 2 kW/V S+ 0.2 Volts kW Furnace 500 (s + 0.1)(s +25) Thermometer T'(s) T'm(s) 0.01 V/°C Volts °C Note that our system's setpoint is in volts rather than °C. a) Determine the closed-loop transfer function for measured temperature setpoint changes, Tm(s) R'(s)' b) Create Bode plots of this system using controller gains of Kc = {1, 10, 100}. c) If the compensator is replaced by a PID-controller, determine the initial controller parameters for this system under PID control using the Ziegler-Nichols initial tuning method. d) Model both the original system and the system under PID control obtained in Part (c) in Simulink. Simulating a step change of 0.01 V in R'(s), obtain time-domain plots for both models showing the actual temperature, T', and the measured temperature, T responses. e) Lastly, we will simulate some unwanted cooling effects to our system. Modify your simulation from part d) to apply a -100 kW step disturbance to the input of the furnace, while R'(s) = 0. Compare each model's ability to reject disturbances.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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Consider a temperature control loop composed of a voltage-controlled power source (gain coefficient of 2 kW/V), a furnace, a compensator (which acts as a controller), and an electrical thermometer to obtain a measurement of the room temperature. This system can be represented by the following block diagram, with all units shown: Controller Heater R'(s) Volts 8(s + 1.6) 2 kW/V S+ 0.2 Volts kW Furnace 500 (s + 0.1)(s +25) Thermometer T'(s) T'm(s) 0.01 V/°C Volts °C Note that our system's setpoint is in volts rather than °C. a) Determine the closed-loop transfer function for measured temperature setpoint changes, Tm(s) R'(s)' b) Create Bode plots of this system using controller gains of Kc = {1, 10, 100}. c) If the compensator is replaced by a PID-controller, determine the initial controller parameters for this system under PID control using the Ziegler-Nichols initial tuning method. d) Model both the original system and the system under PID control obtained in Part (c) in Simulink. Simulating a step change of 0.01 V in R'(s), obtain time-domain plots for both models showing the actual temperature, T', and the measured temperature, T responses. e) Lastly, we will simulate some unwanted cooling effects to our system. Modify your simulation from part d) to apply a -100 kW step disturbance to the input of the furnace, while R'(s) = 0. Compare each model's ability to reject disturbances.
Transcribed Image Text:Consider a temperature control loop composed of a voltage-controlled power source (gain coefficient of 2 kW/V), a furnace, a compensator (which acts as a controller), and an electrical thermometer to obtain a measurement of the room temperature. This system can be represented by the following block diagram, with all units shown: Controller Heater R'(s) Volts 8(s + 1.6) 2 kW/V S+ 0.2 Volts kW Furnace 500 (s + 0.1)(s +25) Thermometer T'(s) T'm(s) 0.01 V/°C Volts °C Note that our system's setpoint is in volts rather than °C. a) Determine the closed-loop transfer function for measured temperature setpoint changes, Tm(s) R'(s)' b) Create Bode plots of this system using controller gains of Kc = {1, 10, 100}. c) If the compensator is replaced by a PID-controller, determine the initial controller parameters for this system under PID control using the Ziegler-Nichols initial tuning method. d) Model both the original system and the system under PID control obtained in Part (c) in Simulink. Simulating a step change of 0.01 V in R'(s), obtain time-domain plots for both models showing the actual temperature, T', and the measured temperature, T responses. e) Lastly, we will simulate some unwanted cooling effects to our system. Modify your simulation from part d) to apply a -100 kW step disturbance to the input of the furnace, while R'(s) = 0. Compare each model's ability to reject disturbances.
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