II. Control System
The system consists of two types of sensors: contact temperature sensors (FISO Fiber Optic Temperature Probes), and non-contact temperature sensors (Melexis MLX90614 IR Temperature Sensor and FLIR IR Thermal Camera). A National Instruments (NI) myRIO controller and NI LabVIEW software were used to develop a closed-loop feedback temperature controller. The controller will acquire temperature data from the FISO Temperature Probes and automatically tune analog input voltage to control power output on the EASYHEAT Power Supply, based on the target temperature. The NI myRIO controls the power output by varying its analog output voltage between a 0-10 V range. A proportional-integral-derivative (PID) controller was employed in the system. The PID controller functions in the feedback loop by reading the current temperature of the coupon surface from the FLIR probes and comparing it to the target temperature to determine the error, e(t). The size of the error will determine the analog output voltage based on the proportional (Kp), integral (Ki), and derivative (Kd) values. Eventually, the system should reach a steady-state error of zero, where the object temperature remains constant at the target temperature. 

III. Graphical User Interface
A system graphical user interface (GUI) was also designed on LabVIEW to aid the user with operating the system. The GUI was designed with the medical practitioners in mind who will be carrying out the in vitro tests. This requires that the GUI be simple, easy to operate, and intuitive. From the front panel, the user will be able to preset the target and safety threshold temperature, start and stop the heating, view real-time temperature measurements of the coupon surface temperatures, the controller output voltage, as well as the thermal images from the FLIR IR camera. The STOP indicator, Error indicator, and Time Out indicators will light up when any of the functions are triggered. 

IV. Cart Design
The work cart was CAD designed on SOLIDWORKS® with various design criteria. The cart should be able to function as a workspace to perform the induction heating operations while being able to safely store all equipment inside the cart when needed. First, having an additional worktable would give us extra room for equipment. This would ensure that we have the space needed during testing, for things such as cables and our laptops and notepads for recording data. In addition to the worktable, additional holes in the HDPE top shelf would make running the cables and wires easier and more organized. Perforated panels at the sides of the cart also allow for hanging tools and cable management.  

The petri dish holder was designed with additional holes where the coupon samples would be positioned inside the dish, as well as adding a black body plate. The black body plate was designed to act as a black body above the IR sensors. Black bodies are perfect emitters and absorbers of IR radiation so this would help the sensors to only pick up the heat of the metal coupons. The height-adjustable IR sensor stand was designed to position the IR sensors just under the metal coupons for non-contact temperature measurement. With the solenoid shape of our coil, the magnetic field would be strongest from the open sides. We found that the best position for the IR sensors to view the coupons would be from underneath the coil rather than from the side, to help avoid any interference from the magnetic field. 

All three coupon materials and positions reached the target temperature of 80 °C within 4.5 s with Ti64 outperforming all other materials, target temperature within 2.5 s. These idealized simulations show that the flat solenoid coil can heat coupons across all materials tested to temperatures of about 160-260 °C within the 10 s rise time. 

II. Controller Tuning
We explored two methods for PID controller tuning: an analytical calculations method, and a computer simulations method. To determine how the plant behaves, the heating and cooling response is estimated to a first-order model. For this study, we opted to use a first order plus dead time model (FOPDT),

which should provide a reasonable response. K is the steady-state gain and 𝜏 is the thermal time constant of the plant. The dead-time variable, 𝜃, is used to account for the duration at the start of the test when the system is not running. To obtain the compensated closed-loop transfer function, a desired (FOPDT) controlled model is determined based on the design specifications. In standard form, the controlled model, Gc, 

is used to provide integral control action to the system response. The steady-state gain is chosen as K = 1 for the ideal response, while the 1/𝜏c term provides integral control action. Adding the integral control helps eliminate offset which allows the system to reach the steady-state error, e(t) = 0. The design parameter, 𝜏c, provides a convenient controller tuning parameter.

The design specifications for the controller are as follows: 

Ultimately, the analytical calculation method provides a simple approach to tuning the controller to achieve a reasonable response from the system. The design parameters of the FOPDT model can be easily determined by analyzing the heating response of the system. We also explored an alternative tuning method using computer simulations. With the help of computer simulations, we can estimate a second order plus dead time (SOPDT) model, 

which should provide a more accurate estimation of the system response. A standard PID model, 

can also be used with the SOPDT and theoretically provide better control of the system based on the design criteria. 

The computer simulations programmatically calculate an optimized response of the system. The PID model and SOPDT model are first combined to first obtain a closed-loop transfer function. Next, a range of PID gain parameters are preset and each combination of values is tested. Based on the %O.S. range and desired peak time, optimal PID gain parameter combinations that meet all the design criteria will then be output for the user to evaluate. The computer simulations approach provides a quick and easy approach to determining the gain parameters. 

III. Temperature-controlled Heating Tests
Before running a temperature-controlled heating operation, a pulse response test is carried out on the system to determine the heating and cooling response of the system for process identification of the pulse response with the FOPDT and SOPDT models.

From this data, we can extract the model parameters of the plant transfer function. For the FOPDT model, the peak represents the steady-state gain, 𝐾, and the thermal time constant, 𝜏, can be calculated with the following equation, 

where t63.2 and t0 are the time values at temperatures T0 and T63.2. T63.2 can be determined by,

with T63.2 representing the temperature at 63.2% of the total change in temperature, from T0 to Tp. With the estimation of a FOPDT model of the system response, initial PID gain parameters (Kp, Ki, Kd) were calculated. The PID controller was further tuned through trial and error. 

The two coupons reached the target temperature of 80 °C within 17 s, with ~10 % overshoot in temperature, but the system then settled at the 80 ± 5 °C target temperature for the duration of the 60 s treatment time. The controller varied its analog output voltage by measuring the error of the coupon temperatures in the feedback loop. As multiple coupons are being heated simultaneously, an average of the coupon surface temperatures was fed as input into the controller. 

The responses from the initial tests could be improved, however, so a PID controller was implemented next. From the PID temperature responses, we noticed a lower %O.S., which reduced from 14.65 % to 9.31 %. Additionally, at the time points circled in blue for both the PI and PID Controller Output plots, the derivative control eliminated a spike in the response which could otherwise have caused a disturbance. However, the peak time of the PID-controlled heating increased from 13 s to 14.5 s which could have helped in reducing the %O.S.. 

Additional safety features were added to the LabVIEW code as a safety precaution, but also to help the system achieve the design criteria. A maximum and minimum threshold can be preset by the user, with the controller verifying the coupon temperature in real-time with the set values. This will help limit the overshoot and decay of the system, allowing the temperatures to operate within a range.