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Active Suspension System Design Using Fuzzy Logic Control and Linear Quadratic Regulator and PID controller

1.0 Introduction - Active Suspension System Design Using Fuzzy Logic Control and Linear Quadratic Regulator and PID controller

1.1 Introduction

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 In recent years, many studies have been performed on how to make a safe and comfortable ride on the road. Keeping one most vital thing in mind "Safety First", everyone in our society is very much concerned and aware about their health. In the 21st century, people around the globe are doing anything that can help keep themselves safe. As road accidents are increasing day by day, people have become very much concerned about that not only for their own life but also for their near and dear one's life and emotion. For this purpose, They always search for a system providing them a more secure and safe journey through the road and they are always looking for some system that provides fewer accidents as well as providing a stable ride on the road.

When most citizens think of getting automotive performance, they want power, the engine's roaring sound, the need for speed, and from zero to 80 miles per hour how quick the vehicle will go. However, if the driver cannot find comfort while driving on the road and is unable to control the vehicle, all this speed and power is nothing but a waste of time. Therefore, the automotive suspension is known as a crucial vehicle system for safe and stable drive on the road.

The primary functions of the suspension system consist of maximizing the contacts between the road surfaces and the tires, supporting the frame weight, body weight, and the engine weight, and also by providing the stability of the steering and the maintaining of the steering and also making sure about the passengers comfort by damping and absorbing the shock.

Suspension systems are of three main types including active, passive and semi-active. For the “passive suspension system”, the suspension system and spring are situated between the car wheels. Forward compensation is allowed by them between the stroke deviation of the suspension and the comforts during the driving. In the active suspension system, the feedback controller controls a force actuator. The feedback controller is situated between the main body of the car. Many studies are being performed about the active suspension for the vehicle for getting the good working of the active suspension system, thus by improving the active suspension system, both handling the road and making the comfortable ride improves. In this project report, the designing of the active suspension system will be described properly with the concept of Fuzzy logic control and the PID controller and also with the concept of. The concept of “PID controller”, “Fuzzy logic controller”, and also “Linear Quadratic regulator'' will be described in this project report and the implementation of these things for making the active suspension system will also be explained proficiently.

1.2 Aim

The overall intention of making this report is to develop a tuning of an active suspension so the car behavior in different tract and road conditions can be found by looking for the right compromise for the comfort of the passenger while road journey and also to make the journey safe, stable and secure. The aim of doing this project lies in the safety and the comfort of the citizen while they journey on the road. To avoid the accidents transforming fatal situations, the

The role of this suspension system is very important. By various methods like “Fuzzy control”, “Linear Quadratic Regulator”, and “PID controller'', the design of this active suspension system is described to reduce road accidents and to make the journey safe and comfortable.

1.3 Objective

 The main objectives of performing this project report are as follows:

  • To identify the drawbacks of the existing suspension system.
  • To design this Suspension System for the safety of the passengers while road journey.
  • To imply Fuzzy Logic Control for making this type of Suspension System.
  • To imply Quadratic Equation Regulator to design the Suspension System.
  • To imply the “PID controller” to design the suspension system.
  • While in motion, To preserve the vehicle stability in rolling or pitching.
  • To identify the importance of an active suspension system in road journeys.
  • To protect the occupants from road shocks.
  • To provide a safe and tension-free journey for the passenger.
  • To be familiar with the concept of Fuzzy Logic Control and the operations of this control while designing the suspension system.
  • To maximize the contact between the road surface and the tires or wheels of the vehicles.

By doing this project it will be crystal clear how Active Suspension system will be designed and implemented using various kinds of methods and also the impact of this suspension system will be realized for saving the valuable life of the passenger while road journey not only for themselves but also for their news and dear ones.

1.4 Background

The automotive suspension design has become a compromise between the three criteria of road holding, passenger comfort, and load-carrying traditionally. The suspension system should support the vehicle from getting into an accident. The suspension system also provides directional control during handling the ride and also provides effective and right isolation of passengers from the disturbances occurring on the road. A soft and smooth suspension is very much needed for a good and comfortable ride. On the other hand, Rough suspension is needed for the insensitivity to applied loads. Due to these important demands, the design of the suspension has to be something for taking into consideration. To quench the thirst for a safe and secure journey on the road, the design of the suspension system in a vehicle matters a lot (Ahmed 2021). Active suspensions are considered to be a better option of increasing the freedom of the journey as due to this people are very much sure about the nice commencement of the journey and also the freedom of the characteristics of carrying the load, handling the load and making a quality ride.

In the case of a “passive suspension system”, the system can store the energy through spring and through a damper dissipate it. Generally, It has fixed parameters, which are chosen to obtain a certain level of compromise between load carrying, load holding, and comfort. On the other hand, the “active suspension system” has the power for storing, introducing, and dissipating energy to the suspension system. It may vary its parameters depending upon the conditions of its operation, the parameters of this suspension system may vary. The suspension system of any vehicle refers to the group of mechanical components which is a connection between the body or the frame and the wheels. Because of an unfinished effort for the improvement of vehicle rides and with passenger comfort and safety, great use of engineering effort has been made into the design of suspension systems. In the days of buggy and horse, the suspension system included merely an axle extended across the vehicle width. The wheels were mounted to the end part of the axle in the front and at the center, rotation of the axle was done for providing steering. The one?piece axle design was used by automobiles in the early ages but instead of the rotation at the center, from road inaccuracies, it was fixed?mounted to the vehicle through springs for providing the smoothing of shock loads.The Suspension System is the most important part heavily affecting the performance of handling the vehicle and the quality of the vehicle. The suspension system includes the tires, the air in the tires, shock absorbers, struts, linkages, springs, arms, bars, joints, bushing, and The components or the parts of the suspension system are located between the road and the frame of the vehicle (Diwakar 2020). The well-tuned suspensions will absorb high bumps and by other imperfections, the people situated inside the vehicle on the road are allowed to travel comfortably and safely.

 1.5 Research Questions

Q1. What challenges exist in the existing Suspension System for a safe journey on road?

Q2. How can Fuzzy Logic Control be implemented in developing an Active Suspension System?

Q3. With a real-life example, define a fuzzy controller?

Q4. What thing will cause the overshooting in the PID?

Q5. In the evaluation of the Active Suspension System, what techniques can be used?

Q6. What components are related to the Active Suspension System?

Q7. What are the advantages of the suspension system designed in this report?

Q8. What are the disadvantages of the Fuzzy logic control system?

Q9. Can an Active Suspension System be a helpful thing for the safety and stability of the journey on road?

Q10. For the development of the Active Suspension System, what Software platforms are going to be used in this project?

Q11. How will the Active Suspension System create an important role in the safety of the vehicle in the future generation?

1.6 Research Hypothesis

H1: The challenges that existed in the existing Suspension System for the journey on road to be safe, smooth, and comfortable are known.

 H2: The process of how the Fuzzy Logic Control can be implemented in developing an “Active Suspension System” is known.

 H3: The definition of the fuzzy controller is obtained with a real-life example by performing this project. For air conditioners, for recognizing the facial pattern, for the working of washing machines, in vacuum cleaners, in transmission systems.

H4: When the error is decreasing and small, the application of so much integral in the controller will cause the overshoot.

H5: By this project, the techniques used in the evaluation of the Active Suspension System are known properly.

H6: The components related to the Active Suspension System are known.

H7: Advantages of the active suspension system are known. This suspension system reduces body rolling during the high vehicle speed.

H8: The major drawbacks of the Fuzzy Logic Control System are familiarized with.

H9: It is clear from the report that the Active Suspension System will be a really helpful thing for the safety and stability of the journey on the road.

H10: Softwares like MATLAB etc are used for the implementation of the Active Suspension System with “PID Controller”, “Fuzzy Logic Control”, and the “Linear Quadratic Regulator”.

H11: The Active Suspension System will play an important role in the safety of the vehicle in the future generation as it can maximize the contact between the road surface and the tires or wheels of the vehicles.

1.7 Research Rationale

Recently a variety of suspension systems have been implemented in various areas in our daily life regarding the safety and stability of the road journey. The importance of doing this project or doing the design of this suspension system lies in the various advantages of the Active Suspension System. An active suspension system always performs better than an adaptive passive or partially active suspension which depends on the cost of vehicle parameters.

The advantages of Active Suspension are as follows:

  • It is not dependent on the overall suspension condition.
  • The active suspension system independently stabilizes the vehicle.
  • This system reduces the body rolling during high speed.
  • The traditional complex suspension linkages are replaced by a Trailing arm suspension.
  • Space requirement for suspension is reduced by the simple trailing arm, which will result in low drag of the air.
  • In case of the cornering or when meeting a bump, the tires can be aligned to the axis which gives the maximum desired performance
  • By varying loads, climbing height is not affected.
  • While using an active system, the Antiroll bar is not taken into consideration.
  • The roughness of the system is minimal as compared to the traditional systems increasing the comfort index.
  • The Active Suspension system has adjustable characteristics even during the period of driving.
  • As this system enhances the contact of the tire with the road at, the overall control of the vehicle is enhanced that will help to make a safe, smooth and comfortable journey.

 For the above advantages, this research work has been done keeping one thing in mind that safety is very much needed and it is the main thing than anything.

 2.0 Research Philosophy

A mechatronics framework has been shown by the engine vehicle industry with astute command frameworks. “Mechatronics” alludes to a fruitful mix of electronic and mechanical frameworks. In “mechatronics”, conventional frameworks of machine-like designing are consolidated along with segments from software engineering electrical and arithmetic,designing. This paper presents upgrading a functioning suspension of a quarter vehicle model to work on its presentation by applying a particular regulator. Isolating a vehicle's body from street anomalies is the significant motivation behind a framework, to give the most extreme ride solace to travelers and keep hold of consistent street wheel contact to give street holding (Gnanaraj 2019). The first regulator applied is the “fuzzy rationale regulator (FLC)”,or the subsequent one is a “Linear Quadratic Regulator”, the vehicle's conduct, for example, vehicle body dislodging, suspension diversion, and wheel go is considered to get the greatest damping power in the button. A near report has been checked by the archive exhibition in order to solace the traveler's ride or street overseeing.

2.1 Pragmatism

Since the primary utilization of fuzzy rationale in the field of control designing, it has been broadly utilized in controlling a wide scope of uses. The human information on controlling mind-boggling and non-straight cycles can be consolidated into a regulator as phonetic terms. Nonetheless, with the absence of a logical plan study, it is turning out to be harder to auto-tune regulator boundaries. Fuzzy rationale regulator has a few boundaries that can be changed, for example, participation capacities, rule-base, and scaling gains. Besides, it isn't in every case simple to discover the connection between the kind of enrollment capacities or rule-base and the regulator execution (arxiv.org, 2021). This investigation proposes another efficient auto-tuning calculation to adjust fuzzy rationale regulator gains. A fuzzy PID regulator is proposed and applied to a few second request frameworks. The connection between the shut circle reaction and the regulator boundaries is broken down to devise an auto-tuning technique (joace.org, 2018). The outcomes show that the proposed technique is profoundly powerful and produces zero overshoot with upgraded transient reaction. Moreover, the strength of the regulator is researched on account of boundary changes and the outcomes show an agreeable presentation.

2.2 Positivism

All suspension system designs referred to in papers demonstrate that both fluffy rational and PID regulators have the capacity of expanding vehicular security and can adjust to changes in the framework boundaries because of the presence of sporadic street aggravation. Because of these benefits, scientists have examined the suitability of this crossover approach in the suspension framework. A fuzzy-based PID controller is utilized in semi-dynamic control of the MR Dampers of a vehicle suspension framework. The examination uncovered that the Fuzzy-based PID controllers can accomplish a pinnacle decrease of the recurrence of vibration up to 84% of regular recurrence of vibration under no influence. Anyway minimization of the body speed increase and uneasiness factors expands actuator powers and force utilization to a colossal degree. Hence to forestall material harm proficient streamlining calculations ought to be utilized to tune PID regulators. In another PID tuning calculation by the fuzzy set, the hypothesis has been created, which lessens overshoots and rises time to a degree bigger than the dynamic and latent suspension formwork. In this fuzzy set, all PID controllers investigate the utilization of a clever crossbreed control technique that coordinates the PID control, to decrease suspension contortion, and fuzzy logic control to give the variable damper power. The PID regulator is tuned with the versatile chaotic "fruit fly" calculation and the fuzzy logic controller depends on a phonetic guideline set which takes the account variability of force damper on move permanent look like a suspension warp. The show of the put forward strategy exists compared the active suspension system and also PID systems adjusted by "Genetic Algorithms"(GA), "Bacterial Foraging Optimization"(BFO), and "Particle swarm optimization"(PSO).

2.3 Realism

In this work, two distinctive control approaches are proposed, viz., regular strategy (CM) and speed increase subordinate technique (ADM). A quarter vehicle models with 3 levels of opportunity have been considered for the investigation. The presentation of the dynamic suspension framework with two control approaches has been contrasted and that of the detached one. It is presumed that the dynamic suspension framework has a superior potential to further develop both the ride solace and street holding since the RMS (Root Mean Square) traveler speed increase has been diminished by 54.23% for dynamic CM framework and by 93.88% for dynamic ADM framework contrasted with latent one, and suspension make a trip has likewise decreased to about 37.5%.

2.3.1 Direct Realism

A vehicle dynamic suspension framework assumes a basic part insufficiently ensuring the soundness of the vehicle, holding the non-stop street wheel contact, and further developing the suspension exhibitions. In this system, proportional integral derivative (PID), fuzzy rational, and heat regulators are utilized to control the vehicle suspension framework dependent on the half vehicle model. In addition, a self-tuning PID regulator dependent on fluffy rationale is created to work on the presentation of the framework. The proposed structure conquers the trouble of having appropriate reactions in controlling the interaction in all conditions, particularly when the framework boundaries are evolving. The regulators are planned dependent on the numerical model of the framework. Through the proposed technique, suspension working space is limited and the best solace of the driver is accomplished. The examination between reenactment results shows that by applying the introduced technique, the presentation of the suspension framework will be improved essentially.

2.3.2 Critical Realism

The suspension framework assumes a significant part in both the solace and strength of a vehicle. This system presents displaying and controlling for a Three Degree of Freedom(DIF) dynamic suspension framework. Four regulators are intended to control the reaction of the dynamic suspension framework, to be specific "LQR", "PID", "Fuzzy logic controller" (FLC), and "Artificial Neural Network"(ANN). The reaction for both the dynamic suspension framework and the suspension framework is also looked at. For the suspension framework, it has been discovered that it is difficult to further develop both traveler solace and street dealing simultaneously, because of the descent boundaries that can't be changed during the work. Then again, in a dynamic suspension framework, both ride solace and street dealing can be improved. This work has shown that ANN, FLC, LQR, and PID regulators can be utilized with a functioning suspension framework to work on the presentation, the security, and the ride agreeableness contrasted with the detached suspension framework. This load of regulators is mimicked utilizing MATLAB and "Simulink". Diverse street profiles are utilized to test the dynamic suspension framework reaction, for example, a stage contribution of 0.1 m, and a sine wave of the playfulness of 0.3m, and a recurrence of 0.318Hz. Every one of the regulators showed a better reaction contrasted with the inactive suspension framework. A trade-off should be possible to pick the regulator relying upon the ideal states.

2.4 Interpretivism

Two common standards for great vehicle suspension execution are their capacity to give Great Street taking care of and expanded traveler solace. The principal aggravation influencing these two measures is territory anomalies. Dynamic Suspension control frameworks diminish these unwanted impacts by secluding vehicle body movement from vibrations at the wheels. This paper portrays fluffy and versatile fluffy control (AFC) plans for the “car dynamic suspension framework (ASS)”. The plan objective is to give smooth vertical movement to accomplish the street holding and riding solace over a wide scope of street profiles. The adequacy of the proposed control plans is shown employing reproductions. Regarding the ideal direct quadratic controller (LQR), it is shown that predominant outcomes have been accomplished by the AFC.

3.0Research Approach

3.1 Deductive Research Approach

The main features of the active suspension system are to give useful isolation from directional and stability control at the time of handling maneuvers., surface unevenness on the road, vehicle support and ride comfort without loss. Designers are faced with some problems during the design of the suspension system. This system has two parallel components that are dampers and springs (Moaaz and Ghazaly, 2019). These two components help with road holding and ride comfort. This system gives ride comfort and vehicular stability at the time of transportation. This system is used to reduce vibrations during the continuous variation in the road. The active suspension system consists of actuators that control vibration in systems. Whereas active systems tolerate some drawbacks i.e. ratio change weight to power and high rating power consumption. The suspension systems are controlled by the use of a quadratic regulator, PID controller, and fuzzy controller. The “fuzzy controller” is used to implement flexibility for the effect of interaction for various systems which depend on the different events occurring in the system. The PID controllers depend on the calculating variables of the dynamic system (Mustafa et al.2019). This does not depend on the system's physical knowledge. PID controller has a great advantage that there are only two approaches which help to implement in a suspension system of fuzzy and PID hybrid. In the system, the PID decreases the acceleration of the vertical body and the fuzzy controller decreases the acceleration of the pitch. This report represents the active suspension system. It uses three control systems: PID controller, quadratic regulator, and fuzzy controller. This report demonstrated the comfort parameters in a ride like sprung, distortion, tire loading, and mass acceleration of the system.

3.2 Inductive Research Approach

Inductive research is known as inductive reasoning. In this suspension system, controlling the system required some control system. This research part evaluates the amount of these control systems. Some problems are body acceleration, discomfort, vibration, etc. These problems are short out by using the different types of controllers. These problems are reduced by increased force of actuators and also increasing the huge power consumption. Also focused on reducing damages in the devices. This is prevented by using an efficient algorithm that is mainly used to tune the PID controllers. The fuzzy controller with PID controllers that achieve by reduction of a peak value of the frequency vibration up to 84% of vibration of natural frequency under no control (Funde et al.2019). In a PID controller with a fuzzy set theory situated in a new theory by using the tuning algorithm that has been developed. This theory helps to reduce rise time and overshoot to the extent which helps better active susp[ensio systems. The performance of strategy compared with PID systems and active suspension systems tuned by optimization of particle swarm, optimization of bacterial foraging, and genetic algorithm. This suspension system requires choosing the ideal material which is easily tuned with the system. This report is a study that fruit fly algorithms employ in the area of mechanical engineering. This project compared comfort on the ride that proposed strategy in case of the Fuzzy-PID systems and active systems tuned by the use of a different method like Ziegler Nichols, “Bacterial Foraging Optimization” (BFO), “Particle Swarm Optimization” (PSO), and “Genetic Algorithms” (GA).

 4.0 Methodology

4.1 Introduction

This report suggests a structured methodology for optimizing and predicting the presentation of regeneration of energy of a suspension system for capturing efficiently vibratory energy which is created by irregularities on the road. The method gives dramatical design guidelines which select the best damping and stiffness coefficient which is designed for either maximum energy harvesting or better ride comfort. To increase the capability of energy regeneration there is a load resistance that also varies and an electronic circuit with less power is fabricated and developed (Ab et al. 2019). The circuit is to provide for controlling real-time damping coefficients. A test-bed is used to examine the proposed techniques. This result shows the simulation and analytical results for power generation and dynamic control that also matches the experimental results.

4.2 Research Methods

A suspension system also plays an important role in a vehicle for road holding and handling capacity by using the vehicle body segregation from road vibrations and bumps. An active suspension system is most important for a vehicle's driving capability, comfort and ride. To design a suspension system with better quality for the rough or bad condition of the road surface. An ideal active suspension system must have a reducing capability of acceleration, displacement of the sprung mass, (Wang et al. 2020) and also maintain contact of tire terrain. FLC is mainly used to control the variation in an environment at the time of operation processes. Some methods are used i.e. “Fuzzy Logic controller”, “Linear Quadratic logic”, and “PID controller”.

Fuzzy Logic Controller (FLC): FLC is also a part of the control system. Fuzzy logic gives a path of dealing with nonlinearity and imprecision in complex control situations. In this circuit, the Interface engine is used to access input where humans are used to providing an output. In working, FLC has the advantage of imprecise inputs, its handling nonlinearity, and mathematical models that are not needed. FLC contains three stages that are fuzzification, defuzzification, and aggregation. Fuzzification is converted from the numerical input variables to a membership function. Its output has a linguistic connection with the system's inputs. These types of relations are called rules and each rule has an output that is known as a fuzzy set. Greater than one rule helps to increase conversion efficiency. This set is defuzzified into a crisp output by use of the defuzzification process. Aggregation is also one type of process where fuzzy sets' output of each rule is getting together for making an output of a fuzzy set.

Linear Quadratic Regulator (LQR): LQR is a known method that gives feedback with optimal control which increases the closed-loop in a stable position and performance design is high for systems. Optimal control provides a procedure of an automated design. That provides feedback gains in practice. This is used for various purposes i.e static gain, robustness, output variables, expensive control, and cheap control also. It is used to reduce the cost function to control the system.

PID Controller: PID means proportional, integral, derivative. PID control gives an uninterrupted variation of output in control loop feedback to control a process, process efficiency increase, and remove oscillation. A PID controller is a device that is used in the application of industrial control, temperature regulating, speed, pressure, and other process variables. Analog electronics components are used to implement PID control. This system examines feedback variables by use of fixed points which generates error signals. This process will continue up until the error reaches zero. Various types of tuning methods are used to tune PID controllers. It requires more attention to choose the best ratings of integral, derivative, and proportional gains by the operator. The most important methods are used to tune the PID controllers. First is the Error and Trial method, it is an easy method for tuning a PID controller. This is used when the controller or system is working. Here, set the kd and ki values to zero and gain the value of kp i.e. proportional term. Another method is the process reaction curve. It is used for tuning on the open-loop technique. It creates an output response when a step input is used in the system.

4.3 Research Design

This section describes the design part of the active suspension system for a vehicle. This is done by some research papers on this topic. This system is used to design an active model of a suspension system. These are “PID controllers”, “linear quadratic regulators”, and “fuzzy logic controllers”. Here, describes the modeling of the suspension system and also a description of the system.

Fuzzy controller for MR dampers: A fuzzy controller acts on a group of rules which depend on the system modeling and mathematical analysis. The rule-base contains IF-THEN rule statements conditions to control. These parameters are the input of a fuzzification interface which is converted to fuzzy information. The fuzzy set is compared after that defuzzification changes from the conclusion to the actual parameters.

 Figure 1: Fuzzy Controller

(Source: https://www.researchgate.net)

It creates a skyhook surface in a sliding control method to increase road comfort in the active suspension system (Abougarair et al. 2017). This system uses a 2 in 1 FLC rule which has an error variable. There are two errors as inputs and control force. The FLC system also takes sprung mass velocity, suspension distortion, and sprung mass acceleration acts as input and that has been used to measure the variable term. The membership function is one type of function which describes the scaling of input values to a membership value in 0 and 1 to provide differentiability and smoothness at all points. Free parameters are tuned by using a membership function which is introduced by asymmetry.

PID tuning with Fruit Fly Algorithm: This algorithm is an optimization process, which uses the finding behavior of food from fruit files. The FOA initializes and generates an area for swarms. This member is allocated a direction (Ahmed, 2021). The best area is provided depending on the judgment function. When they are reached in a new position from distance to origin. The optimal solution is to go through an iteration in series. This literature focuses on the uses of modified and conventional Fruit Fly algorithms for controlling the PID systems.

PID tuning using CFOA: This introduces the use of a Chaotic fruit fly algorithm for tuning a PID to control a suspension distortion (Gomonwattanapanich et al.2020 ). This function is calculated by and described by the dynamic performance of the closed-loop of a suspension system. That was minimized after the location initiation of PID controllers (Diwakar et al.2020). Reduction of the judgment function gives back the examined values of PID controllers. In the CFOA, first, initialize the parameters and then logistics parameters. The dynamic results of PID controllers are calculated using the output variable and error input.

Mathematical Modeling: In mathematical modeling, the vehicle body is presented by sprung mass. The Assembly of the wheel and axle is presented by a unsprung mass. The surface of the road is guaranteed to contact the tire when the vehicle i.e. car is traveling and this is designed as a linear spring with flexibility and stiffness. The design of the fuzzy controller is dependent on experts. The experience of operative to set up with fuzzy rules bank.

4.3 Research Limitation

Suspensions are used in vehicles. The suspension forces generated concerning response signals by vigorous elements offer incremented design elasticity to regular suspension utilizing passive materials like dampers and spring. Often it is presumed that if hands-on difficulties are rejected, active systems can take part to produce arbitrary behavior and ideas. Utilizing a basic linear system it is shown two degrees of freedom suspension model system. It can be used to complete state feedback. The systems which are controlled by control theory there are some limitations to use this suspension system in a fully active case. Ideal suspension performance can be described in the basics of low pass filtering of roadway inconsistency inputs (Diwakar et al.2017). A suspension system performs less well than an adaptive passive or partially active suspension which depends on the cost of vehicle parameters. Fuzzy control is used to remove deformation of the tire from variable to control by use of grey predictor.

4.4 Conclusion

Published work treating active suspension theory and its improvements have been briefly described in this whole paper. Depending on tested findings, the electromagnetic suspension system was suggested to be the future of active suspension design as it has energy regeneration power. It doesn't have a complex structure, flexibility, and appropriate force management, high bandwidth facility, good handling performance as well as ride quality. Some days ago implementation in “power electronics'', “permanent magnet” material, and microelectronics have improved a lot in the electrical domain. Steady-state and dynamic performance, volume and weight decrement, electronics management system corrupted incorporation in reliability, cars as same as downscaling are important factors.

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Shojaei Barjuei, E. and Ortiz, J., 2021. A comprehensive performance comparison of linear quadratic regulator (LQR) controller, model predictive controller (MPC), H_ ∞ H∞ loop shaping and μ μ-synthesis on spatial compliant link-manipulators. International Journal of Dynamics and Control, 9, pp.121-140.

Wang, Q., Zeng, J., Wu, Y. and Zhu, B., 2020. Study on semi-active suspension applied on carbody underneath suspended system of high-speed railway vehicle. Journal of Vibration and Control, 26(9-10), pp.671-679.

Youness, S.F. and Lobusov, E.C., 2019. Networked control for active suspension system. Procedia Computer Science, 150, pp.123-130.

Youness, S.F. and Lobusov, E.C., 2019. Networked control for active suspension system. Procedia Computer Science, 150, pp.123-130.

Youness, S.F. and Lobusov, E.C., 2019. Networked control for active suspension system. Procedia Computer Science, 150, pp.123-130.

Zare, K., Mardani, M.M., Vafamand, N., Khooban, M.H., Sadr, S.S. and Dragi?evi?, T., 2019. Fuzzy-logic-based adaptive proportional-integral sliding mode control for active suspension vehicle systems: Kalman filtering approach. Information Technology and Control, 48(4), pp.648-659.

Online Article

arxiv.org, 2021, Quarter and Full Car Models Optimisation of Passive and Active Suspension System Using Genetic Algorithm , Available at: https://arxiv.org/ftp/arxiv/papers/2101/2101.12629.pdf, [Accessed on: 31.07.21]

eurodyn2020.org , 2019, OPTIMIZATION OF NONLINEAR QUARTER CAR SUSPENSION-DRIVER SEAT MODEL USING GA BASED PID CONTROLLER, Available at: https://eurodyn2020.org/proceedings/pdf/18892.pdf, [Accessed on: 31.07.21]

iopscience.iop.org, 2020, Optimized state feedback control of quarter car active suspension system based on LMI algorithm , Available at: https://iopscience.iop.org/article/10.1088/1742-6596/1502/1/012019/pdf, [Accessed on: 31.07.21]

joace.org, 2018, Optimal Control of Vehicle Active Suspension System Available at: http://www.joace.org/uploadfile/2018/0627/20180627054303956.pdf, [Accessed on: 31.07.21]

researchgate.net , 2018, CONTROL AN ACTIVE SUSPENSION SYSTEM BY USING PID AND LQR CONTROLLER, Available at: https://www.researchgate.net/profile/Anh-Nguyen-Tuan-2/publication/343477660_Control_an_Active_Suspension_System_by_Using_PID_and_LQR_Controller/links/5fb5330fa6fdcc9ae05f4d48/Control-an-Active-Suspension-System-by-Using-PID-and-LQR-Controller.pdf, [Accessed on: 31.07.21]

researchgate.net, 2021, Vibration Control of Quarter Car Model Using Modified PID Controller, Available at: https://www.researchgate.net/profile/Ameen-Nassar/publication/349685416_Vibration_Control_of_Quarter_Car_Model_Using_Modified_PID_Controller/links/603ca9b14585158939d99548/Vibration-Control-of-Quarter-Car-Model-Using-Modified-PID-Controller.pdf, [Accessed on: 31. 

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