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Hidrolik bir servo sistemde pol atamalı adaptif konum kontrolü

The Pole assignment adaptive position control in a hydraulic servo system

  1. Tez No: 21862
  2. Yazar: AYHAN KURAL
  3. Danışmanlar: DOÇ. DR. CAN ÖZSOY
  4. Tez Türü: Yüksek Lisans
  5. Konular: Makine Mühendisliği, Mechanical Engineering
  6. Anahtar Kelimeler: Belirtilmemiş.
  7. Yıl: 1992
  8. Dil: Türkçe
  9. Üniversite: İstanbul Teknik Üniversitesi
  10. Enstitü: Fen Bilimleri Enstitüsü
  11. Ana Bilim Dalı: Belirtilmemiş.
  12. Bilim Dalı: Belirtilmemiş.
  13. Sayfa Sayısı: 64

Özet

ÖZET Bu çalışmada dijital algoritmaların özel bir sınıfı olan kutup atamalı kendi kendini ayarlayan kontrolörün, lineer olmayan elektrohidrolik tahrikli silindir sürücü gibi yüksek hızda kontrolün gerektiği sistemler için uygunluğu incelenecektir. Elektrohidrolik tahrikli silindir sürücü aslında lineer değilse de dinamiğini, kontrolörü geliştirmeye uygun kılacak kadar yeterli hassasiyette tanımlayan bir lineer transfer fonksiyonu elde edilmiştir. Bu çalışmada kullanılan self-tuning tekniği hesaplamada karşılaşılan zorlukları yenmek için parametre kestirimi ve kontrol sentezini iki ayrı bölüm halinde düşünüp, sonradan uygun tekniklerle birleştirilmesi esasına dayanmaktadır. Çalışma boyunca fortran dilinde yazılmış iki ana programdan faydalanılmıştır. îlk programda, kestirim için model ayrık formda oluşturulmakta ve dört farklı kestirim algoritmasının her biri için bilinmeyen sistem parametreleri bulunmaktadır. Programda kestirimin yapılması için gerekli olan bilgiler, 6 serbestlik dereceli manipülatörün hidrolik silindirle tahrik edilen ikinci eklemine P-D kontrol uygulanması sonucu elde edilen giriş (kumanda) ve çıkış (konum) değerlerinden sağlanmıştır. İkinci programda, kestirim sonucu elde edilen parametreler kulanı larak sistem modeli tanımlanmakta ve kontrolör tasarımında T polinomu ile belirlenen çalışma bölgesi için kontrolör parametreleri üretilmekte ve hesaplanan kumanda (giriş) değerleri için sistemin konum (çıkış) cevabı elde edilmektedir. Daha sonra gerçek sisteme yani manipülatöre geçilmiştir. P-D algoritması çıkarılarak elde edilen kontrol paremetre değerleri ve kumandayı üreten ayrık formdaki eşitlik programa girilmiş ve gerçek sistem çalıştırılmıştır. Sonuç olarak P-D algoritmasında elde edilen titreşimli konum cevabına nazaran titreşimsiz, hızlı bir konum cevabına ulaşılmıştır. iv

Özet (Çeviri)

SUMMARY THE POLE ASSIGNMENT ADAPTIVE POSITION CONTROL IN A HYDRAULIC SERVO SYSTEM This study investigates the suitability of particular class of digital algorithms, namely pole assignment self tuning controllers for the control of high speed, nonlinear electrohydraulic cylinder drives. (When used in high performance servomechanism, this type of drive often needs some form of compensation to increase the servo damping in order to produce an acceptable closed loop performance). For systems which are relatively slow in performance, such as process control systems, self tuning can be used in a continuous manner to adapt the control laws to compensate for variations in the system parameters. However, for the case of high performance servo mechanisms, where fast sampling rates are required, continuous adaption is not always feasible due to the time required for computation. The technique of self tuning presented in this study, associated with the conventional techniques by seperating the control synthesis and parameter estimation into two distinct sections. In this study has been used a manipulator which have six revolute joint. Hydraulic actuators have been preferred for the first three joints of manipulator. Pneumatic actuators have been chosen for driving the wrist. For driving the base joint has been used the hydraulic motor and for driving the other two joints has been used hydraulic cylinders. Timing belt has been used at the base joint for providing the reduction. Electrohydraulic cylinder drive servomechanisms combine the versatility and the precision available from electrical measurement and signal processing techniques with the rapid response and loading capacity of hydraulic cylinder drives. A schematic diagram of the electrohydraulic cylinder drive used in this study is given in Fig. 1. It consists of a symmetrical cylinder drive rigidly connected to a load mass that is supported on a table mounted on frictionless bearings. The position of the load is provided by a transducer. The hydraulic fluid flow the into the cylinder drive is controlled by a four way electrohydraulic servo valve. The cylinder drive is robust, fast and accurate but the stroke is limited by the compressibility of the hydraulic fluid.Although electrohydraulic cylinder drive are inherently nonlinear, linear transfer function has been developed that the describe their the dynamics with sufficient accuracy to facilitate controller development. The dynamic response of the electrohydraulic servo valve is far faster than the dynamic response of the cylinder drive and can be neglected. If drive is operating outside its threshold region but it is not saturating, a transfer function that approximates the response obtained from the experimental rig is y(s) Kw' üT^T 2 2 s(s +2wÇs+w ) where y(s) is the position of the load, u(s) is the input to the electrohydraulic servo valve, u> is the natural frequency of the loaded cylinder drive and Ç is its damping ratio. K is the forward gain, it is necessary to increase the load's damping to improve the closed loop response. Fig. 1 Electrohydraulic cylinder drive. viThe development of a digital compensation scheme where the control parameters can be determined semi-automat ically, on-line is the aim of this study. Self-Tuning Control Strategy: Self-tuning control algorithms realize the on-line and semi-automat ically synthesis and implementation of digital controllers. Explicit self-tuning controllers essentially consist of three stages: (i) periodically measuring the input and the output of a process and using the data to form a discrete time model, (ii) using the discrete time model to derive a digital controller, (iii) using the digital controller to control the process. This three stage procedure is normally executed at every sampling Instant. Model parameter estimation is often accomplished by recursive least squares algorithm or by one of its extensions such as the square root filter. Controller synthesis, in an explicit algorithm may be achieved using a pole assignment procedure such as the Extended Self-Tuner. If stages i and i i are combined, the algorithmis implicit. Two useful implicit algorithms are the Minimum Variance Regulator and the Generalized Minimum Variance Controller. The procedure is normally initiated every sampling instant and therefore the fastest achievable sampling rate indicated by the time required to compute the three stages. Work undertaken suggests that 0.5-2.0 seconds computation might be needed every sampling instant for a high order pole assignment algorithm. The sampling frequency chosen must also be at least twice and in practice greater than five times the desired closed loop bandwidth. A pole assignment algorithm can not be implemented in the normal manner unless, perhaps, the computer used is extremely fast such as an array processor. The strategy, depicted in Fig 2, essentially consists of four stages : (i) with the process under the control of a prespecified fixed coefficient digital controller, measure and store the input u(t) and the output y(t) of the process periodically for a specified number of sampling instants, (ii) using the stored data compute a discrete time model of the process whilst the prespecified controller ensures stability, (iii) when the model estimates converge, use of one set of coefficient to synthesize an alternative fixed coefficient controller by a pole assignment algorithm, (iiii) replace the prespecified controller with the pole assignment synthesized controller. viiA u(t)/ i VE(t) Eleotr ohydr aul ic Cylinder Drive A, y(t) - - ^ ¦¦ ^ I Controller ~K Controller Synthesis /N ¦^ Parameter Estimation İ Fig. 2 Self-tuning control strategy The discrete time model of the process, usually used in self-tuning controller analysis, is a difference equation. If z is the backward shift operator, time model can be represented by: A(z“1)y(t)=B(z”1)u(t)+C(z“1)e(t) where u(t) and y(t) are the control signal and the measured process output at sample instant t and e(t) is an uncorrelated sequence of random variables with a zero mean. The process time delay is incorporated in the B(z~ ) polynomial. Since the level of the external noise in the servomechanism is negligible a modeling of noise is unnecessary and C(z”) is fixed at 1. The electrohydraulic cylinder drive's contribution to the total process time delay is insignificant when compared with the microprocessors computational time delay. The continuous time transfer function, given by equation (1), contains an integrator in series with a quadratic lag and hence the A(z ) polynomial is assumed to be third order and the B(z ) polynomial is assumed to be second order. Therefore the A(z ), B(z ) and C(z~ ) polynomials are: A(z_1)=1.0 + hx'1 + A z“2 + A z”3 B(z-1)=B z“1 + BoZ”2 CCz_1)=1.0 viiiSince the noise in the closed loop servomechanism is considered Gaussian with a zero mean level, unbiased estimates of A, A, A, B and B can be obtained using the recursive least 12 3 1 2 ö square. Recursive Least Square Method: The usual RLS method estimation to update the parameter G(t) and the inverse covarians matrix P(t) formulated as the following algoritms; P(t-l) x(t) Gain: K(t) = w + xT(t) P(t-l) x(t) Matrix: P(t) = ( P(t-l) - K(t) xT(t-l) P(t-l) )/ w Error: Ç(t) = y(t) - 9(t-l) x(t) Estimates: 6(t) = 6(t-l) + Ç(t) KT(t) This method is by far the most widely used technique for the self-tuning controllers of dynamic systems. Other Estimation Methods: The square root algorithm is introduced to avoid the possibilty for the positive definite matrix P(t) to lose this property due to rounding errors. This method involves factorizing P(t) as P(t) = S(t) S (t) with S(t) being an upper triangular matrix updated at each sampling instant. Recursive U-D factorization involves factorizing P(t) as P(t) = U(t) D(t) U (t) where U(t) is an upper triangular matrix unit diagonal element and D(t) is a diagonal matrix. Variable forgetting factor method was suggested to track both slow and sudden changes in parameters. Forgetting: w(t) = 1 - ( l-KT(t) x(t) )2 Controller Synthesis: The controller configuration of the electrhydraulic cylinder drives with pole placement controller is depicted in Fig. 5. ixGo+G^+GâZ'5 Fig. 3 Controller Configuration The pole placement controller syntesis procedure equates the closed loop characteristic equation of the system in Fig. 3 with a user defined polynomial T(z~ ) and then solves for the unknown controller polynomials F(z~ ) and GCz“1). A control signal can then be generated by: u(t) = ( H(z_1) w(t) - G(z_1) y(t) ) / F(z_1) The pole placement equation is : T(z_1) = F(z_1) A(z_1) + G(z_1) B(z~X) Since polynomial A(z~ ) is third order and B(z-1) is second order, this equation can be solved as a set of simultaneous equatios with a unique solution The closed loop transfer function is given by: y(t) = H(z_1) B(z_1) w(t) T(z_1) F(z_1) n(t) T(z_1) The chosen form the of the precompensator HCz”1) ensures that the process output y(t) tracks the demanded signal w(t) in the steady state if the rigth hand side noise term in equation is negligible. H(z~ ) is a given by: H = o 1 + T +T +T +T 12 3 4 B + B 1 2 X

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