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PID Controller Tuning 1.Introduction 2.Model-based PID tuning methods 3.Two degree of freedom controllers 4.On-line PID controller tuning 5.PID tuning guidelines and troubleshooting 6.Simulink example

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Introduction l PID control law l Transfer function l Controller tuning »Need to select PID parameters (K c, I, D ) that yield good closed-loop response to disturbances and setpoint changes »Only know: KK c > 0, I > 0, D >0 »Trial-and-error tuning difficult and time consuming »Need methods to determine good initial parameter values »Refine parameter values by trial-and error fine tuning

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Impact of Controller Tuning

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Closed-Loop Performance Criteria 1.Stability of closed-loop system 2.Minimization of disturbance effects 3.Rapid, smooth tracking of setpoint changes 4.Elimination of steady-state offset 5.Avoidance of excessive control action 6.Robustness to changes in process conditions 7.Robustness to errors in process model

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Model-Based PID Controller Tuning l Often based on first-order- plus-time-delay model l Integral error criteria

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ITAE Tuning Rules

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General Trends l The controller gain (K c ) is inversely proportional to the process gain (K). K c decreases as the ratio of the time delay and the dominant process time ( ) constant increases. Both the integral time ( I ) and the derivative time ( D ) increase as / increases. A reasonable initial guess for the derivative mode is D = 0.25 I. l K c decreases as integral control is added to a proportional controller. K c increases as derivative control is added to a PI controller.

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ITAE Controller Tuning Example l Process model l ITAE tuning for disturbance (more aggressive) l ITAE tuning for setpoint (less aggressive)

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Two Degree of Freedom Controllers l Seek to tune the setpoint tracking response independent of the disturbance rejection response l Setpoint filtering »Controller operates on Y * sp instead of Y sp »Tuning parameter f determines speed of response l Setpoint weighting »Tuning parameter determines speed of response

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On-Line PID Controller Tuning l Often a process model is not available for controller tuning l Need to determine tuning parameters directly from plant data l Continuous cycling method »Utilizing a proportional controller, find the K c value that produces sustained oscillations. This is the ultimate gain K cu. »Determine the period of the sustained oscillations. This is the ultimate period P u. »K c and P u can also be found from an available transfer function model by direct substitution.

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Tuning Rules Based on Ultimate Gain

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Shortcomings of Continuous Cycling Method l Time consuming for processes with large time constants l Process pushed to stability limit l Ultimate gain does not exist for first- and second-order systems without time delays l Generally not applicable to integrating and open-loop unstable systems because stability is achieved only for intermediate K c values l First two shortcomings can be overcome using relay autotuning method to determine K c and P u (see text)

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Step Test Method l Model structure

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Step Test Method cont. l Model structure Calculation of and »Determine times when output has reached 35.3% (t 35 ) and 85.3% (t 85 ) »Calculate and l Then use tuning method for FOTPD models

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Shortcomings of Step Test Method l Experimental test performed under open-loop conditions l Method is not applicable to open- loop unstable processes l Step response can be sensitive to the direction and magnitude of the step change if the process is nonlinear

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Guidelines for Common Control Loops l Flow rate control – aggressively tuned PI controller due to fast dynamics and few disturbances l Liquid level control – conservatively tuned P or PI controller depending on whether offset- free performance is required l Gas pressure control – moderately tuned PI controller with little integral action due to small time constants and stability concerns l Temperature control – PID controllers with application dependent tuning l Composition control – PID or more advanced controller due to sampling delay and measurement noise

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Troubleshooting Control Loops l Surveys indicate that as many as 35% of industrial controllers are placed in manual at any given time l Determine if control problem is attributable to: »Transducer – degradation or complete failure »Controller – poor tuning or inadequate design »Final control element – control valve stiction »Process – change in operating condition l Troubleshooting procedure »Collect data on control system performance »Determine if operating conditions have changed »Check individual control system components »Retune or redesign the controller

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Simulink Example: continuous_cycling.mdl

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Determining the Ultimate Gain

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PID Controller Tuning l K c = 7.88, P u = l Ziegler-Nichols tuning rules

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