ebook img

Finch. Tuning of PI Speed Controller in DTC of Induction Motor Based on Genetic Algorithms and Fuzzy Logic Schemes PDF

6 Pages·0.393 MB·English
Save to my drive
Quick download
Download
Most books are stored in the elastic cloud where traffic is expensive. For this reason, we have a limit on daily download.

Preview Finch. Tuning of PI Speed Controller in DTC of Induction Motor Based on Genetic Algorithms and Fuzzy Logic Schemes

Tuning of PI Speed Controller in DTC of Induction Motor Based on Genetic Algorithms and Fuzzy Logic Schemes Shady M. Gadoue, D. Giaouris and J. W. Finch University of Newcastle upon Tyne Power Electronics, Drives and Machines Group, School of Electrical, Electronic and Computer Engineering Merz Court NE1 7RU Newcastle upon Tyne, UK {Shady.Gadoue, Damian.Giaouris, J.W.Finch}@ncl.ac.uk Abstract- PID controllers are very common Flux hysteresis in industrial systems applications. The tuning of Flux controller command tnvhaoernsileain tieoacnrosin.t iter so Illne rastn hdi si s pcaogpnoevtrien,r unaoe uds c ombypp alertaseym seatetnemdr CoSmpme eadn d Speed + - + sOswpetiltateicbmchl te uion m rg vi InPvWerMte r I.M ras(DpilggeTooeCrrdoi )tu hcssom cnchsot.erm mo lp eTal horaioeps popP nliiI nei sd c a mo onaDntdr ireoae lnblce etr itn wTdweouearcnqst uitouwens oe C dmtou noninttiron orgal. + -ωr ControllercoTmormqaune d - Torqcuoen throysllteerr esis θi θ 4 θθ 35F Slueθθxl 26 e θ cs1 eticoT t no e r ASEntasdtt oiTmr oaF r tlqouu rx e The first method applies off-line genetic |λ s | algorithm (GA) strategies and the other one makes use of an online Fuzzy Logic (FL) tuning Fig.1 Block diagram of DTC with speed control loop scheme. DTC is then tested with the two schemes for two cases, with normal operating conditions and they can offer a satisfactory performance and with a sudden change in load torque applied over a wide range of operation. to the motor. Results obtained show that the The main problem of that simple fuzzy logic on-line tuning technique can provide controller is the correct choice of the PID gains better speed control performance when system and the fact that by using fixed gains, the parameter variations occur. On the other hand controller may not provide the required control for nominal operation the genetic algorithms scheme is preferred. performance, when there are variations in the plant parameters and operating conditions. Therefore, a tuning process must be performed Index Terms – Speed control, induction motor, direct torque control, Fuzzy logic, Genetic to insure that the controller can deal with the algorithms. variations in the plant. To tune the PI controller (usually in drives applications the derivative part of the controller is not used) a lot of strategies have I. INTRODUCTION been proposed. The most famous, which is frequently used in industrial applications, is Recently there has been a fast growth in the Ziegler-Nichols method which does not industrial applications of the DTC technique. require a system model and control parameters This is due to its quick torque response, are designed from the plant step response. simplicity and robustness against rotor Tuning using this method is characterised by a parameters variation. Compared with a vector good disturbance rejection but on the other control scheme, DTC provides similar hand, the step response has a large percentage dynamic performance with simpler controller overshoot in addition to a high control signal architecture [6]. The basic block diagram that is required for the adequate performance representation of the direct torque control of of the system. Another technique uses three-phase induction motors with a speed frequency response methods to design and tune control loop is shown in Fig.1. PI controller gains based on specified phase The most common choice for the speed and gain margins as well as crossover controller shown in Fig. 1 is the so called PID frequency. Furthermore, root locus and pole compensator since they have a simple structure assignment design techniques are also proposed in addition to transient response three switching functions s , s , s and the DC 1 2 3 specifications. All these methods are link voltage (V)as: considered as model based strategies and then u (s,s ,s )=u + ju the efficiency of the tuning law depends on the s 1 2 3 sd sq accuracy of the proposed model as well as the 2 ⎡ ⎛ j2π⎞ ⎛ j4π⎞⎤ (1) assumed conditions with respect to actual = V⎢s +s exp⎜ ⎟+s exp⎜ ⎟⎥ operating conditions. 3 ⎣ 1 2 ⎝ 3 ⎠ 3 ⎝ 3 ⎠⎦ Artificial Intelligence (AI) techniques Where u and u are the d-axis and q-axis sd sq such as neural networks, fuzzy logic and stator voltage components. genetic algorithms are gaining increased In direct torque control schemes the interest nowadays. magnitude of the stator flux linkage vector is A lot of techniques have been proposed to controlled which can further be decomposed to tune the gains of PI controller based on AI its orthogonal components expressed at a techniques: Self tuning FL and neural network stationary reference frame as: techniques are some of these methods proposed for the online adaptive tuning of PI ψ =∫(u −Ri )dt (2) controller. In such application, the controller sd sd ssd gains are tuned with the variation of system ψ =∫(u −Ri )dt (3) conditions. Moreover, GA is proposed for sq sq ssq both online and offline tuning procedure [4] where ψ and ψ are the d-axis and q-axis sd sq even though this may require high processing stator flux linkage components. power. The advantage of tuning with GA is the ability of choosing controller gains which The stator flux position (θs) is determined by optimize drive performance based on multi dividing the d-q plane into six 60˚ regions and objective criterion without tripping in a local three sign detectors are used to determine the minima solution. Furthermore, combinations sector over which that vector passes. of AI techniques are also introduced such as The basic DTC strategy is that the status Neuro-Fuzzy and Genetic-Fuzzy techniques of the errors of stator flux magnitude | ψ | and s [8]. The advantage of these techniques is that electromechanical torque (T ) can be detected em they are model free strategies because they use and digitalized by two- and three-level the human experience for the generation of the hysteresis comparators. The optimum tuning law. switching table is then used to calculate the This paper provides a comparison between status of three switches s , s , s that will 1 2 3 two strategies used for tuning the PI speed determine the location of the voltage space controller in the direct torque controlled vector u which depends on the stator flux s induction motor. The first one is based on angle (θ). s Genetic Algorithms (GA), while the second one is based on Fuzzy Logic (FL). In the first If the drive contains a speed control loop, method, GA searches for the optimal gains of then the reference speed input is compared the PI speed controller based on a fitness with the actual motor speed and the speed error function and the search procedure is such that is fed to a speed controller. The output of the a performance index is minimized. In the other speed controller is the reference method, FL is used for tuning the PI controller electromagnetic toque. online based on a group of IF-THEN control In an induction motor, the mechanical rules which mimic the human logic and are balance equation can be written as: generally derived from experts’ knowledge. J • B (4) II. DTC STRATEGY T −T = ω+ ω em L P r P r In principle, DTC is a direct hysteresis And the electromagnetic torque is given by: stator flux and electromagnetic torque control scheme, which triggers one of the eight T = 3 P ψ i sinα (5) available discrete voltage vectors generated by em 2 s s a Voltage Source Inverter (VSI) to keep the Where T is the load torque, J is the combined stator flux and torque within the limits of two L motor and load inertia, B is the friction predefined bands. The correct application of coefficient, P is the number of motor pole this principle allows a decoupled control of pairs, ω is the rotor electrical speed, ψ is the flux and torque [6]. r s stator flux linkage space vector, i is the stator The primary space voltage vector of the s current space vector both expressed in the PWM inverter u can be expressed in terms of s stationary reference frame and α is the angle applications [4], multi population techniques between the stator flux linkage and stator and others. current space vector. In the case of using a GA method to tune the PI gains in the previously mentioned speed III. PI CONTROLLER TUNING, USING GA control loop, the fitness function used to GA is a stochastic global search evaluate the individuals of each generation can optimisation technique based on the be chosen to be the integral time of absolute mechanisms of natural selection. Recently, error (ITAE): GA has been recognised as an effective technique to solve optimisation problems and ITAE=∫e(t)tdt (6) compared with other optimisation techniques; GA is superior in avoiding local minima which During the search process, the GA looks is a common aspect in nonlinear systems. for the optimal setting of the PI speed GA starts with an initial population controller gains which minimizes the fitness containing a number of chromosomes where function (ITAE). This function is considered each one represents a solution of the problem as the evolution criteria for the GA. The which performance is evaluated by a fitness choice of this fitness function has the function. Generally, GA consists of three main advantage of avoiding cancellation of positive stages: Selection, Crossover and Mutation. and negative errors. Each chromosome The application of these three basic operations represents a solution of the problem and hence allows the creation of new individuals which it consists of two genes: the first one is the Kp may be better than their parents. This value and the other one is the Ki value: algorithm is repeated for many generations and Chromosome vector = [Kp Ki]. It must be finally stops when reaching individuals that are noted here that the range of each gain must be the optimum solution to the problem [3, 7]. specified. The genetic algorithm parameters The GA architecture is shown in Fig.2. chosen for the tuning purpose are shown in Table I. Here the GA starts by generating an Start initial population containing 8 chromosomes then the fitness value of each chromosome in Create Initial the initial population is calculated. Population TABLE I Gen=er 0at ion GENETIC ALGORITHM PARAMETERS Number of generations 20 Evaluate Fitness No of chromosome in Value each generation 8 For each No of variables in Chromosome 2 each chromosome Chromosome length 40 bit Perform Selection, Selection method Stochastic Crossover and Universal Selection (SUS) Mutation Process Crossover method Double point Crossover probability 0.7 Mutation rate 0.05 Gen > max Gen = Gen+1 No generation Or min The three main parts of GA: Selection, performance index reached Crossover and Mutation take place and then a new generation is produced. This procedure continues for some generations and then a Yes convergence to the optimal solution Stop represented by a given chromosome is reached. Fig.2 Genetic Algorithm Architecture A lot of techniques have been proposed to IV. FUZZY SELF TUNING PI CONTROLLER increase the convergence speed of GA such as Fuzzy Logic Control (FLC) has been Parallel Genetic Algorithm based on the Allied found to be excellent in dealing with systems Strategy (PGAAS) which is suitable for online that are imprecise, non-linear, or time-varying. FLC is relatively easy to implement, since it this case, the weights represent the output does not need any mathematical model of the scaling factors of FLC. Mokrani et al. [5] controlled system. This is achieved by proposed a fuzzy adaptation scheme for the converting the linguistic control strategy of purpose of tuning the scaling factors of FLC. human experience and knowledge into an Each input of the FLC has 5 triangular automatic control strategy. membership functions with equal width and FLC has become very popular in the field overlap. The first output (∆Kp) has 3 of industrial control applications. triangular membership functions, while as the On-line tuning of controllers becomes of second output (∆Ki) has 5 membership interest since it is very difficult for off-line functions. The inference rules base has 25 tuning algorithms to deal with the continuous rules. Membership functions can be tuned by variations in the induction motor parameters trial error techniques or using any other tuning and the nonlinearities present in inverter, strategies such as GA. The Fuzzy inference motor and/or controller. The stator and rotor rules used for on-line tuning of PI controller resistances of induction motor may change gains are shown in table II and table III [1]. with the temperature variation up to 50%, The flow chart of the Fuzzy self tuning PI motor magnetizing inductance varies with the speed controller is shown in Fig.4. magnetic operating point and becomes nonlinear near the saturation level. TABLE II Furthermore, the load torque and inertia FUZZY INFERENCE RULES FOR UPDATING THE may change due to mechanical disturbances. PROPORTIONAL GAIN (∆Kp) e NB NS ZE PS PB Nonlinearity also arises in the drive system ∆eω ω due to voltage and current limits of the power NB PB PB PB converter and the load torque nature. NS PB PS ZE When FL is used for the on-line tuning of ZE PB ZE PB the PI speed controller of induction motor PS ZE PS PB DTC drive, it receives the scaled values of the PB PB PB PB speed error and the change in speed error. Its output is the updating in PI controller gains TABLE III (∆Kp and ∆Ki) based on a set of rules to FUZZY INFERENCE RULES FOR UPDATING THE INTEGRAL maintain excellent control performance even in GAIN (∆KI) e NB NS ZE PS PB the presence of parameter variation and drive ω ∆e nonlinearity [1]. ω NB ZE NS NB NS ZE The most important parameters of Fuzzy NS PS ZE NS ZE PS Logic are the scaling factors. The input ZE PB PS ZE PS PB scaling factors affect the FLC sensitivity while PS PS ZE NS ZE PS the output scaling factors affect the system PB ZE NS NB NS ZE stability [7]. The block diagram of the control system is shown in Fig.3. Start k= 0 Ψ s Receive ωr* eωr Te* e ω(k) and ∆eω(k) Calculate ∆Kp(k )and ∆KI(k) ⎡∆K ⎤ From FLC P ⎢ ⎥ ⎣∆KI⎦ ∆e Set ωr ∆Kp(k ) No eω(k) < 2% and ∆KI(k) from FLC Fig.3 Fuzzy self tuning PI speed controller Yes Set A lot of researches have proposed tuning ∆Kp(k ) = 0 And ∆KI(k) = 0 methods for the FL scaling factors: Han et al. [2] proposed a neural network with variable learning rate. The artificial neural network is used to represent the output part of the FLC, k = k +1 and then a back propagation algorithm is used to adjust the weights of the neural network. In Fig.4 Flow chart of Fuzzy self tuning PI speed controller V. SIMULATION RESULTS AND DISCUSSION again to track the reference value (50 rad/s) with a total ITAE of 0.1641. The ITAE To compare the two tuning strategies, obtained by each tuning technique is shown in DTC of a 10 hp squirrel cage induction motor Fig.7. The results are summarised in table V. with speed control loop shown in Fig.1 is simulated using Matlab-Simulink software. 51 GA is first applied to the PI speed controller tilaoundnaddduiint cigttooi.on rqn u temoD. ou tAtrohir ne sg ips e realtodhtea edrd e eftdeus rtneawintnoictgrhe o2fpfl5r u%o5xc0 e osrlfasi n,d rk/asatt ehgidnee Rotor speed (r/sec) 505.05 49.5 magnitude is the input commands to the drive. The speed response of the motor is observed and the ITAE is recorded for each 409.12 0.125 0.13 0.135Tim0e . 1(s4ec)0.145 0.15 0.155 0.16 (a) chromosome in each generation. After 20 70 generations, the optimal solution proposed by 60 GwaniAdth K Wuthni hed=e e cn3rh .r9tthoh8emi.s do lrsoiovamed eisn ycgso tnecsmoins tdiisin tgisoi monf u iKlsa ptae c=dh 1uie5svi1ne.6gd Rotor speed (r/sec) 23450000 the proposed gains, which are set to be 10 constant during the simulation period, with the 00 0.05 0.1 0.15 motor operating with a load torque of 25 % for Time (sec) (b) 2 s, the ITAE is equal to 0.1269. Fig.5 Transient response (a) GA tuning (b) FL tuning The Fuzzy self-tuning PI speed controller, with the parameters listed in Table IV, is 100 % Load 50.4 Torque simulated with the same conditions and the change Iw“ToapAst Eiem xupomebct”at eindge adsiin nsic se f o0trh. 1et3 hG1e9A .s psTechchiiesfmi cde icsfoconruednpidtai nothcnyes Rotor speed (r/sec) 45905..082 applied while the FLC used the “imperfect” human 49.6 knowledge and experience. 49.4 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 TABLE IV Tim(ea )(s ec) FUZZY LOGIC PARAMETERS 51 Input scaling factors K,K 1.1, 0.1 1 2 1 00 % Load OuDtpeufut zszcKiaflipicn aigtni ifotanica tmlo resth Ko3d, K4 Centr0e.2 1o,0 f1 g.1ra vity Rotor speed (r/sec) 505.05 cTahoparpqnliugeeed 49.5 Ki initial 12 49 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 To investigate the performance of the Time (sec) (b) tuning strategies under system parameter Fig.6 Speed response at time of application of 100% load variation, the induction motor is subjected to a torque increase at t=1s (a) GA tuning (b) FL tuning 100 % load torque change (from 25% to 50% of the motor rated torque) at t = 1 s. 0.25 GA As shown in Figs.5 and 6, the speed 0.2 1i0n0c%re aLsoea adp tpolriqe ude roevseproshnoseo t uosf in0g.6 %GA w htiulen inthga t hfraosm aF Ls paeuetdo AE (rad) 0.15 tuning has no overshoot and the drive system IT 0.1 Fuzzy behaves like a critical damped system. At t=1s Logic 0.05 when the load is increased, the speed response using fixed gains (obtained by GA) drops to 00 0.5 1 1.5 2 Time (sec) 49.94 rad/s with a speed regulation of 0.12 % Fig.7 ITAE for GA and FL tuning with a total ITAE (after 2 s) of 0.2132, while as that obtained by FL self tuning drops rapidly to 49.6 rad/s before the speed builds up TABLE V FL auto tuning since it contains the optimal SUMMARY OF RESULTS controller gains. GA FL When a change in system parameters takes Kp = 151.6, Ki = 3.98 Variable Gains place, the results show that self tuning FL is ITAE 0.1207 0.125 superior in terms of speed reference tracking (t=0to t=1s) than fixed gains controller obtained from GA tuning. This is due to the adaptive behaviour (t=1ITtoA tE= 2s) 0.0925 0.039 of FL when used with an online tuning strategy. Total ITAE 0.2132 0.1641 REFERENCES [1] L. Mokrani and R. Abdessemed, “A Fuzzy self-tuning Transient 0.6 % speed response overshoot No overshoot PI controller for speed control of induction motor drive”, Proceedings of 2003 IEEE Conference on Initial drop Control Applications, IEEE Part vol.2, 2003, pp.785- Response to Speed drop with 0.12 then quickly 90 vol.2. ‘Istanbul, Turkey’. load torque % speed regulation regain the application speed [2] Woo-Yong Han, Sang-Min Kim, Sung-Joong Kim and Chang-Goo Lee, “Sensorless vector control of induction motor using improved self-tuning Fuzzy The PI controller gain variations for the PID controller”, SICE 2003 Annual Conference. Soc. self tuning Fuzzy Logic scheme are shown in of Instrum. and Control Eng. Part Vol.3, 2003, pp.3112-17 Vol.3. Tokyo, Japan. Fig.8 (a) and Fig.8 (b). The gains increase [3] The MATLAB Genetic Algorithm Toolbox v1.2 gradually until the command speed is reached. User's Guide, Department of Automatic Control and After that, the gains are kept constant. When Systems Engineering of The University of Sheffield, the load torque increase occurs, they rise again UK. to compensate for the speed decrease and to http://www.shef.ac.uk/acse/research/ecrg/gat.html return the speed back to the command value. [4] Lin Feng, Zheng Hongtao and Yang Qiwen, That is, to ensure complete speed tracking. “Sensorless vector control of induction motors based on online GA tuning PI controllers”, Fifth 40 International Conference on Power Electronics and 35 100 % Load Drive Systems. IEEE Vol.1, 2003, pp.222-5 Vol.1. N.m/ r/s) 30 cTahoparpqnliugeeed [5] L‘S. iMngoakproarnei’ .a n d K. Kouzi, “Influence of fuzzy adapted Kp ( 25 scaling factors on the performance of a Fuzzy logic n Proportional gai 112050 [6] AciEnon.dn gLutirc.no teMiloelernori h nagbmm,a Vsaoedtodoel ri.n5 o,5n ,Rd Nr.ai voHne. a ” im7,n -dd8iy,Jr 2eoac0unt0rd n4 vaS, elhp captdo.1oyrf8 M8c-o1E.n 9Glte4raco.d tlr oicufoaerl, 5 “A Comparison Between Two Direct Torque Control 00 0.5 1 1.5 2 Strategies For Flux And Torque Ripple Reduction For Time (sec) Induction Motors Drives”, Proceedings of the Ninth (a) International Middle East Power Systems Conference 10 (MEPCON'2003), Shebeen Al-Koum, Egypt, December 16-18,2003. 8 [7] P.Vas, “Artificial-Intelligence-Based Electrical m / r) 100 % Load Machines and Drives-Application of Fuzzy, Neural, n Ki (N. 6 cTahoparpqnliugeeed FTueczhzyn-iNqueeusr”a,l Oxfaonrdd UnGiveenrestiitcy PreAslsg, o1r9it9h9m. Based Integral gai 4 [8] JPRiIenDsgp -oCnChsuoennsg”tr , SolIhlEeeEnr ,E “ fFoTurrz aznyPs aNlacentiutosrn asl wNoientth w FourUzkzsny df oeSrrd yTasumtenpminesdg, 2 Vol.9, No.2, April 2001. 0 0 0.5 1 1.5 2 Time (sec) (b) Fig.8 Fuzzy Self tuning Performance (a) Proportional gain (b) Integral gain VI. CONCLUSION A comparison between two artificial intelligence based techniques used for the tuning of the PI speed controller in DTC of induction motor has been presented. Under normal operating conditions, an off-line GA tuning scheme shows better performance than

See more

The list of books you might like

Most books are stored in the elastic cloud where traffic is expensive. For this reason, we have a limit on daily download.