A Proportional Integral Derivative (PID) controller is a generic feedback control loop mechanism widely used in industrial control systems. A PID controller is the most commonly used type of feedback controller.
This set of functions implements (PID) controllers for Q15, Q31, and floatingpoint data types. The functions operate on a single sample of data and each call to the function returns a single processed value. S
points to an instance of the PID control data structure. in
is the input sample value. The functions return the output value.
 Algorithm:
y[n] = y[n1] + A0 * x[n] + A1 * x[n1] + A2 * x[n2]
A0 = Kp + Ki + Kd
A1 = (Kp )  (2 * Kd )
A2 = Kd
 where
Kp
is proportional constant, Ki
is Integral constant and Kd
is Derivative constant
Proportional Integral Derivative Controller
 The PID controller calculates an "error" value as the difference between the measured output and the reference input. The controller attempts to minimize the error by adjusting the process control inputs. The proportional value determines the reaction to the current error, the integral value determines the reaction based on the sum of recent errors, and the derivative value determines the reaction based on the rate at which the error has been changing.
 Instance Structure
 The Gains A0, A1, A2 and state variables for a PID controller are stored together in an instance data structure. A separate instance structure must be defined for each PID Controller. There are separate instance structure declarations for each of the 3 supported data types.
 Reset Functions
 There is also an associated reset function for each data type which clears the state array.
 Initialization Functions
 There is also an associated initialization function for each data type. The initialization function performs the following operations:
 Initializes the Gains A0, A1, A2 from Kp,Ki, Kd gains.
 Zeros out the values in the state buffer.
 Instance structure cannot be placed into a const data section and it is recommended to use the initialization function.
 FixedPoint Behavior
 Care must be taken when using the fixedpoint versions of the PID Controller functions. In particular, the overflow and saturation behavior of the accumulator used in each function must be considered. Refer to the function specific documentation below for usage guidelines.
◆ arm_pid_f32()
Process function for the floatingpoint PID Control.
 Parameters

[in,out]  *S  is an instance of the floatingpoint PID Control structure 
[in]  in  input sample to process 
 Returns
 out processed output sample.
Definition at line 5088 of file arm_math.h.
◆ arm_pid_q15()
Process function for the Q15 PID Control.
 Parameters

[in,out]  *S  points to an instance of the Q15 PID Control structure 
[in]  in  input sample to process 
 Returns
 out processed output sample.
Scaling and Overflow Behavior:
 The function is implemented using a 64bit internal accumulator. Both Gains and state variables are represented in 1.15 format and multiplications yield a 2.30 result. The 2.30 intermediate results are accumulated in a 64bit accumulator in 34.30 format. There is no risk of internal overflow with this approach and the full precision of intermediate multiplications is preserved. After all additions have been performed, the accumulator is truncated to 34.15 format by discarding low 15 bits. Lastly, the accumulator is saturated to yield a result in 1.15 format.
Definition at line 5171 of file arm_math.h.
◆ arm_pid_q31()
Process function for the Q31 PID Control.
 Parameters

[in,out]  *S  points to an instance of the Q31 PID Control structure 
[in]  in  input sample to process 
 Returns
 out processed output sample.
Scaling and Overflow Behavior:
 The function is implemented using an internal 64bit accumulator. The accumulator has a 2.62 format and maintains full precision of the intermediate multiplication results but provides only a single guard bit. Thus, if the accumulator result overflows it wraps around rather than clip. In order to avoid overflows completely the input signal must be scaled down by 2 bits as there are four additions. After all multiplyaccumulates are performed, the 2.62 accumulator is truncated to 1.32 format and then saturated to 1.31 format.
Definition at line 5123 of file arm_math.h.