Tuning rules for a reset PI compensator with variable reset Alfonso Ba˜ nos and Miguel A. Dav´ o DIS Department, University of Murcia, 30100 Murcia, Spain. Abstract: The PI+CI compensator is a simple reset compensator, its base system is a PI, which has been shown to be effective in a number of practical applications. One fundamental parameter to be tuned is the reset ratio; for lag dominant systems or systems with integrators it is known to give good results overcoming PI compensation. In this work, a systematic method for the tuning of a variable reset ratio (variable at the reset instants) is developed for first and second order plants. Keywords: hybrid control systems, reset control systems, PID tuning rules, PI+CI compensator 1. INTRODUCTION Reset control systems were started to be developed fifty years ago with the founding work of Clegg (Clegg (1958)), that introduced a nonlinear integrator based on a reset action. Basically, since the integrator output is set to zero when its input is zero, a faster system response without excessive overshoot may be expected, thus avoiding limita- tion of its LTI counterpart. The seminal works (Krishnan and Horowitz (1974); Horowitz and Rosenbaum (1975)) developed for the first time control synthesis methods for reset compensator based on the Clegg integrator (CI) and the First Order Reset Element (FORE). More recently (see the monograph (Ba˜ nos and Barreiro (2012))), reset control systems have started to be an attractive approach to improve stability and performance of linear and time invariant (LTI) compensators. This work is focused on a specific reset compensator, referred to as the PI+CI compensator (Ba˜ nos and Vidal (2011)). PI+CI is a simple modification of a PI compen- sator, which includes a Clegg integrator (CI) in parallel. It has been shown that PI+CI compensation gets better performance indices than PI compensation in some specific cases: in particular, in lag dominant systems and systems with integrators (Ba˜ nos and Barreiro (2012)). In general, a limitation of reset compensation, and also of the PI+CI, is the appearance of undesirable undershoots that limits its performance in control practice. Several modifications of the PI+CI has been already considered in Ba˜ nos and Vidal (2011), including a variable reset ratio to improve the setpoint traking, specifically reducing the undershoot of the response step. In this case, PI+CI parameters like the reset ratio is tuning following an heuristic method based on extensive simulation. In this work, the goal is to obtain a systematic method for PI+CI tuning, including the case of variable reset. By simplicity, basic plants including first order and second order systems (with and without integrators) will be ⋆ This work was supported by ‘Ministerio de Ciencia e Innovaci´ on’ under project DPI2010-20466-C02-02 considered. More general plants, including plants with time delays will be treated elsewhere. The outline of this paper is as follows. The PI+CI compen- sator and the resulting closed loop system are introduced in Section 2. In Section 3, a description of a reset system as a set of LTI systems is given; this representation allows the analysis of the time response of an nonlinear/hybrid system by using standard techniques like the root locus. Finally, in Section 4, tuning rules are devoloped for first order plants; and in Section 5, for second order plants. 2. PRELIMINARIES 2.1 The PI+CI controller The PI+CI compensator is simply a parallel connection of a PI compensator and a Clegg integrator (Fig. 1). The main motivation of this setup is to overcome the performance/robustness properties of a PI compensator without increasing the cost of feedback. By cost of feedback (Horowitz (1993)) it is meant the increasing on the sensi- tivity of a control system with respect to the sensor noise, which is specially important in designs with derivative terms in the compensator. As a result, the PI+CI compensator will have three terms as shown in the blocks diagram structure of Fig. 1: k p and τ I are the proportional gain and the integral time constant, and p r is the reset ratio that represents the part of the integral term over which the reset action is applied. Note that for p r = 0 a PI compensator is obtained (it will be referred to as PI base compensator), and that for p r = 1 the result is a full reset P+CI compensator. In general, the reset is not applied on the whole of the integral term, because the fundamental asymptotic property of the integral term would be lost, for example the steady-state error of the step response would not disappear for plants with no integrators. In the state-space, the PI+CI compensator can be ex- pressed by a two dimensional state x r =(x i ,x ci ) ⊤ : x i is IFAC Conference on Advances in PID Control PID'12 Brescia (Italy), March 28-30, 2012 FrA2.4