The Ziegler-Nichols tuning method is used to determine PID controller gains (Kp, Ki, Kd) based on the process model's stability point. The method involves: 1) Increasing Kp until the output oscillates at a frequency f0, defining the maximum gain Kmax. 2) Calculating gains using formulas based on Kmax and f0. 3) Applying the gains to a simulated hydraulic valve position control model, reducing steady state error and stabilizing the output. Further tuning can refine the gains.

1. Control Systems Design PID Controller Tuning Method Parul Goyal

2. PID Tuning ( The Ziegler-Nichols Method ) A Popular Method of Tuning PID Controller Setting for P,I,D Gains According to Ziegler-Nichols Method Where: Kmax= the value of Kp at the point of instability (zeroing the integral and differential gains and raising the proportional gain until the system is unstable): f0= frequency of oscillation 0.125/f0 2.0*f0 0.6*Kmax PID Controller 0 1.2*f0 0.45*Kmax PI Controller 0 0 0.5*Kmax P Controller Kd Ki Kp Controller Type

3. PID Tuning ( The Ziegler-Nichols Method ) Application A Simple Model is Developed in Simulink to Demonstrate the PID Tuning by Ziegler-Nichols Method Position Control of a Hydraulic Proportional Control Valve

4. PID Tuning ( The Ziegler-Nichols Method ) Application Input to the Model : Desired Position of the Valve Output of the Model : Controlled Position of the Valve

5. PID Tuning ( The Ziegler-Nichols Method ) Application Setting PID Gains: Kp=increase until output becomes unstable Ki=0, Kd=0 At Kp=21.5*1.1, Position Output is still Stable

6. PID Tuning ( The Ziegler-Nichols Method ) Application Setting PID Gains: Kp=increase until output becomes unstable Ki=0, Kd=0 At Kp=21.5*1.3, Position Output has become Unstable

7. PID Tuning ( The Ziegler-Nichols Method ) Application Calculation of Kmax & f0: Kmax = 21.5*1.3 f0 = frequency of oscillations = 33.33 hz PID Controller Parameters: Kp=0.6*Kmax = 0.6*(21.5*1.3) Ki=2.0*f0 = 2.0*33.33 Kd=0.125/f0 = 0.125/33.33 At Kp=21.5*1.3, Position Output has become Unstable

8. PID Tuning ( The Ziegler-Nichols Method ) Application Setting PID Gains: Kp = 21.5*1.3*0.6 Kd = 66.6 Ki = 0.00375

9. PID Tuning ( The Ziegler-Nichols Method ) Application Model Output Study: Reduced Steady State Error Stable Output More fine-tuning of PID Gains can be Done by Trial and Error