Sabit mıknatıslı senkron motorların servo uygulamalarında PID kontrolör parametrelerinin otomatik ayarlanması
Auto tuning of PID controller parameters for permanent magnet synchronous motor servo applications
Yazar: GÖKHAN ERÜNLÜ
Danışman: PROF. DR. METİN GÖKAŞAN
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / Kontrol ve Otomasyon Mühendisliği Ana Bilim Dalı / Kontrol ve Otomasyon Mühendisliği Bilim Dalı
Derece: Yüksek Lisans, 2014
Konu: Elektrik ve Elektronik Mühendisliği = Electrical and Electronics Engineering

Özet:
Teknolojinin gelişmesiyle birlikte kullanım alanları da artan elektroniğin getirdiği yenilikler günlük hayat ile sınırlı kalmayıp endüstriyel sistemleri de kapsamıştır. Servo sistem de bunlardan biridir. Bu tez kapsamında sabit mıknatıslı senkron motorların servo uygulamalarında PID kontrolör parametrelerinin otomatik ayarlanması işlenecektir. Servo sistem genel olarak motor sürücü, kontrolör ve servo mekaniği olmak üzere üç başlık altında incelenebilir.
Motor sürücü kısmını ele alırsak, bu kısım şu birimlerden oluşur: elektrik motoru, elektronik komütatör ve sensörleri. Elektrik motoru olarak alternatif akımlı sabit mıknatıslı senkron motor kullanılmıştır, elektronik komütasyon için vektör kontrol algoritması ve PWM üretimi için de uzay vektör modülasyonu yöntemi kullanılmıştır. Üretilen PWM IPM tabanlı kuvvetlendiriciye girmiş ve kuvvetlendirici tarafından motor fazları sürülmüştür Vektör kontrol algoritması çalışmak için rotorun açısal pozisyonuna ihtiyaç duyar ve bunun ölçülmesi için 2500 artımlı mutlak pozisyonlu dördül enkoder kullanılmıştır.
İkinci olarak da dijital kontrolör kısmını ele alırsak, bu kısım da mikrokontrolör devresi, haberleşme birimleri ve kontrolör yazılımından oluşur. Mikrokontrolör devresinde mikro işlemci tabanlı bir dijital sinyal işleyici (DSP) ve bunun çalışması için gerekli diğer elektronik devre elemanları bulunur. Haberleşme birimi olarak Visual C# dilinde kullanıcı arayüzü yazılmıştır. Kontrolör yazılımında i_q akımını, i_d akımını ve motor hızını kontrol etmek için 3 farklı dijital PID kontrolör vardır.
Üçüncü olarak ise ve servo mekaniğinden bahsedebiliriz. Motor, elektronik devreler, sensörler ve eğer gerekliyse dişli kutusu gibi parçaları birbirlerine sabitleyen ve tüm sistemi toz, su, darbe gibi dış etkilerden koruyan kısımdır.
PID hız kontrolör parametrelerinin otomatik ayarlanması için gerekli olan ilk adım sistem modelinin elde edilmesidir. Bunun için sisteme uyarı sinyali yollanır ve sistem cevabına bakılır, uyarı sinyali olarak sisteme 10 saniye boyunca değişken frekanslı sinüs sinyali uygulanmış ve bu süre zarfında sinüs sinyalinin frekansı 0,5Hz'den başlanarak lineer olarak 10Hz'e kadar artırılmıştır. Ardından ISE kriterini sayısal olarak optimize edecek şekilde sistem parametreleri bulunmuştur. Bulunan bu parametreler hız kontrolörü tasarımında kullanılmıştır.
Hız kontrolörü için dijital PID kontrolör kullanılmış ve örnekleme periyodu 0,001Hz olarak belirlenmiştir. Sistem modelinin parametreleri yüzde aşım, yerleşme zamanı gibi kriterlerin de dâhil edildiği IKH maliyet fonksiyonunu minimize edecek şekilde aranmıştır.Algoritmalar farklı sistemler için çalıştırılmış, simülasyon ve gerçek test sonuçları incelendiğinde kullanılan yöntemin başarılı olduğu görülmüştür.

Abstract:
Development of the technology also brought the improvement of the electronics and made it part of the daily life. It also entered to the industrial area and the servo system is one of the results of industrial development of electronics. Purpose of this theses is auto tuning of PID speed controller parameters for permanent magnet synchronous motor servo applications.
Permanent magnet synchronous motors are kind of brushless motors and they have several advantages and disadvantages when they compared with the conventional brushed motors. Advantages of brushless motors are; no electrical sparks, voltage drops and EMI generation because of mechanical brushes, they can work in oil and dust, they can work long time without any maintenance, they produce higher torque, they have less weight and they have less size. Disadvantages of brushless motors are; need of electronic commutator and higher price.
It can be easily seen that, advantages of the brushless motors are more than the disadvantages and this is the reason why usage of brushless motors in industry increases and usage of brushed motors decreases. Brushless motors have two different types one of which is brushless DC motor and the other is brushless AC motor. Brushless DC motor, also named as permanent magnet DC motor, is 3-phase motor and it has trapezoidal back EMF, this means that when it is rotating it generates voltage shaped as trapezoidal. Because of this trapezoidal back EMF it is needed to be powered with the square wave voltage and it has own driving procedure that is named as 6-step commutation. The other type of brushless motors is brushless AC motor and it is also called as permanent magnet synchronous motor. This is also 3-phase motor but difference of this type is sinusoidal back EMF. This means that when it is rotating it generates voltage shaped as sinus function. Because of this sinusoidal back EMF it is needed to be powered with the sinus wave voltage and it has own driving procedure that is named as vector control.
When compared with the brushless DC motor, permanent magnet synchronous motors have some important advantages over them. Because of the sinusoidal back EMF, they produce less EMI and their torque output has fewer ripples. Usage of the vector control algorithm also increases the dynamic load performance and this is the reason why washing machine producers use permanent synchronous motors, this motor kind gives the best performance for these kinds of nonlinear loads.
Permanent synchronous motors are synchronous motors and that means that magnetic flux produced with the rotor magnets and the stator windings must be at the same frequency. They also need to be orthogonal (90º) to each other for the maximum torque production.
Servo system that is designed in this project is a digital servo system, this means that its controller is not analog controller, instead it has microprocessor based digital controller. In general, digital servo system can be divided in three main parts, first part is motor driver, second part is controller and the last part is servo mechanic.
First part is the motor driver part and it has sub parts as permanent magnet synchronous motor, electronic commutator and amplifier. Electronic commutator and amplifier take the function of brushes in brushless motors. It calculates the commutation frequency, phase and voltage amplitude, then it generates PWM signals and amplifier amplifies these signals to power the motor phases. Motor used in this thesis is 220V motor and nominal RMP is 5000. It has integrated absolute quadrature encoder with 2500 increment, this makes the resolution of 10000 increments. Encoder is the part of commutation electronics because commutation algorithm needs to know the actual motor angular position in every step. Commutation procedure used in this thesis called as vector control and also named as field oriented control (FOC) algorithm. This algorithm can be summarized in seven steps. 
First step is measurement of the phase currents, only two of three phase currents is sufficient because third one can be found with the usage of the other two.
Second step is Clarke Transform, that converts three phase currents to a two-axis system. This conversion produces i_α and i_β from i_a,  i_b and  i_c.
Third step is Park Transform, that converts two axis orthogonal i_α and i_β system to the new two axis orthogonal system that rotates with the rotor flux. This conversion produces  i_d and i_q currents. I_d current produces magnetic flux and independent from torque production, i_q current produces torque and independent from flux production, this allows controlling the produced flux and torque independently
Fourth step is PID control loop. Control loop includes two different PID controllers, first one controls the i_d current and the second one controls the i_q current, purpose is maket the i_d current zero and track the refference i_q command. I_q controller produces V_q reference as an output and i_d controller produces V_d. 
Fifth step is finding the θ (angular position of the rotor), there are two different methods to find θ. First one is sensorless algorithm and it only uses V_α, V_β, i_α and i_β for estimation. Second method is using absolute positon sensor and reading sensor data, this is also the chosen method for this project because it gives more precision results at the full range of speed.
Sixth step is Inverse Park Transform, that transforms V_q and V_d back to the stationary reference frame using the new θ value, that finds the V_α  and V_β commands.
Seventh and the last step is converting V_α  and V_β commands to the motor phase voltages V_a, V_b and V_c. This is done with the space vector algorithm and it produces the PWM duty cycles to produce the destination voltages.
Second part is controller part and it has also some sub parts as, digital controller board, user interface and digital controller code. Digital controller board designed for this thesis and it includes 32-bit, 150MHz, floating point Texas Instruments C2000 family Delphino series TMS320F28335 digital signal processor (DSP). This board also includes ASRAM, EEPROM, linear and switchmod regulators, analog and digital buffers, two CAN, one RS232 and one RS485 interface, two quadrature encoder interface, analog inputs for ADC, external digital inputs and outputs. Board is six layer PCB and gold plated, all connector pins have ESD and EMI protection filters.
The other sub part of controller is user interface, it is a computer program and used for testing the system and setting some EEPROM parameters. It is written in Visual C# language and communicates with servo system via RS232 port.
More important sub part of controller section is digital controller part, that includes control algorithm and other DSP codes. It has three control loops, first one is speed control, second one is i_q current control and third one is i_d current control. All controllers are digital PID controllers. Speed controller works at the 1 kHz and two current controllers works at the frequency of 1 kHz. Speed controller gives its output to the i_q controller as the reference value, i_d controller works for ragulate the i_d at the zero value.
Servo system mechanic is not explained in detailed in this thesis because it is out of the scope of this thesis. It holds all the mechanics and electronic parts of the servo system together and prevents them from dust and damage.
Last part of this thesis about the auto tuning of the PID speed controller. To control the system, firstly system model needs to be known. Because of the change of the system model with the usage area of the servo system, system model is also needed to found automatically. To find the system model, controller produces excitation i_q signal. Most common used two types of excitation signals are multi-sine and chirp signals. Chirp signal is used in this thesis and its frequency changes between 0,5Hz – 10Hz in 10 seconds, its amplitude is 0,05 which is chosen for not to damage the system with high power vibrations. Numerical method used to find the best fit transfer function parameters and ISE cost function is used for this purpose. System transfer function is first order and so finding the two parameters is sufficient to modeling the system. One of these two parameters (K) are searched at 201 points and the other one (A) is searched at 401 points because it is logarithmic parameter and precision is more important from the other linear parameter that searched at 201 points. Starting and ending points of searching points are found according to the general 750W motor parameters, this means that parameters searched around the parameters of the common motor model parameters. But search area is too wide not to be affected from large parameter changes. Then these system parameters are used to find PID controller parameters.
PID speed controller is found with the usage of cost function like in optimal control. In addition to the ISE criterion some additional rules like overshoot and settling time is used. To protect the PID controller from wind up, anti-wind up mechanism is used. Controller output is saturated to be similar with the real system.
Motor model estimation algorithm and PID auto tuning algorithm is tested via Matlab m-function and results are simulated at the Matlab/Simulink pocket program. Results show that both of model estimation and PID auto tuning algorithms are successful. For the system that has gain of 84 and time constant of 0,1 real K and A parameters of the discrete time model are 0,8358 and 0,99 respectively. Estimated model parameters found as 0,8312 for K and 0,99 for A, step responses of two system is nearly identical. For the worst result, gain error found with the %3,75 error and this is also negligible. 
When auto tuned PID controller's performance is analyzed, it is seen that first controller gives 0,0015 second settling time for %2 band, no steady state error and nearly no overshoot. Second controller is designed for soften the system response and it gives %1,4 overshoot, 0,045 second settling time and no steady state error.