A Study On Control Method For Vehicle Active Suspension Subject To Constraint And Uncertainty

Compared with passive or semi-active suspension systems,the active suspension systems(ASSs)are able to better balance between the riding comfort and maneuverability of vehicle owing to the actuator.A salient feature of ASS is that they are usually underactuated.That is,it has fewer control inputs than the degrees of freedom.Furthermore,time-varying uncertainty and nonlinear characteristics widely exist in ASS.In addition,ASSs are required to isolate the vibration from the sprung mass and ensure boundary conditions of the suspension deflection and the tire dynamic displacement.Therefore,control design for ASS is a challenging problem encountered by researchers.This dissertation aims to develop advanced control algorithms for ASSs,based on theoretical analysis,simulation and experimental validations.The main contents in the dissertation are summarized as follows.(1)A quarter-car model and a simple two freedoms of degree(2-DOF)model are presented.The equivalence between the quarter-car model and the 2-DOF model is validated.Based on the2-DOF ASS,the suspension spring and the shock absorber are modelled as nonlinear stiffness and nonlinear damping,respectively.We formulate control goals of ASSs as the constraints of the sprung mass displacement,which may be holonomic or nonholonomic.A constraint-following control approach is proposed for the nonlinear ASS,whose effectiveness is demonstrated by rigorous proof.By the platform of MATLAB/Simulink and the experiment equipment of ASS from Quanser company,the results of the sprung mass displacement and acceleration under the constraint-following control,standard linear quadratic regulator(LQR)control and no control are compared and analyzed.It is shown that the peak values of the sprung mass displacement and acceleration are smaller under the constraint-following control,which indicates that ASSs with the constraint-following control can yield effective attenuation of the sprung mass vibration.(2)The suspension deflection and the dynamic displacement of tire in ASS are bounded and formulated as an inequality constraint of the sprung mass displacement.By using diffeomorphism,the inequality constraint can be transformed into the equality constraint.The constraint-following control approach with diffeomorphism is proposed and its effectiveness is demonstrated by rigorous proof.Numerical simulation and experimental results on a nonlinear 2-DOF ASS are presented for validations.It is indicated that the constraint-following control with diffeomorphism can render ASS to converge to the inequality constraint(hard constraint)without violating the inequality constraint at all times,which validates the effectiveness of the proposed control approach.However,the sliding mode control based on the skyhook model,the LQR control and the constraint-following control without diffeomorphism cannot ensure the ASS to satisfy the inequality constraint condition in theprocess of convergence.(3)Due to the non-ideal actuator,the matched and bounded uncertainty of the input matrix exists and is considered in ASS.A robust constraint-following control approach is proposed for dealing with the uncertainty.By the Lyapunov minimax approach,it is concluded that the robust constraint-following control ensures uniform boundedness and uniform ultimate boundedness of ASS.Furthermore,experimental and numerical simulation results on a nonlinear 2-DOF ASS are presented for demonstrations of the control.It is indicated that compared with the LQR control,the constraint-following control and no control,the robust constraint-following control is more effective in dealing with constraints of ASS subject to the considered uncertainty.(4)The bounded uncertainties,including mismatched portions(e.g.,sprung mass,suspension spring stiffness,damping coefficient and external disturbance),are considered in ASS.We creatively decompose the uncertainties into matched and mismatched portions,which enables the mismatched portions to “disappear” in the stability analysis.Consequently,we are able to design a robust constraint-following control based on only matched portions and free from mismatched portions.By the Lyapunov minimax approach,we show that the robust constraint-following control ensures uniform boundedness and uniform ultimate boundedness for ASS.Furthermore,experimental and numerical simulation results on a 2-DOF ASS are presented for demonstrations for the control.It is indicated that compared with the LQR control,the sliding mode control with disturbance observer and no control,the robust constraint-following control can better deal with the sufficiently large mismatched uncertainties of the external disturbance and constraints in ASS.The constraint-following control studied in this dissertation is a model-based state feedback control,and can be employed for other mechanical control systems subject to equality and inequality constraints,matched and mismatch uncertainties.