Stabilizing fuzzy controller design for quarter-vehicle suspension system

This paper presents new stability conditions satisfying decay rate for both continuous and discrete fuzzy control systems. Linear matrix inequality (LMI) based designs for decay rate are also considered using the concept of parallel distributed compensation (PDC). To design fuzzy control systems, nonlinear systems are represented by Takagi-Sugeno fuzzy models. The PDC is employed to design fuzzy controllers from the Takagi-Sugeno fuzzy models. The stability analysis discussed here is reduced to a problem of finding a common Lyapunov function for a set of LMIs. Convex optimization techniques involving LMIs are utilized to find a common Lyapunov function and stable feedback gains satisfying decay rate. A simple example demonstrates the utility of the LMI-based designs proposed in this paper.

Linear matrix inequality (LMI) methods, novel techniques in solving optimisation problems, were introduced as a unified approach for vehicle's active suspension system controller design. LMI methods were used to provide improved and computationally efficient controller design techniques. The active suspension problem was formulated as a standard convex optimisation problem involving LMI constraints that can be solved efficiently using recently developed interior point optimisation methods. An LMI based controller for a vehicle system was developed. The controller design process involved setting up an optimisation problem with matrix inequality constraints. These LMI constraints were derived for a vehicle suspension system. The resulting LMI controller was then tested on a quarter-car model using computer simulations. The LMI controller results were compared with an optimal PID controller design solution. The LMI controller was further tested by incorporating a nonlinear term in the vehicle's suspension model; the LMI's controller degraded response was enhanced by using gain-scheduling techniques. The LMI controller with gain-scheduling gave good results in spite of the unmodelled dynamics in the suspension system, which was triggered by large deflections due to off-road driving.

International audience

This paper presents new stability conditions and LMI (linear matrix inequality) based designs for both continuous and discrete fuzzy control systems. First, Takagi and Sugeno's fuzzy models and some stability results are recalled. To design fuzzy control systems, nonlinear systems are represented by Takagi-Sugeno fuzzy models. The concept of parallel distributed compensation is employed to design fuzzy controllers from the Takagi-Sugeno fuzzy models. New stability conditions are obtained by relaxing the stability conditions derived in previous papers. The stability analysis of the feedback system is reduced to a problem of finding a common Lyapunov function for a set of linear matrix inequalities. Convex optimization techniques involving LMIs are utilized to find a common Lyapunov function. A procedure to design the fuzzy controller is constructed using the parallel distributed compensation and the relaxed stability conditions. Some stability issues are remarked. A simple example demonstrates the effects of the derived stability conditions.

This brief addresses the problem of control for active vehicle suspension systems in finite frequency domain. The performance is used to measure ride comfort so that more general road disturbances can be considered. By using the generalized Kalman-Yakubovich-Popov (KYP) lemma, the norm from the disturbance to the controlled output is decreased in specific frequency band to improve the ride comfort. Compared with the entire frequency approach, the finite frequency approach suppresses the vibration more effectively for the concerned frequency range. In addition, the time-domain constraints, which represent performance requirements for vehicle suspensions, are guaranteed in the controller design. A state feedback controller is designed in the framework of linear matrix inequality (LMI) optimization. A quarter-car model with active suspension system is considered in this brief and a numerical example is employed to illustrate the effectiveness of the proposed approach.

In this study, we investigate a robust H∞ controller for a quarter-car model of an active inerter-based suspension system under parameter uncertainties and road disturbance. Its main objective is to improve the inherent compromises between ride quality, handling performance, suspension stroke, and energy consumption. Inerters have been extensively used to suppress unwanted vibrations from various kinds of mechanical structures. The advantage of inerter is that the realized ratio of equivalent mass (inertance relative to the mass of the primary structure) is greater than its actual mass ratio, resulting in higher performance for the same effective mass. First, the dynamics and state space of the active inerter-based suspension system were achieved for the quarter-car model with parameter uncertainties. In order to attain the defined objectives, and ensure that the closed-loop system achieves the prescribed disturbance attenuation level, the Lyapunov stability function, and linear matrix inequality (LMI) techniques have been utilized to satisfy the robust H∞ criterion. Furthermore, to limit the gain of the controller, some LMIs have been added. In the case of feasibility, sufficient LMI conditions by solving a convex optimization problem afford the stabilizing gain of the robust state-feedback controller. According to numerical simulations, the active inerter-based suspension system in the presence of parameter uncertainties and external disturbance performs much better than both a passive suspension with inerter and active suspension without inerter.

In order to improve the control effect of automotive semi-active suspension, a 2-degree-of-freedom (2-DOF) model was set up. Based on the Mamdani fuzzy control strategy, a two-input single-output fuzzy controller based on damping control was established, the computer simulation was carried under the excitations of road surface in the MATLAB/Simulink environment. The simulation results shown that under the excitations of pulse and white noise road surface, the semi-active suspension system with fuzzy control strategy effectively enhanced performance than passive suspension system in vehicle ride smoothness and travel comfort, with peak body acceleration reduced respectively by 31.3%, 22.0% and 22.2%, and with root-mean-square value reduced respectively by 16.9%, 15.6% and 15.5%.

This study details an efficient fuzzy logic controller (FLC) to improve the performance of active automotive suspension system. A comparison between passive and FLC active suspensions is performed. A mathematical model of automotive active suspension has six degrees of freedom and two input forces generated by two separate actuators are solved using Matlab Simulink. In order to evaluate the effectiveness of the proposed controller under random road disturbance, several performance criteria are assessed based on the dynamic response of the half automotive suspension system. Simulation results of the active suspension system based on the fuzzy logic clearly have been provided to illustrate the effectiveness of the FLC under different road conditions and confirmed that fuzzy logic is very effective for enhancing ride comfort and stability of the vehicle.

<div class="section abstract"><div class="htmlview paragraph">The performance of suspension system has a direct impact on the riding comfort and smoothness. For the traditional suspension can not effectively alleviate the impact of road surface and the poor anti-vibration performance, The dynamics model of vehicle suspension system is established, and the control model of vehicle four-degree-of-freedom active suspension is designed with fuzzy control strategy. On this basis, a comprehensive simulation model of the control model of vehicle active suspension coupled with road excitation is established. and the ride comfort of vehicles under different types of suspension are tested through Simulink. The simulation results show that compared with the passive suspension, the reduction of vehicle acceleration and dynamic deformation of the active suspension controlled by fuzzy PID can reach 33.76% and 22.45%. and the reduction of pitch Angle speed and dynamic load of the active suspension controlled by fuzzy PID can reach 16.18% and 10.72%. Under fuzzy PID control, the amplitude of each evaluation index of active suspension in the suspension system is substantially reduced than that of the passive suspension, and the root-mean-square value decreases by about 10% on average. It can be seen that the active suspension with fuzzy PID control can improve the performance of the suspension system on the basis of ensuring the stability and rapid response of the system, and can well reduce the random vibration caused by the impact of the vehicle on the random road surface during the driving process, improve the ride comfort, smoothness and ride safety of the vehicle, and achieve a good control effect on the vehicle suspension.</div></div>

Robotic manipulators are widely used in applications that require fast and precise motion. Such devices, however, are prompt to nonlinear control issues due to the flexibility in joints and the friction in the motors within the dynamics of their rigid part. To address these issues, the Linear Matrix Inequalities (LMIs) and Parallel Distributed Compensation (PDC) approaches are implemented in the Takagy-Sugeno Fuzzy Model (T-SFM). We propose the following methodology; initially, the state space equations of the nonlinear manipulator model are derived. Next, a Takagy-Sugeno Fuzzy Model (T-SFM) technique is used for linearizing the state space equations of the nonlinear manipulator. The T-SFM controller is developed using the Parallel Distributed Compensation (PDC) method. The prime concept of the designed controller is to compensate for all the fuzzy rules. Furthermore, the Linear Matrix Inequalities (LMIs) are applied to generate adequate cases to ensure stability and control. Convex programming methods are applied to solve the developed LMIs problems. Simulations developed for the proposed model show that the proposed controller stabilized the system with zero tracking error in less than 1.5 s.

Ride comfort and handling qualities of a vehicle have attained much attention in the field of automobile. Vehicle manufacturers are trying to introduce as much ride comfort as possible without compromising handling qualities of vehicle. The two characteristics of the vehicle are linked with suspension system of vehicle. Good ride comfort means that the suspension system does not let road disturbance to reach the body of vehicle, while good handling qualities implies good road grip and maneuverability of the vehicle. Main objective to improve ride comfort is to elude physical fatigue and tiredness of driver while improvement in handling qualities will minimize chance of road accidents. Different suspension systems like passive, semi-active and active have been studied for long. Semi-active suspension system can provide change in damping coefficient to fulfill requirements of a good suspension system in a simple, easy and cost-effective way without requiring change in vehicle. Therefore, semi-active damper systems have gained more popularity in automobiles field. Designing control algorithm for semi-active suspension system is a complicated and challenging task. There have been many control algorithms to control damping coefficient, but no algorithm has utilized semi-active dampers to their full potential. This study investigates shortcomings of existing approaches, root cause of the problems and provides optimal solution to the problem. A suspension system involves different regions of operations that can be separated on the bases of operational constraints and stability of system. Existing methods do not use stability for designing their controllers or separating different regions. Furthermore, existing control strategies are based on linearized models and require gain adjustment and tuning to get better performance. Through analysis, it was found that there are three distinct regions. Damping force requirements for each region are different and critical. If wrong damping force is generated in any region, it may induce more acceleration/disturbance on vehicle, which is the main problem that existing methods suffer from. Proposed method generates right amount of force required at right time to suppress vibration by designing better control algorithm based on energy equations and dynamic equations. The proposed methods are validated by using simulations and experiments. For experimental validation of suspension system and attaining higher performance, accuracy of measurement system and parameters involved cannot be overlooked. Therefore, detailed investigations on accurate measurement system and parameter estimation methodology for suspension system were conducted. Thorough analysis on existing measurement system revealed critical errors in existing measurement system. To find out root cause of problems an analytical formula for evaluation of measurement system was derived. To overcome measurements issues it is required to use time, instead of encoders, as scalar base. This is not possible in existing methods, as sampling time of existing methods is dependent on other associated systems. Therefore, new measurement system is proposed, which uses high frequency clock and high sampling frequency to measure accurate time as soon as change in displacement occurs. This is same as using a stopwatch with a resolution as low as Nanoseconds. Simulations and experiments proved the proposed strategy and its effectiveness. The achieved accuracy from proposed method is comparable to the speed measurements system based on laser interferometer system. After having accurate measurement system for suspension system, accuracy of systems’ parameters is evaluated from accuracy point of view. The estimation problem is a mathematical problem in which number of independent equations are less than parameters to be estimated, which makes this problem unsolvable. Existing approaches use excitation method to generate additional equations and convert system to an overdetermined system and hence to be solved and an optimization problem. Getting overdetermined system is not a solution to the problem as independent equations are still the same. Furthermore, existing methods do not take care of coupling effects, eliminating or isolating noise and parameters from each other. Therefore, parameters estimation is not accurate. This motivated to develop an algorithm to estimate parameters with more accuracy and reliability. The proposed method converts estimation problem into a control problem and the parameters are updated by generating step-by-step update based on state feedback and projecting input on error of states or their functions. Properly designed desired trajectories for different parameters are used to decouple the parameter from other parameters. A systematic way of updating one parameter at a time in different cycles ensured convergence of parameters to true value even if absolute decoupling between parameters is not possible for complicate and nonlinear systems. The proposed method is validated, for linear and nonlinear problems by simulations and experiments.

Suspension system is used to fulfil the criteria of ride comfort and road handling. In this paper, a quarter car active & semi-active suspension systems are designed using Matlab/Script software. Comparison of active & semi-active suspension systems are done using robust control theory for the control targets suspension deflection, body acceleration and body travel. H infinity controller is selected to compare the two suspensions using time domain analysis. Finally the simulation result prove the effectiveness of the active suspension system by decreasing the body acceleration & sustaining the suspension deflection and body travel outputs.

A passive suspension system is used by the automotive industry to control the motion of the vehicle. Nowadays, semiactive and active suspension systems are a requirement of commercial vehicles to improve performance characteristics and road comfort. The objective of the paper is to present a comprehensive analysis of passive, semiactive, and active suspension systems. The fuzzy logic controller is used to present the active suspension system. The characteristic of the shock absorber (damper) is non-linear and hysteresis in nature. Hence, a Magneto-rheological (MR) damper-based Bouc-Wen model is utilized to present the semiactive suspension. The comparative analysis of vehicle suspension characteristics has been carried out by using a bump road profile. The modeling of the Bouc-Wen model and quarter car system is carried out in the Simulink environment. The simulated results show that the semiactive and active suspension systems can be a better option for vehicle suspension systems to provide passengers with road comfort.

The present work is concerned to solve the problem of nonlinear robotic control systems on the basis of Takagi- Sugeno (T-S) fuzzy models. In addition, controllability and observability studies for T-S fuzzy model systems are considered for Single-Input Single-Output (SISO) and Multiple-Input Multiple-Output (MIMO) systems. In particular, the robust pole assignment approach is extended to the fuzzy field. This approach is used to design fuzzy stabilizers and fuzzy observers directly on the overall T-S fuzzy system. The latter one is the representation of the nonlinear robotic system, which is linearized around certain operation regions. The suggested method is considered for either SISO or MIMO systems. Furthermore, the method allows inducing an arbitrary behavior into the fuzzy plant in a relatively easy way. Two examples are used to verify the effectiveness of the proposed approach. The results are compared with the well-known Parallel Distributed Compensation (PDC) method, which is designed on the basis of Linear Matrix Inequalities (LMIs).

This paper proposes a design method of H <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sup> control performance for structural systems using Takagi-Sugeno (T-S) fuzzy model. The structural system with tuned mass damper is modeled by T-S type fuzzy model. By using parallel distributed compensation (PDC) scheme, we design a nonlinear fuzzy controller for the tuned mass damper system. According to the control system, a sufficient stability condition is derived in terms of Lyapunov theory and this control problem is reformulated into solving linear matrix inequalities (LMI) problem.