Automation, Robotics

PID controller tunning: CHR and CC methods

This post’s subject is the description of other methods to tune a PID controller. CHR (Chien, Hrone e Reswick) and CC (Cohen e Coon).

In case you don’t know what is PID, access the link below before continuing.

PID Controller Click here

The CHR method

All tuning methods for PID controller consist in calculate values of proportional (K_{p}), derivative (K_{p}) and integral (K_{i}) gains. The CHR method was developed in 1952, as an alternative to solve problems with step response. Despite gains being smaller than the ones obtained by Ziegler-Nichols, the system has more stability when adopts the CHR method.

Comparison of stability between Ziegler-Nichols (Z&N) and CHR (lines below Z & N). Limite de estabilidade = Stability limit, Sobrevalor = Overshoot. Source: UnB.

Defines tuning laws for setpoint change and regulation resistant to disturbances.

Performance criteria

The following tables show gain calculations to obtain the fastest response as possible with 0 or 20% of overshoot for both problems.

Transient step response
T_{u} is delay time, T_{g} is time constant and K_{s} is the gain factor. Source: Beckhoff Information System.

Gain calculation table for problems with regulation with robustness

T_{N} and T_{V} are integral and derivative times. Reminding that integral Ki and derivative Kd gains are calculated with the equations below.


Kd=Kp\cdot T_{V}

Gain calculation table for servo problem (setpoint change)

Cohen-Coon (CC) method

Developed in 1953, this method is also used for step response and for a system with longer dead time, considering 0,6<\frac{\theta }{\tau }<4,5. However, robustness with be bad if \frac{\theta }{\tau }\leq 2.

step response graphic
Symbols used by many sources to represent dead time \theta and time constant \tau. Source: Responde Aí.
cohen_coon TABLE-1
Table for calculation of gain and times with CC method. Source: Control de Procesos.

The method Ziegler-Nichols and Cohen-Coon were created to obtain a quarter amplitude damping. In case you want to avoid oscillation, the gain K_{c} must be smaller than the calculated.

Quarter Amplitude Damping
Quarter amplitude damping. B is 4 times smaller than A.

In addition to the ones presented today, exist other PID tuning method which will be for future posts. 

About Pedro Ney Stroski

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