PID Controller

A PID is a method that comes from control engineering, the controller continuously determines the deviation between the current value of a process to be controlled and a specified setpoint. On the basis of this deviation three components are calculated and added up, the proportional part to the deviation $K_{p}$, the part to the change in relation to the past $K_{I}$ and the part to fast change $K_{D}$. Through the interaction of these components, an actuating value is calculated, which in turn acts on the process to reduce the deviation. The simple-pid library is used in this project to simplify the implementation of the PID controller to regulate the boost converter output voltage to the specified setpoint.

In Listing a simple control loop is implemented, this controls the output voltage of the boost converter constantly to $25V$. The controller is additionally limited at its output to the minimum and maximum duty cycle $0\%$ to $70\%$ of the boost converter.

Listing simple pid loop

device.pid.tunings = (1.82, 60.45, 0)
device.pid.output_limits = (0, 70)
device.pid.setpoint = 25.

while(True):
    device.getfilteredADC()
    device.calcADCData()
    duty = device.pid(device.voltage[1])
    device.setDutyCycle(duty)

The Ziegler-Nichols method of stability limit is a common method of adjusting PID controllers based on determining the critical gain and period at which the system is just at the limit of stability. In this process, the gain $K_{P}$ is gradually increased until the system begins to oscillate. The period of these oscillations is measured with an oscilloscope, which determines the time constant of the boost controller, here a critical gain of $K_{u}=4.03$ and a time constant of $T_{u}=36ms$ is obtained.

In this project, a PI controller is initially chosen because the control deviation should be kept to a minimum and overshoot is undesirable. The parameters $K_{p}=1.82$ and $K_{i}=60.45$ for the PI controller are calculated according to pid parameter table. For further optimization, an ordinary PID controller and a controller without overshoot are also listed here.

Table PID parameters

Type	$K_{p}$	$K_{i}$	$K_{d}$
PI	$0.45K_{u}$	$0.54 K_{u} / T_{u}$	-
classic PID	$0.60K_{u}$	$1.20K_{u} / T_{u}$	$0.075K_{u} T_{u}$
no overshoot	$0.20K_{u}$	$0.40K_{u} / T_{u}$	$0.066K_{u} T_{u}$