Aktif süspansiyon sistemine ters optimal kontrol yaklaşımı
Inverse optimal control approach for active suspension system
Yazar: SADIK KIVANÇ SÜNGÜ
Danışman: PROF. DR. MÜJDE GÜZELKAYA
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / Kontrol Mühendisliği Ana Bilim Dalı / Kontrol ve Otomasyon Mühendisliği Bilim Dalı
Derece: Yüksek Lisans, 2022
Konu: Bilgisayar Mühendisliği Bilimleri-Bilgisayar ve Kontrol = Computer Engineering and Computer Science and Control ; Mühendislik Bilimleri = Engineering Sciences
Dizin: Aktif süspansiyon = Active suspension ; Kontrol yöntemleri = Control methods ; Motorlu taşıtlar = Motor vehicles ; Optimal denetim teorisi = Optimal control theory ; Optimal kontrol = Optimal control ; Optimallik = Optimality ; Süspansiyon sistemleri = Suspension systems ; Tekerlekli taşıtlar = Wheeled vehicles

Özet:
Araç süspansiyon sistemleri, temel olarak yoldan kaynaklı olan her türlü etkiyi araç gövdesinden ve yolculardan izole etmeye yarayan, alçak geçiren filtre gibi diyebileceğimiz, şasi elemanlarıdır. Otomotiv teknolojisinin ilerlemesi ile araçlardan artan beklentiler dolayısıyla, sürüş güvenliği ve konforu konusundaki anahtar parçalardan biri olan süspansiyon sistemlerine olan ilgi de artmıştır. Temel olarak esnek bir yay ve sönümleyici elemandan oluşan süspansiyon sistemleri aktif, pasif ve yarı aktif süspansiyonlar olarak üç kategoriye ayrılabilir. Nihayetinde üç tip süspansiyonun da temel görevi sürüş konforu ve güvenliğini sağlamaktır.
Pasif süspansiyonlar; maliyetlerinin az olması, enerji ihtiyacı olmaması, çok fazla yer kaplamamaları ve denge çubukları ile kullanıldıklarında güvenlik anlamında sorunsuz olmaları sebebiyle endüstride sıkça kullanılmış ve günümüzde de bu yaygın kullanım devam etmiştir. Fakat özellikle lüks segment araçlarda, sağladıkları konfor belli frekans aralıklarıyla sınırlı kalmakta ve her şartta aynı başarımı gösterememektedirler. Bu sebeple yarı aktif süspansiyon ve sisteme aynı anda hem kuvvet girdisi ekleyebilen hem de sistemden enerji çekebilen aktif süspansiyonlara olan ilgi zamanla artmıştır. Bu çalışma da ilgili başarım kriterlerini gerçekleştirmek için en avantajlı süspansiyon sistemi olan aktif süspansiyon üzerine yoğunlaşacaktır.
Aktif süspansiyonların kontrolü için geçmişten günümüze birçok kontrol yöntemi önerilmiştir. Bu yöntemlerden biri de optimal kontroldür. Önceden belirlenmiş olan başarım ölçütlerine karşı düşen en uygun kontrol yasasını bulmak olarak tanımlanacak olan optimal kontrol, bir regülatör problemi olan aktif süspansiyonlar söz konusu olduğunda da literatürde kendine sıkça yer bulmuştur. Fakat regülatör problemlerinde optimal çözümü analitik olarak bulabilmek için Cebrik Riccati Denklemleri'nin çözülmesi gerekir ve bu çözüm, oldukça zordur.
Ters Optimal Kontrol yaklaşımı, geleneksel optimal kontrol yaklaşımının aksine önceden belirlenmiş bir maliyet fonksiyonu için uygun kontrol kuralını hesaplama problemi değil; önceden belirlenmiş olan bir kontrol kuralının minimum yaptığı maliyet fonksiyonunu bulma problemidir. Önceden belirlenmiş olan bu kontrol kuralı, Lyapunov Kontrol Fonksiyonu adı verilen özel bir fonksiyon kullanılarak bulunur ve bu fonksiyonun varlığı, sistemin stabilize edilebileceğinin bir göstergesidir.
Bu çalışmada da aktif süspansiyon sisteminin konfor ve sürüş güvenliği isterlerini karşılamak adına, ters optimal kontrol metodu kullanılmıştır. Bu metot ile tasarlanan iki tip kontrolör, yine durum geri beslemeli kontrolör tipleri olan Doğrusal Matris Eşitsizliği tabanlı kontrolör ve Doğrusal Kuadratik Regülatör kontrolör ile karşılaştırılmış ve bu kontrolörlere alternatif olabileceği gösterilmiştir.

Abstract:
Nowadays, with the increasing requirements and expectations for vehicle performance metrics, suspension systems become a key element for vehicle's road handling and comfort of occupants by isolating them from road noise, shocks, vibrations, etc. A well-designed suspension system can fulfill all these requirements effectively. Basically, the vehicle suspension system consists of a spring and damper element to ensure the balance of force between the vehicle body and the road and to filter road noise. Suspension systems in vehicles can be categorized into three types: passive, semi-active, and active suspensions. Ultimately, all these types are utilized for assuring two essential criteria: driving comfort and safety.
Many factors play a role in evaluating passenger comfort performance. These can be thought of as the driver's condition (age, health, physical characteristics), vibrations, and noises in the vehicle chassis. Although the driver's condition is an uncontrollable factor outside of the control system framework, chassis vibrations and noises are problems that can be solved by a well-designed suspension control system. Therefore, passenger comfort can be directly related to isolating/filtering road noise from the vehicle body. It can be said that passenger comfort is also very effective in maintaining the driver's focus and in the driver's performance.
Road handling is a performance criterion related to the contact of the vehicle's tyre with the ground, and it is very important for filtering road noise. On the other hand, it is critical for the vehicle to continue driving without tipping over and is directly related to the tire load.
Passive suspension has been widely used in automotive, due to the low cost and not requiring any control effort. And although anti-roll bars are commonly integrated with passive suspensions, this system is not capable of providing both road holding and vehicle comfort at the same time. Although the high damping ratio provides good comfort at low frequencies, it cannot filter out high-frequency road noise. On the other hand, the low damping ratio can filter out high-frequency road noises but provides poor comfort. A high damping ratio performs very well in road handling in low frequency; however, it fails in medium frequency road noise; a low damping ratio provides safer driving in mid-frequency noises but fails in other ranges.
All in all, good road holding, and comfort cannot be achieved at all frequencies, and there exists a trade-off among these with a constant damping ratio, the interest in passive suspensions has turned to semi-active and active suspensions over time. Suspensions can be divided into three categories as passive, semi-active, and active suspensions in terms of their dynamics.
In this study, suspension systems, one of the most important elements in the driving safety and comfort of the vehicle, were examined. Passive, semi-active, and active suspension systems used from past to present are explained and their advantages and disadvantages are mentioned. It has been underlined that the main control problem in
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suspension systems is to stay within the suspension's range of motion and to provide the most comfortable ride without compromising driving safety.
In order to solve the related control problem, active suspension systems are presented, and control-oriented modeling is made. It has been underlined that the active suspension is in a more advantageous position than other suspensions because it can actively generate force and dissipate energy from the system, but it also consumes energy actively and its structure is complex.
In literature, there are many control methods proposed for this problem. Sliding mode and backstepping control performed well in models with nonlinear elements, especially in actuators. With the increasing interest in fuzzy logic research, various control methods have been brought to the literature. The fuzzy controller, designed without a model, considering the nonlinear dynamics of the actuators, is improved by predicting and tyre deflection feedback.
One of the most popular control methods used in active suspension control is Linear Quadratic Regulator controllers. Linear Quadratic Regulator is performing very well in filtering out road disturbances, it performs even better when fed back with state derivatives, resulting in a significant increase in driving comfort.
When Linear Quadratic Regulator is mixed with H-Infinity control, really good performance is obtained even in possible sensor errors, showing that a safe and comfortable drive is possible not only for the nominal situation but also for the error conditions.
A combination of Linear Quadratic Regulator and non-linear back-stepping techniques gave good results, especially in the presence of non-linear actuator dynamics. In cases where the system matrix can be reversed, the Linear Quadratic Regulator variation, in which the feedback of the state and output derivative is used instead of the regular state feedback, has been found to be applicable and effective as a result of the simulations.
For this control problem, optimal control is also widely used in literature. The optimal control problem is, to put it simply, to find the most appropriate control law for a given system and performance criteria. These performance criteria are usually expressed as a function and include the observable states of the system and the energy consumed. In this method, performance criteria are embedded into cost function and the Hamiltonian expression utilized to obtain the optimal control law. In order to find the control law analytically, the Algebraic Riccati Equation is needed, and it is very well known that this equation is very difficult to solve.
To tackle this difficulty, an inverse optimal control approach is presented in this study which can be utilized to avoid solving this equation. In the inverse optimal control approach, instead of finding a control law that minimizes a given cost function priori, the cost function that a predetermined control law makes optimal is subsequently created. The Lyapunov Control Function is used when creating the control law and the presence of this function means that the system can be stabilized.
In order to apply the inverse optimal control method to the active suspension system, the system is first discretized and the analytical expressions determining the comfort and road handling, while searching the positive defined symmetric matrix P, are embedded into the cost function. The search of P is handled via Big Bang-Big Crunch
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algorithm which is an easily configurable global optimization algorithm with adequate speed.
Obtained positive symmetric P is then utilized to calculate the inverse optimal control law which showed very superior performance compared to the passive suspension in all criteria when noisy road input (according to ISO8608 standards) is employed.
In addition, speed bumps having different characteristics depending on the vehicle speed are employed during the tests as well. It's concluded that active suspension with inverse optimal controller provides a safer drive experience with increased comfort at all speeds.
Based on the state feedback gain of the designed inverse optimal controller, another modified inverse optimal controller is obtained, this time the estimation of the next state is used while providing state feedback. This method even outperformed the standard inverse optimal method, by the cost of energy consumption. Body acceleration was greatly reduced, suspension deflection remained within suspension travel range, and tire deflection was kept in the safe zone. Although it has increased the energy consumed, this method may also be preferred according to the electrical possibilities of the system to be designed.
Later, two inverse optimal controllers are compared to Linear Quadratic Regulator and Linear Matrix Inequality based controller with state and output derivative feedback and they are proven to be sufficient considering all the performance criteria.
As a result, inverse optimal control is shown to be a decent alternative for the other state feedback controllers in terms of performance, ease of design, not requiring any additional toolbox in the design process, and not requiring Algebraic Riccati Equation solution, which is very difficult to obtain.