Design of robust H ∞ controller for a half-vehicle active suspension system with input delay

This paper is concerned with the problem of sampled-data H ∞ control for a half-car active suspension system. First of all, by regarding the heave and the pitch accelerations, and the suspension deflection as the optimization objectives, the vehicle suspension system will be established. Then, an input delay approach is employed to transform the resulting active vehicle suspension system with sampling measurements into a continuous-time system with a delay in the state. Thirdly, by constructing a novel Lyapunov functional, a sufficient condition for the existence of sampled-data H ∞ controller is given to ensure asymptotical stability of the closed-loop system and also satisfy the constraint performance. The corresponding condition can be converted into a convex optimization problem and verified easily by means of standard software. Finally, a design example is exploited to demonstrate the effectiveness of the proposed design method.

This section is concerned with designing the dynamic properties of vehicle suspension systems to improve the dynamic properties of vehicles. The performance of suspension systems can be assessed quantitatively in terms of four parameters: passenger comfort, suspension deflection, tire load variation, and energy consumption, see Gillespie (1992), Cole (2001). Vehicle vibrations excited by road irregularities might lead to the fatigue of the driver and passengers, as well as damage to the vehicle and the payload. It is widely accepted that there is a correlation between passenger comfort (or ride comfort) and the heave, pitch, and roll accelerations of the sprung mass.

The dissipative analysis and control synthesis for uncertain singular systems with interval time-varying state and input delays are investigated in this paper. The parametric uncertainty in this paper is assumed to be norm bounded. A sufficient condition, in the form of linear matrix inequality (LMI) with nonlinear constraints, on the existence of robust dissipative controller is established based on the Lyapunov stability theory. In order to solve the nonlinear problem, Cone Complementarity Linearization (CCL) is offered.

Two methods which are computationally simple and easy to apply are developed by using state dependent Riccati equation (SDRE) approach and approximating sequence of Riccati equation (ASRE) approach to control active suspension system in the presence of nonlinear spring and damper. Additionally, effectivenesses of the both control methods developed by utilizing two recently introduced SDRE and ASRE techniques are compared. First, methodologies of both approaches are presented. After that, nonlinear dynamics of the vehicle suspension system is described in terms of conveniently selected state variables for better control performance. Then, a cost function is written by using suspension and tire deflections, sprung mass velocity and acceleration, and unsprung mass velocity variables to improve ride quality, suspension deflection, and tire deflection. Additionally, a convenient representation of this cost function in terms of state variables is obtained to realize better control. A bump expressed as sinusoidal function and roughness of the road expressed as white noise are taken into consideration as the disturbances from the road. Finally, quarter vehicle suspension system equivalent model of Ford Fiesta Mk2 is used as an example and simulations obtained by using the developed control methods are checked against the performance requirements and corresponding passive suspension system.

This paper investigates the problem of robust sampled-data Hinfin control for active vehicle suspension systems. By using an input delay approach, the active vehicle suspension system with sampling measurements is transformed into a continuous-time system with a delay in the state. The transformed system contains possibly non-differentiable time-varying state delay. The controller design is cast into a convex optimization problem with LMI constraints. A quarter-car model with active suspension system is considered and the effectiveness of the proposed approach is illustrated by a realistic design example.

This paper deals with the problem of output-feedback H∞ control for a class of active quarter-car suspension systems with control delay. The dynamic system of the suspension systems is first formed in terms of the control objectives, i.e., ride comfort, road holding, suspension deflection, and maximum actuator control force. Then, the objective is to the design of the dynamic output-feedback H∞ controller in order to ensure asymptotic stability of the closed-loop system with H∞ disturbance attenuation level and the output constraints. Furthermore, using Lyapunov theory and linear matrix inequality (LMI) approach, the existence of admissible controllers is formulated in terms of LMIs. With these satisfied conditions, a desired dynamic output-feedback controller can be readily constructed. Finally, a quarter-vehicle model is exploited to demonstrate the effectiveness of the proposed method.

The study presents a simple way to optimally design a Proportional-Differential (PD) controller and apply it to the vibration control of a quarter car model's active suspension system. First, the optimization objectives are determined, including minimizing the vehicle body acceleration and the suspension deflection. The tyre deflection and road holding constraints are also considered. Next, the variables, including the components in the gain vector of the PD controller, are optimized using the Balancing Composite Motion Optimization (BCMO) algorithm. Different controller configurations, according to the two above optimization objectives, are simulated to verify the performance of the controllers for the nominal system and for the system when its mass and stiffness are varied. An H¥ controller in a reputable published study is also included for comparison. The simulation results show the proposed PD controllers' high control efficiency and robustness, especially the PD controller, which is based on minimizing the vehicle body's acceleration.

Observer-based multi-objective integrated control for vehicle lateral stability and active suspension design

Improved robust stabilization method for linear systems with interval time-varying input delays by using Wirtinger inequality

Robust stabilization and robust H∞ control problems for a class of uncertain neutral system with state and input delays are considered. By choosing a Lyapunov-Krasovskii functional, an alternative delay-dependent sufficient condition for the existence of a controller is derived in terms of linear matrix inequalities. Furthermore, a convex optimization problem can be formulated to obtain an H∞ controller which minimizes an upper H∞ norm bound of the closed-loop state-input delayed system.

A novel robust model predictive control strategy is presented for a class of discrete-time time-varying system with delays. The modified quadratic Lyapunov-Krasovskii functionals for uncertain discrete-time system with both states and input delays is proposed. A robust model predictive control law is derived such that the closed-loop system is asymptotically stable and a dasiaworst-casepsila infinite horizon performance objective is minimized. A feasible state feedback model predictive control law is obtained by using linear matrix inequalities approach. And then, a convex optimization problem is formulated to design the robust model predictive controller which minimizes the upper bound of the closed-loop performance objective. The robust model predictive controller design is illustrated with numerical examples.

Delay dependent stability results for fuzzy BAM neural networks with Markovian jumping parameters

This paper is concerned with stability analysis problem for uncertain stochastic neural networks with interval time-varying delays. The parameter uncertainties are assumed to be norm bounded and the delay is assumed to be time varying and belong to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. Both the cases of the time-varying delays which may be dif- ferentiable and may not be differentiable are considered in this paper. Based on the Lyapunov-Krasovskii functional and stochastic stability theory, delay/interval-dependent stability criteria are obtained in terms of linear matrix inequalities. Some stability criteria are formulated by means of the feasibility of a linear matrix inequality (LMI), by introducing some free-weighting matrices. Finally, three numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed LMI conditions.

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.

In this paper, the problem of delay-dependent robust H∞ filtering for discrete-time singular systems with time-varying delay and polytopic uncertainties is investigated. Without introducing the free-weighting matrices to deal with the cross terms, a delay-dependent H∞ performance analysis result is established for error singular system by considering the relationship between the time-varying delay and its bounds at first. Based on this result, a linear robust H∞ filter is designed such that the filtering error singular system is regular, causal and asymptotically stable with a H∞ norm bound. Numerical examples are given to show the advantages of the proposed results.