Controller Design, Tuning

Must be stable. Provide good disturbance rejection---minimizing the effects of disturbance. Have good set-point tracking---Rapid, smooth responses to set-point changes Eliminate steady state error (zero offset) Avoid excessive control action. Must be robust( or insensitive) to process changes or model inaccuracies. Performance Criteria for Closed-loop systems

Methods for PID controller settings Classical methods: By reaction curve for a quarter decay ratio. By on-line cycling experiment for quarter decay ratio. By tuning rules using reaction curve and integral performance criteria.

Reaction Curve + - L R + + y Manual input Reaction curve

Classical methods

Relay Feedback

Modified Z-N settings for PID control controllerKcKc II DD Original Some overshoot No overshoot 0.6 K CU 0.33 K CU 0.2 K CU P U /2 P U /3 P U /8 P U /3 P U /2 controllerKcKc II DD P PI PID 0.5 K CU 0.45 K CU 0.6 K CU - P U /1.2 P U /2 - P U /8 Original Z-N settings for PID control

Controller type PI PID Tyler-Luyben’s Tuning Rule

Controller type PI PID Tyler-Luyben vs Z-N Tuning

Model characterization by reaction curve FOPDT (First Order Plus Dead Time) model –Fit 1

FOPDT (First Order Plus Dead Time) model –Fit 2 Model characterization by reaction curve

–FOPDT (First Order Plus Dead Time) model Fit 3

Model-based tuning rules for QDR

PID PI P Controller

controllerKcKc II DD P PI PID 0.5 K CU 0.45 K CU 0.6 K CU - P U /1.2 P U /2 - P U /8 controllerKcKc II DD PI PID 0.31 K CU 0.45 K CU 2.2P U - P U /6.3 Tyreus-Luyben’s Tuning (1997) Original Z-N Tuning (1942)

Controller type PI PID Tyreus-Luyben vs Z-N Tuning

G(s) Hagglund & Astrom’s PI Tuning Rules

Integral performance indices ISE : IAE: ITSE: ITAE:

Tuning rules for optimal integral performance measures Optimal tuning parameters are obtained via simulating a basic loop: The results apply specifically to set-point change or to disturbance change. G L =G P

Tuning rules for optimal integral performance measures The controller used is considered as of parallel and ideal form; Parameters are Dimensionless groups, such as : K c K p,  R / ,  D / 

Tuning rules for optimal integral performance measures The resulted tuning parameters are fitted into the following forms: The values of a and b are tabularized.

Model based tuning rules for optimal integral performance measures ---II Optimal tuning parameters are obtained via simulating a basic loop: The results apply specifically to set-point change or to disturbance change. G L =G P

Model based tuning rules for optimal integral performance measures ---III The resulted tuning parameters are fitted into the following forms: The values of a and b are tabularized.

Remarks on tuning rules with integral performance indices: Remember that conversions between a series PID controller and the parallel PID controller is necessary in order to use the tuning rules. The tuning parameters for disturbance change will be too aggressive when controlling a set-point change. The reverse happens in using set-point tuning parameters to disturbance regulation. No significance in difference among rules of different integral criteria.

Late methods Method of Synthesis Using IMC tuning (internal model control ) or other model based rules Using ATV test to characterize the process dynamics.

Direct synthesis method Specify desired closed-loop transfer function. Derive PID controller follows. Tuning parameters are directly synthesized. Exactly PID controller form applies to FOPDT or SOPDT processes.

G p (s)G c (s) - + G o (s) r y r y H(s) ry Specified to meet requirement

In order to be implementable, the reference H(s) should: not allow to be assigned as “1”, in other words, a system can not be perfect in control. contain all RHP zeros of G p (s) contain the dead time of G p (s)

Example Choose:  =  3

G p (s) - + r y 1/G p (s)H(s) + + d + Structure evolution from direct synthesis

G p (s) - + r y H(s) 1/G p (s) + + G p (s) - + ry 1/G p (s) + + G p (s) - d d H(s)

G p (s) - + r y 1/G p (s)H(s) + + G p (s) - d - + r y 1/G p (s)H(s) + + G p (s) - d C(s)

G p (s) - + r y 1/G p (s)H(s) + + G p (s) -C(s) G p (s) - + r y C(s) G p (s) - Known as IMC d d

G p (s) - + r y C(s) G p (s) - d

Internal Model Control

Basic equations of IMC system When  G p (s)=0,

Equivalent conventional controller from IMC system G p (s) - + r y C(s) G p (s) - d

Equivalent IMC controller from conventional loop G p (s) - + r y G c (s) G p (s) - -

Conclusion:

Thus, G c (s) in a conventional loop can be designed according to how G p (s) is factorized and what F(s) is assigned.

PID-series filter

ModifiModifi Modification of set-poin to reduce overshoot

Modification on the proportional part, i.e. :

Auto-tune by relay feedback

Use Z-N rules to compute PID settings

Controller type PI PID Tyler-Luyben vs Z-N Tuning

DS-d-PI Tuning Rules

DS-d-PID Tuning Rules