05 tuning.pid.controllers
- 1. Tuning PID Controllers Eng. Mahmoud Hussein RTECS 2010 1 RTECS 2010 1 Gc(s) Controller + + n sensor noise + w load disturbance + Gp(s) Plant u control y output + - r reference input, or set-point e sensed error
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- 3. Analytical Vs. Empirical Techniques • Analytical Tuning Techniques ▫ Frequency response analysis • Empirical Tuning Techniques ▫ On-line tuning after the control system is installed ▫ Computer simulation RTECS 2010 3
- 4. Empirical Tuning Techniques • Two Steps: ▫ Determination of the dynamic characteristics of the control loop ▫ Estimation of the controller tuning parameters that produce a desired response • Tuning Techniques ▫ Ziegler-Nichols Oscillation Method ▫ Ziegler-Nichols Reaction Curve Method ▫ Cohen-Coon Reaction Curve Method RTECS 2010 4
- 5. Z-N Closed Loop Method Z-N Continuous Cycling Method By Ziegler and Nichols (1942) RTECS 2010 5
- 6. Quarter Decay Ratio Response By Ultimate Gain • Use the proportional controller to force sustained oscillations. • Goal is to determine ultimate gain and ultimate period of oscillation of the control loop RTECS 2010 6
- 7. Quarter Decay Ratio Response By Ultimate Gain • Ziegler-Nichols method specifies a decay ratio of one-fourth (1/4) • Decay ratio = ratio of the amplitudes of two successive oscillations RTECS 2010 7
- 8. Tuning Procedure • Set the true plant under proportional control, with a very small gain • Increase the gain until the loop starts oscillating ▫ Note that linear oscillation is required and that it should be detected at the controller output. • Record the controller critical gain (ultimate gain) Kp = Kc (Ku) and the oscillation period of the controller output, Pc (Pu). RTECS 2010 8
- 9. Tuning Procedure • Calculate the parameters according to the following formulas RTECS 2010 9 Controlle r Type Proportional Gain (Kp) Integral Time (tI) Derivative Time (tD) P-only Ku/2 - - PI Ku/2.2 Pu/1.2 - PID Ku/1.7 Pu/2 Pu/8
- 10. Example • Consider the given plant ▫ Find the parameters of a PID controller using the Z-N oscillation method. ▫ Obtain a graph of the response to a unit step input reference. RTECS 2010 10 3 1 1 )( + s sGp
- 11. Example Solution • Applying the procedure we find ▫ Kc = 8 and ωc = 3 • Hence, from Table we have ▫ Kp = 4.8 ▫ Tr = 1.81 ▫ Td = 0.45 • Try the same procedure for the second order system RTECS 2010 11 2 1 1 )( + s sGp
- 12. Drawbacks • Time-consuming ▫ If the process dynamics are slow • The process is pushed to the stability limits ▫ Risk of plant damage • For first-order and second-order model without time delays the ultimate gain does not exist ▫ Because the closed-loop system is stable for all values of Kp. However, in practice, it is unusual for a control loop not to have an ultimate gain. RTECS 2010 12
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- 14. Tuning Procedure • Same procedure as Z-N closed loop method • TLC tuning values tend to reduce oscillatory effects and improves robustness. RTECS 2010 14
- 15. Z-N Open-loop Method RTECS 2010 15
- 16. Process Reaction Curve • From the open loop step response, the system dynamics can be determined • The controller settings are based on the open- loop step response, or in other words, the process reaction curve RTECS 2010 16
- 17. Tuning Procedure • With the plant in open loop, take the plant manually to a normal operating point ▫ Say that the plant output settles at y(t) = y0 for a constant plant input u(t) = u0. • At an initial time, t0, apply a step change to the plant input, from u0 to u ▫ This should be in the range of 10 to 20% of full scale • Record the plant output until it settles to the new operating point. Assume you obtain the curve shown on the next slide. RTECS 2010 17
- 18. Tuning Procedure RTECS 2010 18 • Compute the parameter model as follows m.s.t. stands for maximum slope tangent
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- 20. Tuning Procedure • Cohen and Coon carried out further studies to find controller settings which, based on the same model, lead to a weaker dependence on the ratio of delay to time constant. Their suggested controller settings are shown below RTECS 2010 20
- 21. Simulink Control Design 3.0 RTECS 2010 21
- 22. PID Controller Block ▫ PID_Controller_Automated_Tuning.mdl RTECS 2010 22
- 23. Initial PID Design RTECS 2010 23
- 24. Adjusting Response Time To Tune Parameters RTECS 2010 24