Upcoming SlideShare
×

PID gain scheduling using fuzzy logic

570 views
456 views

Published on

1 Like
Statistics
Notes
• Full Name
Comment goes here.

Are you sure you want to Yes No
• Be the first to comment

Views
Total views
570
On SlideShare
0
From Embeds
0
Number of Embeds
0
Actions
Shares
0
0
0
Likes
1
Embeds 0
No embeds

No notes for slide

PID gain scheduling using fuzzy logic

1. 1. ISA Transactions 39 (2000) 317±325 www.elsevier.com/locate/isatrans PID gain scheduling using fuzzy logic T.P. Blanchett a, G.C. Kember a,*, R. Dubay b a Department of Engineering Mathematics, DalTech, Dalhousie University, PO Box 1000, Halifax, NS, Canada B3J 2X4 b Department of Mechanical Engineering, University of New Brunswick, Federicton, NB, Canada E3B 5A3Abstract A simple, yet robust and stable alternative to proportional, integral, derivative (PID) gain scheduling is developedusing fuzzy logic. This fuzzy gain scheduling allows simple online duplication of PID control and the online improvementof PID control performance. The method is demonstrated with a physical model where PID control performance isimproved to levels comparable to model predictive control. The fuzzy formulation is uniquely characterized by; (i) onefuzzy input variable involving the PID manipulated variable, (ii) two parameters to be tuned, while previously tunedPID parameters are retained, and (iii) a gain scheduling dierential equation which relates the fuzzy and conventionalPID manipulated variables and enables fuzzy gain scheduling. # 2000 Elsevier Science Ltd. All rights reserved.Keywords: Gain scheduling; Fuzzy control; Model predictive control; PID control1. Introduction desired and predicted responses. However, chan- ging to MPC is not justi®ed for the majority of Most industrial process control continues to rely industrial PID controllers since its control struc-upon `classical, or `conventional proportional, tures are very dierent from PID, are much moreintegral, derivative (PID) control. Gain scheduling complicated, and have an increased computationalis the most common PID advancement used in cost.industry to overcome nonlinear process character- Fuzzy logic approaches have been shown inistics through the tailoring of controller gains over numerous studies to be a simpler alternative tolocal operating bands. This scheduling is compli- improve conventional PID control performancecated by the need for detailed process knowledge (for example, [1±5] for a recent overview). The pro-to de®ne operating bands and open loop tests which blem of interest here, is the control of a manipulatedmust be performed to locally calibrate the controller variable to a constant set point. Performancegain within each band. An alternative method is improvements for such a problem are usuallypredictive control which uses a `black box model to demonstrated by reductions in the amplitude ofremove the need for detailed knowledge of process undesirable oscillations in the manipulated vari-characteristics. For example, in model predictive able around the set point, shorter times to convergecontrol (MPC), controller moves are determined by to the set point, and the maintenance of controlcontinuously minimizing the dierence between the stability seen in conventional PID control. Since substantial, but similar improvements are found * Corresponding author. Tel.: +1-902-494-3262; fax: +1- from a wide variety of fuzzy logic schemes, the902-494-1801. main feature which delineates these approaches is E-mail address: guy.kember@dal.ca (G.C. Kember). their relative complexity. For those fuzzy logic0019-0578/00/\$ - see front matter # 2000 Elsevier Science Ltd. All rights reserved.PII: S0019-0578(00)00024-0
2. 2. 318 T.P. Blanchett et al. / ISA Transactions 39 (2000) 317±325controllers intended to replace existing conven- Note that a fuzzy logic scheme incorporatingtional PID controllers in the industrial setting, the these features is a true gain scheduler Ð a `fuzzydrive to simplify fuzzy logic controllers is impor- gain scheduler. Fuzzy gain scheduling is com-tant to reduce the costs of their implementation pactly and generally formulated in terms of a `gain[3]. Two features shared by most of these fuzzy scheduling dierential equation: the rate oflogic setups are: each error component (taken change of the fuzzy manipulated variable is equa-from the proportional error and its derivatives) is ted to a function of the rate of change of the con-de®ned as a separate input, and the fuzzy rule- ventional PID manipulated variable. The form ofbases are redundant, that is, the rulebases show a this function is globally determined by details oflinear dependence upon the error components. the fuzzy formulation and the defuzzi®cationSuch `fuzzy redundancy together with appro- strategy. The existence of a limiting linear form ispriate input and output bounds has been shown to used to preserve conventional PID control andlead to stable control in a large class of nonlinear allow the desired online replacement. Then, mod-control problems [6]. However, a practical obser- i®cation of this linear form, to a nonlinear sig-vation [6,7] is that fuzzy input variables taken moidal form, yields fuzzy gain scheduling. The usefrom linear combinations of the error components of a dierential equation also makes this approach(termed here `summed fuzzy input variables) should equally convenient for continuous and discretebe used to reduce the number of input variables control situations.where separated inputs would lead to a more The layout of the paper is as follows. The con-redundant rulebase. Such designs are simpler and trol of a temperature process by conventional PIDthus provide more ecient control than the more is used for illustration (Section 2). The fuzzy gainredundant fuzzy formulations, yet do not sacri®ce scheduling method and approach to independentstability [6]. In addition, control robustness with tuning of parameters is developed (Section 3) andrespect to parameter ¯uctuations, seen in most demonstrated with a physical model (Section 4). Afuzzy designs is related to widespread use of error well-tuned PID controller is substantially improvedcomponents involving the proportional error and to performance levels of the benchmark MPCits derivatives [6], i.e. there is no integral term of after tuning the fuzzy gain scheduling method withthe error, and such control has been coined `slid- a few tests (Section 5). Excellent control robust-ing mode control in [6]. ness and stability to large disturbances and large Therefore, the aim of this study is to provide a set point modi®cations is also demonstrated.new fuzzy formulation which provides a signi®cantsimpli®cation over existing fuzzy-PID schemesintended to improve conventional PID controllers. 2. PID controlThe larger simplicity of the method stems fromthree features: The control of a temperature process to a set point temperature is used to illustrate the fuzzy 1. Fuzzy redundancy is eliminated by using gain scheduling developed here. For the control of only one fuzzy input variable proportional to a temperature process by varying heater power, the derivative of the conventional PID the heater power is determined in conventional manipulated variable. PID control by manipulating 2. Online replacement and subsequent improve-  ! ment of PID control is simpli®ed through the 1 t d Àt  Kp et  eudu  Td et Y I introduction of a dierential equation relat- Ti 0 dt ing the fuzzy input and output variables. 3. Online control improvement is achieved by the where the error at time t is e  Ts À T; T is the independent tuning of only two parameters, process temperature, and Ts is the process set while the previously tuned conventional PID point temperature. The three PID control para- parameters Ti and Td are retained. meters are: the proportional gain Kp , the integral