Damage Simulation by Controlling Hydraulic Actuators

İTÜ ELEKTRIK-ELEKTRONIK FAKÜLTESI KONTROL MÜHENDISLIĞI BÖLÜMÜ Damage Simulation by Controlling Hydraulic Actuators License Graduation Project Mustafa Erkam Özateş 040090151 Supervisor: Ali Fuat Ergenç OCAK/2014

Table of Contents ÖZET... 3 SUMMARY... 5 1. Introduction... 7 1.1. Hydropuls... 7 1.2. Literature Research... 8 1.3. Content and Mission... 8 2. Modelling... 9 2.1. System Introduction... 10 2.2. System Identification through Linearization... 11 2.3. Testing the model... 12 3. Control System Design... 13 3.1. Design Criteria and Design... 14 4. Implementation and Test of Design on Real System... 19 4.1. Test of Success... 19 4.1.1. Step Response (Displacement) Test... 20 4.1.2. Vibration Simulation Test... 22 5. Conclusion... 26 6. References... 27 1

Table of Figures Figure 1: Hydraulic Cylinder (MTS) [3]... 10 Figure 2: System Identification Process... 11 Figure 3: Simulink Model for Error... 12 Figure 4: Error of the Model... 13 Figure 5: Root-Locus 1... 15 Figure 6: Root Locus 2... 16 Figure 7: Model Step Response... 17 Figure 8: Model Error for Sinusoid... 18 Figure 9: MTS Control System... 19 Figure 10: Real System Step Response... 20 Figure 11: Iteration Error Decrease... 22 Figure 12: Acceleration Simulation Signal... 23 Figure 13: PSD for Acceleration Signals... 24 Figure 14: Pseudo Damage Calculation in ncode... 25 2

ÖZET Hidrolik silindirler, dikey yönde kuvvet uygulayarak hareket sağlayan eyleyicilerdir. Bu eyleyiciler basınçlı yağın servovalfler aracılığıyla hidrolik silindire uygulanması ile çalışırlar. Otomotiv endüstrisinde dizayn edilen parçaların üretilen aracın beklenilen dayanıklılık kriterlerine uygunluğunu test etmek için çoğunlukla hidrolik simülatörler kullanılır. Benim üzerinde çalıştığım sistemde bu simülatör HYDROPULS olarak isimlendiriliyor. Bu sistem aracılığıyla üretilen otobüslerin bir milyon kilometre dayanıklılık testi üretilen her parçaya ayrı ayrı uygulanıyor. Sıcaklık vs gibi farklı test sistemleri olmakla birlikte bu parçalara hydropuls de titreşim testleri uygulanıyor. Bu tez titreşim testinin uygulanması için kullanılan hidrolik silindirlerin kontrolü üzerine bir çalışmadır. Titreşim testi için temel alınan büyüklük ivmedir. Bu tezde de bir otobüsün bir pist üzerindeki test sürüşü ile test edilmek istenen parçanın çeşitli yerlerinden ivme sensörleri ile toplanan ivme sinyallerinin hydropuls sisteminde hidrolik silindirler aracılığıyla gerçeklenmesi için gerekli hidrolik silindir kontrolüne çalışılacak. Direk olarak ivme gerçeklenemediği için, aslında hidrolik silindirler üzerinde kontrol etmemiz gereken büyüklük konum (displacement) olacak. Konum kontrolü ise bir referans konum sinyalinin (yol sinyali olarak isimlendirilir) gerçeklenmesi için, bir geri beslemeli kontrol sistemi üzerindeki kontrolörümüz olan PİD den servolvalflere giden kontrol işareti ile sağlanacaktır. İleride bu kontrol yapısı ayrıntılı olarak verilecektir. Testi kronolojik olarak açıklamamız gerekirse; öncelikle yoldan toplanmış ivme sinyalleri kısaltılır ve aynı hasarı daha kısa sürede oluşturacak bir ivme sinyali oluşturulur. Bu makina mühendisliğinin alanına girmektedir. Sonrasında bu ivme sinyallerini hydropuls sisteminde test edilen parça üzerinde sağlayabilecek yol sinyali iterasyon ile öğrenme yöntemiyle bulunur. İstenilen ivme değerlerine en yakın yol sinyali bulunduğunda bu yol sinyali ile bir milyon kilometre testi gerçekleştirilir. Hidrolik silindirlerin konum kontrolü bu testin hem iterasyon aşamasında hem de testi gerçekleme aşamasında önemli rol oynamaktadır. İstenildiği gibi kontrol edilen bir hidrolik silindir çok daha kolay bir iterasyon süreci ve test süreci sağlayacaktır. Bu yüzden bizim konum kontrolünü istenilen ivmeyi kolayca yakalayabilecek bir şekilde yapmamız gerekmektedir. 3

Birden çok silindirin birlikte çalışmasından oluşan hydropuls sisteminde her bir silindir ayrı bir kontrolör ile ayrı ayrı kontrol edildiği için, bu tezde üzerine yük bağlı olan tek bir silindirin kontrolü üzerine çalışılmıştır. Sonrasında her bir silindir için tasarlanan kontrolörlerin uygulanması bütün hydropuls sisteminin ivme tutturma performansını arttıracaktır. Hidrolik silindir nonlineer bir sistemdir. Dolayısıyla çalışma aralığımızda silindirin lineerleştirilmiş bir modelini oluşturmamız ve bunun üzerinden çalışmamız gerekmektedir. Sistemin girişi referans yol sinyalimiz, çıkışı ise LVDT sensörü aracılığıyla toplanan cevap olmak üzere seçilmiş hidrolik silindire çeşitli yol sinyalleri uygulanıp cevapları toplanmıştır. Ve bu veriler üzerinden Matlab-System Identification Toolbox ile 0 dan 50 Hz e kadar harmoniklerden oluşan yol sinyalinin en yoğun harmonik içerdiği aralık olan 2 ve 10 Hz etrafında en iyi çalışacak şekilde nümerik yöntemlerle oluşturulmuş bir model elde edilecektir. Simule edilmesi oldukça zor olan bu sinyaller için başarılı ve komplike bir model oluşturulabilmiştir ve bu modelin kontrolü yapılmıştır. Test sürecinin sonunda ise tasarlanan PID kontrolör hidrolik silindirin gerçek zamanlı kontrol yapan donanımı (MTS firmasının sağlamış olduğu bir donanım) aracılığıyla gerçeklenmiştir. Bu gerçekleme sonunda temel alınan cevap kriterlerine yaklaşıldığı ve gerçek bir ivme sinyalinin tek silindir ile gerçeklenmesi sürecinde (iterasyon ve uygulama süreçlerinde) başarı sağlandığı görülmüştür. Simule edilmek istenen hasarın simulasyon başarım oranı, tasarladığımız kontrolör ile yüzde 90 oranında gerçekleştirilebilmiştir. Bu başarı firma tarafından oldukça güzel bir sonuç olarak görülmüş ve bu sayede tasarlanılan kontrolör sistemi ile her bir parça testi başına yeterli başarımlı simulasyonu sağlayabilmek için yaklaşık 10 saat kar elde edilmiştir. 4

SUMMARY Hydraulic actuators creates displacement by applying force vertically. They work by the pressure on the liquid, which is controlled by servo valves. Hydraulic simulators are being used for durability tests especially in automotive industry. The system, I am working on is called HYDROPULS. Every single manufactured component is tested by hydropuls for their durability against vibration. There are also other testing systems, which are for temperature etc., but the most important test is the vibration test. This thesis is about the control of the hydraulic actuators, which are used in hydraulic simulator systems for vibration tests. The main unit of the vibration test is acceleration. In this thesis I will work on the control of a hydraulic actuator, which is used in hydropuls system, where acceleration signals from real roads are collected via acceleration sensors on the components to simulate in hydropuls system. What we can directly create is displacement but not acceleration. Therefore what we want to control on hydraulic actuator is actually the displacement. This control is done by the control signal, which comes out from a PID controller to the servo valves, where the reference is the drive signal, which is created by an iteration process. Chronologically the test process consist of following steps. Firstly the acceleration signals, which are collected from real world roads are summarized to apply the same damage in a shorter time period. After that, a drive signal, which can simulate this acceleration signal in hydropuls, is generated by an iterative learning computer system. When the most successful simulating drive signal is found, the test process is done with this signal. Note that the drive signal is the displacement signal. The displacement control of hydraulic actuator has got an important role for the iteration process as well as for the test process itself. A qualified control system will maintain an easier iteration step and also a qualified test process. Therefore we have to design a displacement control system, which will maintain a qualified acceleration simulation. Hydropuls system includes more than one hydraulic actuator. Every single one of them is controlled individually. In this thesis, I will control a single hydraulic actuator with a load on it. When this study is maid for all of the hydraulic actuators, than the effectiveness of the whole hydropuls system for vibration simulation will increase. 5

Hydraulic cylinder is a non-linear system. So we have to find out a linearized model and work on that. For this purpose, several reference drive signals and the LVDT output of the system are used to generate an approximate model with the help of Matlab-System Identification Toolbox. The system is linearized around 2 and 10 Hz, where most of the harmonics of the drive signals exist. A successful and complex model is found out and a controller design for this model is made. At the end, designed PID controlled is implemented to the system via continuous time controller hardware of MTS company. In testing part, it is found out, that the projected time characteristics criteria of the response is nearly achieved. And also a desired acceleration signal is simulated with success in iteration and testing process. The pure damage amplification of the simulation has got a success of simulation about 90%. With this success, instead of manually tuned pid controllers, the testing company can gain averagely 10 hours for a single test process. 6

1. Introduction Hydraulic simulator systems are commonly used systems in vibration testing especially in automotive industry. Now a specialized hydraulic simulator system for Mercedes-Benz (so called Hydropuls) will be explained. After that in section 1.2. scientific literature about this topic will be adverted. And in section 1.3. mission and content of this thesis will be explained. 1.1. Hydropuls As a leading automotive company Mercedes-Benz makes many kind of tests for its products' components. Vibration testing is the most important one of them, since a dynamic product like a car or a bus is mostly hurt by vibration. The hydropuls system of Mercedes-Benz is a system to simulate a road's vibration to a component to test the component's durability against vibration. Testing in hydropuls system has got following steps. Firstly: Because the measurable unit for vibration is acceleration, acceleration signals of three dimensions are collected from different points of component via acceleration sensors. Secondly: The required displacement signal to effectuate this acceleration is gathered via iteration process. Iteration process is made to find out the displacement signal, which is most successful at simulating the acceleration and the easiest one to implement, from infinite possible signals. Finally: The most successful displacement signal, which is found out at the end of the iteration process, is played through the hydropuls system so many times as it is needed to simulate the damage that will exist in the desired life time of the component. The most important thing is, in every step of this testing in hydropuls system, the displacement control to achieve an acceleration signal (in the iteration process and also real testing process) is made through a feedback control system. In my thesis, this displacement control system is designed successfully. 7

1.2. Literature Research In this thesis, a pid controller is designer for needed displacement control. Some kind of control methods for hydraulic testing systems are summarized in [1]. From that paper, we can understand that even with p type control systems some hydraulic cylinders can be controlled. But in [2], we see, that PI type control systems has got some advantages for hydraulic displacement control systems, like erasing the steady-state error. But it is cleared, that pid control systems are commonly used for displacement control for hydraulic systems, especially for controlling so rapid accelerations as in our case. 1.3. Content and Mission As mentioned before, the quality of displacement control effects the quality of every single step of the testing process in hydropuls. When the displacement is not controlled acceptably, than the iteration process for creating the displacement signals will fail eventually. Or a displacement signal, which is not successful, will be played to generate the desired acceleration signals. And at the end, because the desired acceleration signal, which is collected from real road test, cannot be simulated successfully, the damage simulation would also be unsuccessful. Therefore the main mission of my study is to design a successful control system for the hydraulic cylinders in hydropuls, so that a successful test process will be done. This thesis includes following content for this purpose. Firsly the modelling of the system will be thought. And also how a linear model is found out for a nonlinear system like a hydraulic cylinder will be explained. Secondly the design criteria for this system and how the PID is designed will be explained. Finally, the test of the design will be presented, while explaining how the test of success is done. And the conclusion will be reported. 8

2. Modelling In this section, we will talk about our system, which will be controlled. As explained before hydropuls system is a very complex system, which simulates acceleration signals in 3 dimensions for a whole component. Hydropuls system consist of several hydraulic cylinders. The number of hydraulic cylinders in each dimension changes according to the tested component. And every single hydraulic cylinder is controlled individually with its own control hardware. In my thesis, I studied with a single hydraulic cylinder for a single dimension. But if the results of this thesis is implemented to every one of them, than the success of whole hydropuls system for simulation will increase, as the single one's success has increased. Now let's introduce the hydraulic cylinder system. 9

2.1. System Introduction Hydraulic cylinder (MTS) [3] Figure 1: Hydraulic Cylinder (MTS) [3] A hydraulic cylinder itself is a very complex system, but what we need for displacement control is only a model of the system, that can simulate output of the system in digital world. System's input is the displacement signal, which is played by the computer through the controller to the servo valves on hydraulic cylinder. Serovalves supply the required liquid exchange on the hydraulic cylinder. And the movements of hydraulic cylinder is measured via LVDT sensors on it. Analytical modelling of all these physical parts of the system is quite difficult. Besides, the hydraulic cylinder is not a linear system and this is another hassle [3]. Instead of that, we can generate an approximate model using System Identification Tool of Matlab. 10

2.2. System Identification through Linearization In approximate system modelling with numerical methods, we actually generate a relation between input and output of the system. Besides we have to run the system in all possible working areas, so that a successful model can be generated. But in this case, we have got a non-linear system. That makes it impossible to generate a steady transfer function. Because the approximation to transfer function varies up to input's working area. I generated input signals, which include almost the whole working space. These are some step signals and some sinus signals from 0 Hz to 50 Hz with 0 mm amplitude to 20 mm amplitude. These are the possible signals, than can be physically played in hydraulic cylinder. Although every possible input is used, because of the reasons, I have told in first paragraph, the system identification process is done largely using the most commonly used sinus waves in the harmonics of the displacement signals. So that, the linearization is done around these working points. And after an iterative process the linearized model of the system is found out numerically. Figure 2: System Identification Process 11

2.3. Testing the model In the end of system modelling process we get a successful model for our closed loop system. From that model I calculated the open loop transfer function with initial knowledge, that I played the signals with only P=5 controller condition. It had to be done like that, because the hydraulic cylinder itself cannot be run in open loop. The generated open loop transfer function of the hydraulic cylinder is like that: Now this model has to be tested to find out, if the model's output for a specific input equals or almost equals to the output of the real system. For this purpose a Simulink model is designed as below. (In this model, the pid has got P=5 condition, with a saturation, that is a condition about the controller and servo valves to be explained in [5] and [6].) Figure 3: Simulink Model for Error Here the difference between the output of the model and the real system is calculated and plotted in scope, which is named hata. And for several kind of signals an error plot as below is obtained. This one is for the sinus signal with 5Hz 1 mm. 12

Figure 4: Error of the Model As you can see, the error values are acceptable for a model. So we found out, that this model can be used for designing the controller. 3. Control System Design Now we have a transfer function, which simulates the hydraulic cylinders open loop behavior in a successful way. But an important point is, that this transfer function is a quite complex transfer function, with three zeroes and four poles. Normally in general conditions, in such a case, many of the zeroes and poles, which are not in dominant area, may be cancelled. But in our case, the model is so fragile, that almost none of them can be cancelled. This is experimented in the Simulink model in 2.3. and found out that if any of the zeroes or poles is cancelled, than the modelling error, which is tested in 2.3., dramatically increases. Therefore we have to use this model without any simplification. 13

3.1. Design Criteria and Design Firstly it should be underlined, that in this thesis our overall goal is to create a successful simulation system for vibration. But to achieve required acceleration signal for vibration simulation, we have to design a displacement control system, which is successful in vibration simulation. Because the step response time domain characteristics are most familiar one to our control system design culture, I used overshoot and rise time as the most important criteria in the design process. Besides of course zero steady state error is also expected from this control structure. But still, which of the time characteristics is mostly effective to acceleration simulation success is a question, because the relation between acceleration and displacement has got two times derivation process. But with an experimental method, I found out, that when the overshoot is zero and rise time is the minimum possible one, than the acceleration simulation success also increases. Another point is, that we have more than one criteria and they are all effective for vibration simulation success. So we cannot limit one with respect to another. Therefore we have to make a general approach with considering all of design criteria. In that approach, we cannot define precise time domain characteristics values. Therefore in this study I considered the mentioned ones as the most important ones and made this approach to design a successful pid controller. For this purpose I have used the graphical tuning in root-locus editor of Matlab siso-design tool. Below are the final root-locus graphic and corresponding step response of the model: 14

Figure 5: Root-Locus 1 As you can see in this image, there are poles of the system in a very wide area. We are focusing in the squared area for our design, but of course keeping the conjugate operation points in stable area (on left of imaginary axis). 15

Figure 6: Root Locus 2 As you can see in the image, the dominating area is also quite complex with two system poles at unstable side, but thanks that the zeroes of pid controller bring the operating points to stable area. Even the operating points are very close to the zeroes of pid controller, because of the relationship of the wider operating points with gain about being in stable area. The qualified working area of the controller is around this root locus situation. 16

Figure 7: Model Step Response In this response, which is the best possible response with the approach, which is explained before, the overshoot is 0.0175 mm and rise time is nearly 0.43 seconds. On the other hand, settling time is very big, although there is no steady state error. Using this design on the model that we have created via system identification, we can lastly experiment how good is displacement control system working for a sinusoidal input. 17

The error of output system with designed pid controller for a sinusoidal input with 1 Hz frequency and 1 mm amplitude (this is a quite fast signal for a normal reference tracking problem and a commonly used harmonics in our signals) is below: Figure 8: Model Error for Sinusoid 18

4. Implementation and Test of Design on Real System First of all, it has to be underlined, that a system with big signal values has to be controlled with specifically designed controller systems, because it is not an easy hardware work to perform a continuous control signal to a servo valve as in our hydraulic cylinder system. Under these circumstances a specifically designed continuous pid controller system has to be used [4]. This is a controller of MTS, which is designed exactly for this hydraulic actuator with these servo valves. You can see the model of this system in the picture below. There is also an active feedback for load cell output in this system, but in our case it is not used. Figure 9: MTS Control System 4.1. Test of Success After engaging the controller with our design, we have to make a test to look up if the design is a successful design or not. There are two step of testing in this situation. The first one is to test the step response of the real system, so that we can understand if the displacement controller design works as we want. The second step is directly concerned about the success of our main goal. This is to make the iteration process, which is thought in 1.1. and test the success of this process as well as the success of the simulation of the acceleration signal, which is collected from real road. 19

4.1.1. Step Response (Displacement) Test You can see the collected step response displacement signal from LVDT on the real system overlaid with the reference step input. There is two times step input in 8 seconds. 20 Figure 10: Real System Step Response

As you can see on this plot, there is a steady state tracking error or a very big settling time on these step responses. Because of the model output, we have taken from Simulink model in section 3.1., this may look like a steady state error because of the big settling time. Another point is that we have given a step reference with amplitude of 6 mm but not 1 mm as in the model. In that case, the overshoot is awaited as 6*0.0175 mm, which equals almost 0.1. In the real response, we get an overshoot value as 0.08 mm, which is quite close to our awaited value, but because of the possible modelling error, that is seen in section 2.3. there may be such a difference. It is not seen in the picture, but there is actually a dead time in the step response about 0.02 seconds, which is added to the modelled step response of the system. If we calculate the rise time considering this un-modelled dead time response, the rise time is about 0.16 seconds. This is a quite faster response than we have modelled. One reason for that is the dead time another one is the conventional modelling error. Nevertheless these time domain characteristics values are qualified values for a displacement control system. 21

4.1.2. Vibration Simulation Test Now let s look at the main goal of our thesis and test if the vibration simulation of the real vibration (acceleration) signal, which is collected from real world, is done with how much success. Firstly the iteration process has to be done, to generate a proper drive signal (displacement signal) which ensures the desired acceleration signal. After the iteration process, the final drive signal will be played for test. On the picture below you can see the vibration simulation error decrease during the iteration process. Figure 11: Iteration Error Decrease On the picture below, you can see a cutaway of the desired acceleration and simulated acceleration signals during the final simulation process, which is done by the final drive signal, generated by the iteration process.here the y- 22

axis is the acceleration axis with unit g. Red is the desired and blue is the simulated acceleration signals. Figure 12: Acceleration Simulation Signal You can see on this signals, that nearly the desired acceleration is kept by the simulation. 23

And below you can see the PSD (Power Spectrum Density) of the simulated and desired acceleration signals. Red is the desired and blue is the simulated acceleration signals. Figure 13: PSD for Acceleration Signals In this graph, it is also seen that the corresponding amplitudes to the frequencies with a range from 2 to 35 Hz are almost the same in the Power Spectrum Density. 24

As it can be observed in time domain as well as frequency domain, the simulation success of the system for vibration is good. But we have to determine an analytical success criteria, which can show us how good we have simulated the vibration data, collected from real world. Here comes the concept pseudo damage, which shows the damage simulation effectiveness, in case the damage is created by vibration as in our case. It can also be called as amplified pure damage. This calculation is done by the ncode flow as below, which is in mechanical engineering field and can be talked separately. In our case, the pseudo damage value created by the desired acceleration signal is 7.66, and the damage amplified in our simulation is 6.97. That means we have had a success of 90% in simulation for damage caused by vibration. It is a valuable success in that field, where generally success by the manually tuned controllers can only be around 80% and therefore longer recurrence of simulation is required. Figure 14: Pseudo Damage Calculation in ncode 25

5. Conclusion In this thesis, a linearized model of a nonlinear system is generated with an approximate modelling approach. A controller design approach for displacement control is done, where the main physical reality to control is acceleration. And lastly this controlled is tested on real system to find out if the acceleration control and damage simulation process is done with success. Firstly, that is cleared that instead of manually tuned pid controllers in industry, a control engineer can make an analytical design approach to increase the quality of controller. And this approach will also increase the success of damage simulation in systems like our hydropuls. Additionally the iteration process, which is needed to generate a controllable kind of signal like displacement, in vibration simulation systems will also be easier if the displacement controller is a well-designed one. For a test process of a component, to test the damage applied by vibration, averagely 60 hours of testing time is required. This time increases proportionally with the pseudo damage success. In that case a qualified controller would supply a big profit of energy in testing process. By the way, we have also found out, that digitally generated approximate models can be simply used for controller design for complex systems. Also it can be concluded that although a non-linear system like a hydraulic cylinder can be controlled with a continuous pid controller, another approach of control method (like a generically changing adaptive controller) could increase the success. 26

6. References [1] Plummer, A. R. (2007). Control techniques for structural testing: A review. Proceedings of the Institution of Mechanical Engineers, Part 1: Journal of Systems and Control Engineering, 221(2):139-169, 2007. [2] Tuncelli, A. C., Güner, H. and Longchamp, R. (1990). Hydraulic axis control using pressure feedback. IEEE International Workshop on Intelligent Motion Control, Boğaziçi University, Istanbul, 20-22 Ağustos. [3] MTS System Corporation, RTM No. 211177 (1999). Series 244 Hydraulic Actutators. 100-016-993 HydAct244-01 Printed in U.S.A. 8/99 [4] MTS System Corporation, RTM No. 211177 (2009). Servovalve Service Intervales. 100-192-047a ServovalveIntervals Printed in U.S.A. 8/09 [5] MTS System Corporation, RTM No. 211177 (2012). Servovalves. 100-241-355 Servovalves Printed in U.S.A. 11/12 [6] MTS System Corporation, RTM No. 211177 (2012). Series 252 Servovalve Product Information Manual.011-182-903 H November 1999 27