HO CHI MINH CITY UNIVERSITY OF TECHNOLOGY AND EDUCATION FACULTY OF INTERNATIONAL EDUCATION PROJECT REPORT MODELING AND CONTROL OF ACTIVE AIR SUSPENSION SYSTEM OF 2011 PORSCHE CAYENNE H
INTRODUCTION
The research justification and necessity
The suspension system, among other dynamic systems, plays a critical role in modern automotive engineering which means a great deal in terms of handling, ride quality, load capacity and the overall performance an automobile One would argue that a version equipped with air spring or air chamber can guarantee the enhanced performance and push beyond the limit of an ordinary suspension system, for instance, Land Rover offers products with the electronic, adaptive and height adjustable air suspension to ensure that the driving experience is enhanced Another prime example of this system would be the Airmatic suspension system of Mercedes- Benz, which emphasizes the pneumatic (air) nature of the system and focus on automatic operation prompting a comfortable ride Therefore, it is the essential norm for these luxury and high-performance automotive brands to develop and facilitate their products with either semi-active or active air suspension system and Porsche would be of no exception With an open mind set and eager to learn more about air suspension system, we as a team of two are looking forward to the humble contribution to this automotive field by the means of conducting research in the air suspension system of the 2011 Porsche Cayenne
In this research, the modeling and simulation of air suspension will be presented We will develop the control block diagram in SIMULINK based on the control unit diagram of air suspension system considering all the existing parameters After that we will apply the vehicle parameters to Carsim and run simulation based on SIMULINK control block diagram.
The main purpose of the project
The purpose of this paper is to demonstrate the modeling and simulation of the air suspension system of 2011 Porsche Cayenne This includes designing block diagram control in Matlab SIMULINK using PID controller The acting force and displacement of wheels and air springs of an automobile are formulated and included in the analysis whenever necessary The simulation will be conducted after the successful modeling of the air suspension system in order to evaluate the responsiveness and damping force.
The objective of the project
• Understanding the theoretical basis of the air suspension system, particularly the semi-active air suspension of 2011 Porsche Cayenne
• Developing and establishing the parameters along with control strategy of the air suspension for building block control diagram
• Modeling the air suspension system in Matlab SIMULINK and comparing results of different configuration of the system.
The research methodology
• Reference from material for data, parameters and specifications
• Control logic analysis for building block diagram
• Mathematical model development: simulation, trial and practice.
The limit and scope of the project
The project solely focuses on the modeling and simulation that involves all parameters, damping force actuation and responsiveness of the air suspension system of only 2011 Porsche Cayenne Once the block control diagram is completed, those data will be used for a desirable and optimized simulation in Carsim The outline of this article is as follows:
• Chapter 1: Introduction: The purpose and objective of the project
• Chapter 2: Literature review: a critical and informative summary of some research papers and articles relating to modeling and simulation of air suspension system
• Chapter 3: The structure and operating principle of the air suspension system of Porsche Cayenne: explain design and function, control unit and sensors
• Chapter 4: Modeling the air suspension system: building block control diagram in Matlab SIMULINK and performing simulation in Carsim
• Conclusion: further application and reflection on the objective of the project, summarize the role and performance of the air suspension system
• Reference: a summary of all sources of materials, research papers about modeling air suspension.
LITERATURE REVIEW
Introduction of independent air suspension
The air suspension can be considered to be the pinnacle of automotive suspension system owing to the fact that it is the system utilizing the pneumatic characteristic and high versatility to improve the performance and handling of an automobile The air suspension is notable for its advantages such as adjustable ride height, customizable comfort, and automatic leveling because the majority of air suspension is electronically controlled and equipped with various sensors for the best response times possible, usually in millisecond Therefore, a great number of high-performance and luxury automotive brands keep pursuing the implementation of active or semi-active air suspension in their product ranges The same thing can be said about the Porsche Cayenne and its air suspension furnished with PASM, which can be considered a semi-active suspension system This system utilizes the air spring instead of steel spring and serves as a benefactor of the compelling harmony of both comfort and sportiness, the active adjustment of ground clearance based on operating conditions, the self-leveling features, reduced drag, and improved driving dynamics Such benefits are most likely to satisfy the target customer of Porsche SUV segment.
Literature review
First and foremost, the active air suspension can be considered more advanced and more versatile, dealing better with terrain compromises compared to the conventional passive suspension with a configuration of a spring and a damper The main reason resides in the system configuration of the active air suspension which comprises of the air springs (pneumatic) consisting of chambers (air), dampers (fluid) and control valves in each individual wheel, an air reservoir (air tank containing of adequate capacity for storage), an air compressor with integrated air drier and a solenoid valve block housing a set of control valves and pressure sensors, all working in harmony to fulfill the tasks of distributing, venting, filling the compressed air all the way in the system in accordance with the demand of drivers Therefore, modeling the active air suspension system requires additional parameters compared to the conventional counterpart such as the pressure, effective area, spring rate and volume of both the air springs and air reservoir, all of which can be studied in the “An Analytical Study of the Performance Indices of Air Spring Suspensions Over the Passive Suspension” by M M Moheyeldein*, Ali
M Abd-El-Tawwab, k A Abd El-gwwad, M M M Salem from faculty of Engineering of Minia University, Egypt and “Parametric analysis of vehicle suspension based on air spring and MR damper with semi-active control” by
Mortda Mohammed and Mohammed H R Alktranee As for the 2011 Porsche Cayenne, such parameters can vary by a little degree due to the proprietary control strategy and technical information can be considered in the “Testing and calculation of vehicle adaptive suspension air springs” by D Yurlin and “The closed air suspension system of the Porsche Panamera Vehicle Dynamics Expo
22 - 24 June 2010 at the new Messe, Stuttgart” presskit by Dipl.-Ing Torsten
Nitschke, Aktive und Passive Federungssysteme, Dr Ing h c F Porsche AG.There are various approaches to the control strategy of air suspension, ranging from pid, fuzzy, LQR to H infinity That the most commonly implemented is PID due to its versatility and the easy-to-approach characteristic can be studied in “Modelling simulation and control of an active suspension system” by CHAITANYA
KUBER from the Department of Mechanical Engineering, Sinhgad College of Engineering, Pune, Maharashtra, India and “Modeling and Simulation of PID Controller-Based Active Suspension System for A Quarter Car Mode” by
Nguyen Van Trang and Duong Nguyen Hac Lan The former research shows a generalized method of selecting the K gain value for PID controller while the latter specializes in determining parameters via Graphical User Interface (GUI)
However, these two research papers only illustrate and deals problems with the modeling of the active suspension of spring-damper configuration and that means active Pneumatic suspension system in passenger cars” by FRANZ Davide –
Master of science in mechatronic engineering, Academic year 2018/2019 from Politecnico Di Torino – Department of Control and Computer engineering and
“Experimental and Theoretical Study of Air Suspension System Control for Passenger Vehicles by Using PID and Fuzzy Controllers” by HAIDER JABAUR
ABID and Ameen Ahmed Nassar are more than capable of reaching Both of these research papers focus on modeling the active suspension system, the former exceling at hydraulic damping property of the pneumatic active suspension model in Simulink as well as the mathematic modeling of various versions of air spring configurations Both research papers cover the thorough analysis and methodology of fine-tuning the PID controller for the plant of modeling simulation
The listed research papers may have their own way of conducting assessment of the simulation result, some of them is lacking the property of air suspension system while the other features redundancy to a certain degree In order to sum it up and process an informative discussion and thorough analysis of the simulation results,
“Testing and calculation of vehicle adaptive suspension air springs” by D
Yurlin and “Method for Determining Accurate Initial Air Pressure Range of
Air Suspension Airbag Based on Vehicle Ride Comfort Simulation Analysis” by Quan Zhou are worth looking up The former features the exact air suspension modeling of Porsche system with analysis and formula of relevant parameters, matching our group’s expectation and the latter focuses on the assessment of simulation result of those parameters.
Conclusion of literature review
In conclusion for the literature review, acquiring the parameters for the active air suspension and utilizing those parameters in mathematical model via pneumatic and polytropic equations will bring about the accurate modeling as well as simulation of the proposed air suspension system of 2011 Porsche Cayenne The reviewed research articles have shown that there are numerous methods of fine-tuning the K- gain values for PID controllers as well as various unique simulation properties of an active air suspension system which are accountable for the performance, road handling and ride comfort of the air suspension system such as air spring pressure and volume, air reservoir pressure and volume, variable damping force and air spring rate which are dependent on the selected driving modes With all of that being stated, those sources of data and researches will serve adequate, sufficient purpose in our project of modeling and simulation of the semi-active air suspension system of 2011 Porsche Cayenne.
THE STRUCTURE AND OPERATING PRINCIPLE OF THE AIR
Overview of the active and semi – active air suspension system
The suspension system is a critical chassis system, serving as a dynamic medium and a connection between the body of the vehicle (sprung mass) and the chassis system (unsprung mass) The suspension system has been developed and refined constantly, aiming to reach the balance of both comfort and road handling capability Early and conventional suspension configuration mainly comprises of sa spring with a constant (fixed) stiffness and a damper (shock absorber) with a constant (fixed) damping coefficient, this configuration was the passive suspension system and did a decent job in providing a fairly good handling property, but was not that good at the ride comfort property Automotive manufacturers would later develop new method to address the shortcomings of the passive suspension; most notably, by adopting a spring capable of variable stiffness, for example, air spring, and implementing a damper with adjustable damping force and a controller with the aid of sensors to govern all of the listed characteristics
Advanced suspension technology can equal adjustable and variable ride height as well as the variable damping force Those factors are implemented seamlessly into the advanced suspension system and the automotive manufacturers can fine – tune whatever response and characteristic they are looking forward to in their vehicles, this also results in a wide variety of the adaptive, advanced, and self-leveling suspension system with numerous proprietary designated names
Such innovative approach in developing new suspension system regarding the harmonic and satisfactory combination of ride comfort and road handling capability comes in the form of the adaptive, semiactive, and active suspension, by and large, they are all categorized into the active suspension system (ASS) to distinguish themselves from the passive suspension system This particular system comprised of a wide variety of setup, configuration, damping actuation and linkages types as shown below
Figure 3.1 The ASS components and their variations
As can be seen in the illustration, there are various combination of components in an ASS This project focuses solely on one of the more common type of ASS configuration aiming to fulfill the requirement of both ride comfort and road handling capability, which is the ASS consisting of spring with variable stiffness, damper with adjustable damping force, active hydraulic components; all in either (independent) multi-link or double-wishbone form factor Such configuration of ASS should be able to guarantee the ride quality as well as ride comfort for the passengers, helping to insulate them from all the undesirable noise, vibrations, and harshness caused by the road anomaly and disturbances The one of many factors that help to achieve such ride quality is the controlled damping force which can be monitored alongside the relevant piston speed between the sprung and unsprung mass in the 4-quadrant graph when a suspension model is provided with the random input from road surface The damping force is one of two required component force that result in the total active force which can be controlled and determined by the controller of the suspension system The active suspension system could be equipped with a damper to generate variable damping force that is suitable to either driving style or the road surface
Figure 3.2 The required damping force and relative speed in 4 quadrants
It is noticeable that most of the damping force required are actuated at the 1 st and 3 rd quadrants and only a few are actuated in the other two quadrants The reason for this resides in the damper being unable to generate a downward resistance force (negative damping force) against the contraction (2 nd and 4 th quadrants) Therefore, it is necessary to devise a controlled damping force in the expansion (1 st and 3 rd quadrants) to the required level at optimum value and to the minimum level at minimum value in the contraction (2 nd and 4 th quadrants) in order to achieve a desirable ride quality and ride comfort
Figure 3.3 The optimization of damping force in 4 quadrants
Different types of suspension have different optimum damping force mapping control Each system design has their potential and characteristics in terms of relationship between the piston speed (𝑉 𝑝 ) and damping force (𝐹 𝑑 ) generated For the passive suspension, the damping force can be expressed as a single property, the adaptive suspension combines two or more properties, while the semi-active and active have wider range of property for damping force control with the semi-active focusing the controllability potential in the 1 st and 3 rd quadrants, whereas the active produce the potential in all 4 quadrants, being capable of desirable damping forces, reducing body rolls, nose dive, and nose lift, all of which the semi-active system leaves a lot to be desired
Figure 3.4.The controllability potential of various types of systems
Regarding the area of subcategory for active suspension, the adaptive, the semi- active and the(fully) active suspension system all trend toward the comfort and quality of the ride while not losing out on the integrity of the vehicle handling The adaptive and semi-active bear some similarities such as adjustable damping force due to the road behaviors, leaving the semi-active and active as two main types of suspension system in the discussion and comparison with the conventional counterpart
Figure 3.5 The main differences between the passive and semi-active, active suspension system
The passive system features a conventional mechanism, its springs with a fixed stiffness exert an elastic force and its damper with a fixed damping coefficient produce the damping force against the spring displacement There is no damping force proactively produced by the suspension to counter the oscillation, meaning it can only react passively to external disturbances The semi-active and active are better equipped with advances such as sensors and controller to proactively produce damping force, each with their own significance and controllability potential
As for the semi-active suspension, the system is capable of producing variable damping force based on the sensors signaling the controller The damper with various damping force which can be selected by the driver to suit the demand of either comfortable, relaxing ride or sporty, engaging driving experience, can outperform that of a conventional suspension system in various random road profile and external disturbances via the controller tracking the vertical movement of both sprung and unsprung masses Also, an additional number of semi-active suspension allow the driver to customize the spring stiffness of the system which is either an air spring or hydro-spring alongside the electrically actuated hydraulic damper and magnetorheological (MR) damper via driving programs, meaning more adaptive performance is made possible via customization
The sheer flexible customizability expands even more with the active system Specifically, more advanced electronically controlled actuator are incorporated and utilized to an extent where the driver does not necessarily have to adjust the damping force and spring stiffness manually, the system is processing signals from sensors via onboard controller to dictate the most appropriate active force for the situation or road behavior, preventing excessive body roll, detecting vertical movement as well as optimizing the vertical acceleration of both sprung and unsprung masses Drivers can customize various ride profile with different driving modes for the suspension system and the vehicle will operates with the most suited optimization accordingly
There are various ways to achieve the variable spring stiffness, also known as variable spring rate The most common way, as far as we are concerned, would be adopting the air spring which establishes itself as a part of either an open or closed pressurized air system comprising of the air reservoir, compressor along with multiple control valves for operation; and implements a wonderful mechanism of changing the inner volume and pressure to alter various spring rate, enabling ride height adaptability and ride comfort for various situations Advantages and efficiency of air suspension includes:
• Ride Comfort: Air suspension generally provides a smoother and more comfortable ride compared to traditional coil springs due to the inherent cushioning properties of air
• Adjustable Ride Height: Air suspension allows the driver to electronically adjust the ride height of the car to suit different driving conditions or situations For example, the ride height can be raised for off-road driving or lowered for improved aerodynamic performance at high speeds
• Handling: Active air suspension systems can improve handling by actively adjusting the car's ride height and damping characteristics to minimize body roll and optimize tire contact with the road
• Load Leveling: Air suspension can automatically adjust the car's ride height to maintain a level stance even when loaded with cargo or passengers
Figure 3.6 The overview of the air spring-based (pneumatic) suspension system
One notable instance of the active suspension system equipped with air spring is the AIRmatic system proprietarily developed by Mercedes-Benz The main controlled factors are represented by air springs and hydraulic actuators This configuration enables the adjustment of the spring stiffness and variable damping coefficient This would mean the utilization of both the air spring and of the damper, it is possible to regulate the suspension performances to counter the road behavior and to meet the driver’s demand
Figure 3.7 The AIRmatic system developed by Mercedes-Benz
As can be seen from the schematic, the suspension features a pneumatic system, whose aim is to regulate the air flow in the air spring via changeover valves and pressure sensor
Figure 3.8 The schematic diagram of AIRmatic system
Both two mentioned variants of the ASS excel at their tasks with acceptable trade- offs and compromises; however, the active suspension system can be more complicated and more costly to manufacture compared to the semi-active regarding the components and mechanism Therefore, this project focuses mainly on the semi- active variants with the combination of (pneumatic) air spring, in which the controller enables the manual choice of various spring rate for the air spring and different damping force for the shock absorber, which is closely featuring and depicting the air suspension system of the Porsche Cayenne
Figure 3.9 The Porsche Cayenne equipped with air suspension
Figure 3.10 The components of air suspension system of Porsche Cayenne.
The air suspension system of Porsche Cayenne
3.2.1 The development of air suspension system in Cayenne model
3.2.1.1 The air suspension in Cayenne model 2004-2010
The Cayenne chassis equipped with the air suspension was first implemented in
2003 and received major updates and improvements in the following year model The Cayenne turbo, the top version, offers air suspension as standard feature, which is available as an option for both the Cayenne and Cayenne S version This suspension system is an open-air system, meaning that the air is vented into the atmosphere and redrawn in through the air filter and air drier while conducting height level control, particularly when switching to lower level
A fully capable load bearing air suspension is capable of the following advantages:
• Large difference between comfort and sportiness
• Full load balancing which is constant vehicle height and full compression travel regardless of load
• Active adjustment of ground clearance to the vehicle’s usage conditions such as off-road driving, automatic lowering of the vehicle at high speeds to improve dynamics
• Sporty driving style and reduced drag in low level
• Suitable day – to – day usability
• Adaptive leveling system which is useful during accelerating, braking, lane – changing
The air suspension with level adjustment enables the vehicle to proactively adapt the ground clearance to its load or to the situation in which the vehicle is being used
This system utilizes a control unit that processes the signal from the sensors and , with the aid of solenoid valve block and the compressor, dictates control of the flow of the compressed air mass between the air spring struts and two accumulators which are supply tanks for immediate response of height level control Additionally, there is a tyre filling connection, enabling the reinflation of (spare) tire via the compressed air in the air suspension system
The following diagram illustrates the components of the open – air suspension system of Porsche Cayenne 2004 – 2010 model
Figure 3.11 The overview of components of air suspension system in Porsche
Since this is an open – air system, the air volume can be vented from the air spring struts and air accumulators out into the atmosphere via air intake Based on the component overview, there is a simplified schematic design for open – air system Both the motor and air accumulator are equipped with pneumatic vent valve to enable the venting and filling process of the air spring struts
Figure 3.12 The pneumatic schematics of open – air suspension system
As can be seen from the component overview The accumulators are implemented along with the valve block to enable the process of filling, venting air with little delay The compressor used here are actuated by a relay which works in close cooperation with control unit
The air suspension system is controlled by a control unit which is located at the rear right section of luggage compartment This control unit dictates the volume change of air spring struts, adjustment of damper force, monitoring and running diagnosis on the whole system, and conducting communication using CAN
The CAN information consists of different signals, such as the engine speed signal controlling the compressor, vehicle speed signal performs speed-sensitive level control, brake signal is used to determine the damping force to avoid nose diving of vehicle
3.2.1.2 The air suspension in Cayenne model 2011
The air suspension system in the 2011 Porsche Cayenne is presented with major upgrades, improvements, and optimization in the operating principle as well as the PASM leveling control unit
Figure 3.13 The front and rear axle with air springs of Cayenne model 2011
This Cayenne model year 2011 comes with both the steel and air spring struts, the top version, the Cayenne Turbo, comes equipped with air suspension with amazing specification for guarantee of performance while the base version offers the air spring as an option and it is only equipped with the standard steel spring suspension, which can still be fitted with an option of PASM
Table 3.1 The suspension travel of 2011 Porsche Cayenne (air spring and steel spring)
These values in the table are calculated and published by Julian Edgar on Blog.Autospeed
In this table, the bump travel means the inbound travel (contraction of spring) and droop travel means the rebound travel (expansion of spring) The total of them equals the total travel of vehicle suspension The static deflection is the percentage amount of deflection, dictated by the drool (rebound) travel of the vehicle, the greater the droop travel value is, the more suspension travel the vehicle must use up during the contact with road holes Therefore, it is safe to consider that the wheels are capable of staying on ground as they pass through holes Air springs are also expected to gain stiffness at an increasing rate, with the provided static deflection accounting for more than half way up by the air spring travel
The air suspension system has been upgraded from open – air system to closed – air system, the latter still comprises of the compressor, solenoid block with integrated pressure sensor, pressure air accumulator, and the air spring struts with level sensor; supply tank (air accumulator) by the harmonic combined control effort of the compressor, the solenoid valve block, and the PASM leveling control unit
Figure 3.14 The overview of components of air suspension system in Porsche
As can be seen from the schematic design, the closed – air design doesn’t have the air flow venting to the outside which is different compared to the open – air system The compressor and the solenoid valve block govern the mass air flow between the air accumulator (left) and the control valves of air springs struts (right)
Based on the component overview, there is a schematic design of the closed – air system
Figure 3.15 The pneumatic schematics of closed – air suspension system
The air suspension system is controlled by a control unit which is located at the rear right section of luggage compartment This control unit dictates the volume change of air spring struts, adjustment of damper force, monitoring and running diagnosis on the whole system, and conducting communication using CAN and PSM
The air spring with additional volume changeover valve, and the process of filling, venting, draining, lowering, and raising the air spring struts, whose detail will be discussed in the next section, brings about the change of vehicle height level with various operating boundary and conditions for safety concern as well as guarantee of performance
3.2.2 The components of air suspension system of the 2011 Porsche Cayenne
Figure 3.16 The positions of suspension components of 2011 Porsche Cayenne
As can be seen from the vehicle schematic design, the labeled components are:
• 1 Air spring struts with integrated damper (front)
• 2 Air spring struts with integrated damper (rear)
• 3 Compressor with integrated air drier
The component of the most significant controlled is the air springs with integrated damper With the designated volume of compressed air, it can generate the spring rate accordingly and with the control of PASM, the integrated damper is capable of producing different damping force to live up to the demand
Figure 3.17 The front air spring with integrated damper
The suspension system mainly comprises of the air supply unit and the air supply control unit
The latter is the PASM leveling control unit
Figure 3.18 The main components of air supply unit
All of them will be discussed as followed
The air spring struts are positioned in four corners of the vehicle, attaching to each brake and wheel assembly, connecting the suspension system to the chassis or frame of the car
The adaptive air suspension in integrated and optimized design has 4 air springs with a switchable additional air volume for changing the spring rate In the air suspension system, the air bellows generally acts as the spring
MODELING THE AIR SUSPENSION SYSTEM
Overview of Matlab SIMULINK
Matlab/Simulink is a powerful combination of tools used for numerical computation and simulation MATLAB serves as a advanced computing and simulation program with interactive environment, widely employed for tasks such as data analysis, visualization, and numerical computations On the other hand, Simulink provides a graphical programming environment specifically designed for modeling, simulating, and analyzing dynamic systems It finds applications in diverse industries, including automotive, aerospace, and communication, where it is used for designing and testing complex control and signal processing systems Together, Matlab/Simulink offers a comprehensive solution for technical computing and model-based design
Located at the top, it contains tabs such as HOME, PLOTS, and APPS These tabs provide access to various functionalities and tools within MATLAB Current Folder
Pane is on the left side, you’ll find the “Current Folder” pane It displays files and directories in the current working directory You can navigate through your project files here Command Window is in the center, the “Command Window” is where you enter and execute MATLAB commands It’s an interactive space where you can perform calculations, define variables, and run scripts Workspace Pane is on the right side, the “Workspace” pane shows the variables currently in use You can view their values, data types, and other relevant information This is helpful for debugging and managing your workspace Status Bar is at the bottom of the window, you’ll see a status bar indicating that MATLAB is ready for use
Figure 4.2 The starting page of SIMULINK
The figure displays the Simulink software interface, which includes a grid of tiles Each tile shows a pre-built Simulink model template that users can start with to create their own models The templates include categories such as “Blank Model,”
“Digital Filter,” “Signal Processing,” and “Aerospace Blockset.”
The figure shows the Simulink interface, which is a MATLAB-based graphical programming environment for modeling, simulating, and analyzing multidomain dynamical systems The main focus is on the Library Browser window on the left side of the screen This window allows users to browse and search for blocks to build their models When you find a block you want to use, you can add it to your model by dragging and dropping it from the Library Browser into the main workspace
4.1.2 Basic function of Matlab/ Simulink
Matlab/Simulink can be applied in various fields which include:
Data Analysis: Matlab empowers engineers to tackle complex data sets from various domains Whether it’s climatology, predictive maintenance, medical research, or finance, Matlab provides tools for organizing, cleaning, and analyzing data Its flexibility allows engineers to explore trends, correlations, and anomalies efficiently
Programming: Within the Matlab environment, engineers can express matrix and array mathematics directly The beauty lies in its simplicity: even without extensive programming experience, users can perform complex operations From basic functions to large-scale applications, Matlab streamlines the development process
Graphics: Visualizing data is crucial, and Matlab excels in this area Engineers create custom graphics, turning raw data into meaningful insights Whether it’s plotting time series, histograms, or scatter plots, Matlab offers a rich set of tools Plus, it allows users to save visualizations in various formats (PDF, EPS, PNG) for seamless sharing and exporting
App Building: Matlab’s app builders simplify GUI development Engineers can lay out visual components, design interactive interfaces, and program app behavior The library includes standard components like buttons, check boxes, and tables, making app creation efficient
Web and Desktop Deployment: Sharing work with colleagues, collaborators, and clients is essential Matlab’s deployment products enable engineers and scientists to create secured standalone applications, web apps, Docker containers, and more These deployments cater to unlicensed users, ensuring seamless collaboration
Matlab in the Cloud: Imagine accessing Matlab’s power without worrying about local resources Cloud-based Matlab and Simulink accelerate development by providing on-demand compute resources, software tools, and reliable data storage Engineers and scientists can focus on their work, knowing that the cloud has their back
External Language Interfaces: Matlab plays well with others It supports various programming languages—C/C++, Fortran, Java, and Python Additionally, converting Matlab code to C/C++ is a strength, bridging the gap between different ecosystems
To sum it up, Matlab Simulink isn’t just a toolbox; it’s an ecosystem with a series of algorithms and platforms specialized and optimized for analyzing data, building apps, or deploying models, this dynamic duo empowers engineers and scientists across diverse domains.
Modeling the suspension system
4.2.1 Modeling the conventional active suspension system (quarter car)
An active suspension system will distinguish itself from the passive suspension system by the implementation of the control force (u) as the controllable input signal of the system Modeling the conventional active suspension system requires the element of the spring, the damper, and the mass Specifically, the damper has a constant damping coefficient and the spring which is typical represented by a steel spring has a constant stiffness value, whereas the mass is represented by two factors, the sprung mass (the vehicle body) and the unsprung mass (the suspension, brake and wheel assembly) Such approach is labeled as the Mass – spring – damper system
This particular system could be featured by a series of block diagram that features the basic parameters and properties of both sprung and unsprung masses, the spring stiffness, the damping constant, and the road disturbance/excitation Specifically, they are:
• 𝑋 1 : The displacement of sprung mass
• 𝑋 2 : The displacement of unsprung mass
The following is the illustration of the passive suspension system with mass – spring – damper The 𝑘 𝑆 represent a fixed value of spring stiffness and the 𝑐 𝑆 represents a fixed value of damping coefficient There is no implement of control strategy for an active or reaction force to counter the road disturbance, hence the name of the model: passive system
Figure 4.4 The passive suspension system model
The following is the illustration of the conventional active suspension system with mass – spring – damper system
Figure 4.5 The conventional active suspension model
As can be seen from the block diagram model, the active suspension system features an electronically controlled actuator which is utilized to implement a reaction force, counteracting the majority of road excessive vibration, undesired harshness, and discomfort regarding nearly all scenario of travel More advanced active suspension system features a controller for generating reaction force for the purpose of optimization as well as lightning-quick responsiveness Such reactive force can be a combination of both the elastic force from the spring and the damping force from the shock absorber or either of them, depending on the signal input of sensors equipped in the system such as body acceleration sensor, level sensors, velocity sensors for the sprung mass and unsprung mass
Figure 4.6 The illustration of control actuator for active suspension model
The block diagram of this model features the basic parameters and properties of both sprung and unsprung masses, the spring stiffness, the damping constant, and the road disturbance/excitation, and also the force actuator ensuring the adaptive characteristics of the system Specifically, they are:
• 𝑋 1 : The vertical displacement of sprung mass
• 𝑋 2 : The vertical displacement of unsprung mass
• 𝑘 𝑆 : The spring stiffness of the steel spring (N/m)
• 𝑐 𝑆 : The damping constant of shock absorber (N.s/m)
• 𝐹 𝑆 : The actuator for the active force counteracting the road disturbances
Considering the energy and force of this particular system, the mechanical spring (steel) is capable of compression as well as extension along the displacement since this is the nature of the spring, therefore exerting an elastic force which is one of the component forces of the total active force Additionally, the shock absorber, which can be represented by a piston as illustrated, is capable of generating damping force based on the product of relative speed of moving parts within the piston and the damping coefficient The calculating formula for the elastic force and damping force are as follow:
The elastic force of the mechanical spring:
𝒌 𝑺 : The spring stiffness (N/m) Δx: The displacement in which the extension/expansion occurs (m)
The damping force of shock absorber (piston):
𝒄 𝑺 : The damping constant (N.s/m) Δv: The relative velocity of moving parts within the shock absorber
Considering the force balancing and applying the Newton’s second law for this particular system, a dynamic equation is obtained based on figure (4.5), equation (4.1) and (4.2) makes:
𝑋̇ 1 : the derivative of the 𝑋 1 equals vertical velocity of sprung mass
𝑋̈ 1 : the derivative of the 𝑋̇ 1 which equals vertical acceleration of sprung mass
𝑋̇ 2 : the derivative of the 𝑋 2 equals vertical velocity of unsprung mass
𝑋̈ 2 : the derivative of the 𝑋̇ 2 which equals vertical acceleration of unsprung mass
4.2.2 Modeling the active air suspension system
The active air suspension system is also known as active pneumatic air suspension The controlled actuator for the active force of this particular system gains control of a great number of parameters and components and has a wide range of control method to achieve the harmonic balance between ride comfort and road handling quality
The main difference of this system that sets itself apart from the regular active suspension system resides in the spring component, which in this configuration comes in the form factor of an air lobe or air bag that contains an initial amount of volume and pressure which generally act as a spring using its bellows The air spring in such form factor has wider range of tuning for either comfort or sporty characteristic and capable of maintaining a desired height level regardless of changes in the loads exerted on the air springs as well as featuring variable spring rate without affecting the ride height of the overall system compared to the steel spring However, there are some trade-offs, such capable system comes with supporting hardware such as compressor, change-over valve, and air reservoir in order to manage the pneumatic characteristic of the spring
The following illustrates the active pneumatic suspension model with additional components compared to a regular active suspension model These differences comprise of an additional air reservoir and a control valve which serve as the means of control strategy for the air spring and its characteristics Considering this particular model as the simplified configuration of the air suspension system, there will be no compressor
The parameters of this system are as followed:
• 𝑋 1 : The vertical displacement of sprung mass
• 𝑋 2 : The vertical displacement of unsprung mass
• 𝑐 𝑆 : The damping constant of shock absorber (N.s/m)
• 𝐹 𝑆 : The actuator for the active force counteracting the road disturbances For the air spring:
• 𝑉 𝑆 : The volume of air spring (𝑚 3 )
• 𝑉 𝑆 : The volume of air spring (𝑚 3 )
• 𝑃 𝑆 : The pressure of air spring (𝑃𝑎)
• 𝑉 𝑎 : The volume of air reservoir/ accumulator (𝑚 3 )
• 𝑃 𝑎 : The pressure of air spring/ accumulator (𝑃𝑎)
The dynamic equations based on balancing force as well as the Newton’s second law for the active pneumatic suspension model is identical to that of the regular model counterpart, considering the equation (4.3) and (4.4)
In order to obtain the air spring stiffness (𝒌 𝒔 ) in this particular model, considerable method and additional calculation have to be conducted via utilizing the parameters such as volume and pressure In order to model such parameters, basic fluid dynamics and thermodynamics have to be taken into consideration and there will be implementation for the air spring as well as the air reservoir
The main dynamic equations will involve the ideal gas law and (air) mass flow rate through the valve
Considering the ideal gas law equation, the relation between pressure and volume and the temperature of the nitrogen gas within the air spring:
• 𝑽 𝑺 : The volume of air spring (𝑚 3 )
• 𝑷 𝑺 : The pressure of air spring (𝑃𝑎)
• R: ideal gas constant = 0.2968 (kJ/ kg.K)
Assuming the process is adiabatic with no heat exchange, the relationship between the pressure and volume can be modeled as:
The continuity equation representing the rate of change of air mass in the air spring through the control valve:
Where 𝒎̇ represents the air mass flow rate through the valve
This results in the control valve dynamics to modulate the flow rate of air via opening or closing the valve
Where 𝑪 𝒗 represents the flow coefficient of the dynamic valve
In the event of air spring compression or extension, the internal volume is subjected to the change: Δ𝑽 𝑺 = −𝑨 𝒆 Δ𝑿 (4.12)
Where: Δ𝑽 𝑺 : the change in volume
𝑨 𝒆 : the effective area of air spring (𝑚 2 ) Δ𝑿: The change in vertical displacement of sprung and unsprung masses
Therefore, the actual volume of the air spring can be calculated as:
Where: 𝑉 𝑆 0 is the initial volume of the air spring prior to any adjustment (raising or lowering the vehicle)
Implementing the adiabatic relationship for pressure changes gives: Δ𝑷 𝑺 = −𝒏 𝑷 𝑺
The elastic force of the air spring is the product of the internal pressure and the effective area within the air spring during compression at any given moment
The elastic force generated by the air spring will be proportional to the internal displacement of moving parts through the stiffness or air spring rate, also the change of the elastic force is subjected to the pressure deviation Therefore, the stiffness of the air spring (𝒌 𝒔 ) can be calculated based on the pressure and volume change within the air spring itself
Considering the ideal gas law equation, the relation between pressure and volume and the temperature of the nitrogen gas within the air spring:
• 𝑽 𝒂 : The volume of air reservoir (𝑚 3 )
• 𝑷 𝒂 : The pressure of air reservoir (𝑃𝑎)
• 𝒏: adiatic index = 1.4 (approximately for air)
• R: ideal gas constant = 0.2968 (kJ/ kg.K)
Assuming the process is adiabatic with no heat exchange, the relationship between the pressure and volume can be modeled as:
4.2.3 Modeling the air suspension of 2011 Porsche Cayenne
4.2.3.1 Define the parameters of the air suspension system of Porsche Cayenne
The variant of the suspension system of the 2011 Porsche Cayenne that will be modeled is the pneumatic type featuring the air spring with variable stiffness (spring rate) instead of the steel spring with constant stiffness Such spring rate is controlled by the control valve which regulates the air mass flow rate between the air spring strut and the air accumulator This particular system comprises of the air spring strut, air accumulator, air compressor and a solenoid valve block
Considering the simplified active pneumatic suspension model that has been mentioned previously, the modeling will be conducted with the two – way directional valve with on/off mechanism instead of the solenoid valve along with the omission of the compressor
Figure 4.8 The active Pneumatic model of 2011 Porsche Cayenne
The parameters of the active pneumatic suspension model are as followed:
OF COMPONENTS VALUE UNIT (SI) NOTE
R 0.2968 kJ/kg.K Ideal gas constant
T 126.2 K Ideal air temperature n 1.4 Adiabatic index
Referencing force value from Porsche
AG and Continental testing data
Estimated in the range of damping coefficient of German luxury SUV
Estimated in the range of damping coefficient of German luxury SUV The air accumulator
Estimated from specifications of OEM parts
Table 4.1 The parameters of 2011 Porsche Cayenne
4.2.3.2 Determine control strategy for the air suspension system
Various control approaches can be applied for the control of the active air suspension system The most common would the PID controller which is capable of providing the fine control of the suspension system The transfer function of a PID controller has the following form y(t) = 𝑲 𝒑 𝒆(𝒕) + 𝑲 𝒅 𝒅𝒆