Tuning PID controllers with symmetric send-on-delta sampling strategy

Abstract

A procedure for tuning PID controllers with SSOD sampling for FOPTD systems is proposed. It is based on the definition of a new robustness measure to avoid limit cycle oscillations, called the Tsypkin margin (M T). This margin is based on the Tsypkin method and does not rely on the attenuation of high order harmonics, as the describing function approaches require. Therefore, the avoidance of limit cycle oscillations can be guaranteed for any system, as a difference with the describing function based procedures. The procedure allows to obtain the PID controller that minimizes the disturbance IAE while fulfilling constraints on robustness to oscillations and on control action bumps due to the SSOD sampling. A freely available Java tool has been developed in order to simplify the application of the tuning procedure. In case of a non FOPTD system, it first calculates an approximate FOPTD model. The paper shows that the derivative filter parameter, N is a critical tuning parameter in order to find a compromise between performance and control action bumps.

Regular quantisation with hysteresis: a new sampling strategy for event‐based PID control systems

“…These methods can be easily applied in industry because the controller parameters are straightforward calculated using very simple equations and data collected from the step response or the relay feedback experiments. Some previous studies developed by the authors have proved that AMIGO provides a proper tune for this kind of control scheme when SSOD sampling is used [22]. Among other results, the study in this paper demonstrates the validity of the AMIGO method to avoid the limit cycle oscillations when using PI with the proposed sampling law.…”

“…A new system identification procedure based on the oscillations induced by SSOD sampling strategy was proposed in [21]. More recently, in [22] a procedure for tuning not only PI but also PID controllers with SSOD sampling for FOPTD systems was proposed. It is based on the definition of a new robustness measure to avoid limit cycle oscillations called the Tsypkin margin, presented in [23], which overcome the limitations of the DF approach.…”

Event-Based PID Controllers with Fixed Threshold Sampling Strategies

“…These methods can be easily applied in industry because the controllers parameters are straightforward calculated using very simple equations and data collected from step response or relay feedback experiments. Some previous studies developed by the author have proved that AMIGO provides proper tune for this kind of control scheme when Symmetric-Send-On-Delta sampling is used, [44]. Among other results, the study in this chapter demonstrates the validity of the AMIGO method to avoid the limit cycle oscillations when using PI with the proposed sampling law.…”

“…In Figure 3.2 the locus of −1/N for different values of h/δ is represented. The case where h/δ = 1 represents the negative inverse of N for SSOD and several studies about its robustness have already been presented [58,44]. An important remark is that for PI controllers tuned with reasonable robustness margins the shape of G ol is such that the non intersection with the branch corresponding to m = 1 guarantees to avoid intersections with branches for m > 1, and therefore, no intersection between G ol and −1/N takes place, avoiding limit cycle oscillations.…”

“…A new system identification procedure based on the oscillations induced by SSOD sampling strategy was proposed in [70]. More recently, in [44] a procedure for tuning not only PI but also PID controllers with SSOD sampling for FOPTD systems was proposed. It is based on the definition of a new robustness measure to avoid limit cycle oscillations called the Tsypkin margin, presented in [43], which overcomes the limitations of the describing function approach.…”