Torque-Vectoring Control in Fully Electric Vehicles via Integral Sliding Modes

Transcription

1 Torque-Vectoring Control in Fully Electric Vehicles via Integral Sliding Modes 2014 American Control Conference June 04-June 06, 2014, Portland, Oregon, USA Tommaso Goggia, Aldo Sorniotti, Leonardo De Novellis and Antonella Ferrara UNIVERSITÀ DEGLI STUDI DI PAVIA UNIVERSITY OF SURREY

2 European Project E-VECTOORC Vehicle Concept and Layout Powertrain Design and Safety Brake Design and EM-compatibility Vehicle Dynamics and Control 5/20

3 Outline Introduction and Motivation Vehicle Model for Control System Design The Yaw Rate Controller Results 2/20

4 Electronic Stability Program (ESP) VS Torque-Vectoring (TV) ESP Only when r ref r >th. ON-OFF control By means of: - Friction brakes - Wheel torques (-) TV In any condition (v, a x, a y, δ) At any instant of time By means of: - Friction brakes - Wheel torques (+/-) 3/20

5 Why Integral Sliding Mode for Yaw Rate Control? Conventional yaw rate control systems: PID + FF Good tracking performance and large bandwidth of the closed-loop system Not robust and smooth enough in critical conditions (high lateral acceleration) Many other approaches have been investigated (some examples): 2 nd Order Sliding Mode Control; Internal Model Control; MPC/Linear Quadratic Control; Optimal Control based on LMI. Major motivations for using Integral Sliding Mode Control: Ease of implementation (two parameters only); High level of robustness against unmodeled dynamics and external disturbances, even when implemented with sampling times typical of real automotive control applications. 4/20

6 Outline Introduction and Motivation Vehicle Model for Control System Design The Yaw Rate Controller Results 6/20

7 The Vehicle Model The proposed controller has been designed considering the vehicle yaw dynamics x = f ( x) + B( x) u + h( x, t) rj z= ( Fy, RF sinδrf + Fy, LF sinδlf + Fx, RF cosδ RF Fx, LF cosδ LF ) ( F cosδ + F cosδ + F sinδ + F sinδ ) a + y, RF ( F + F ) b+ ( F F ) M y, RR RF M RF y, LR LF y, LF M x, RR RR LF M x, LR LR x, RF Tr 2 RF x, LF LF Tf 2 + 7/20

8 Design of the proposed ISM controller In the previous model, the overall yaw moment is the control variable Yaw Acceleration contribution due to lateral forces and selfaligning moments k( r, β, δ) = 1 J z ( F sinδ + F sinδ ) y, RF y, LF ( Fy, RF cosδ RF + Fy, LF cosδ LF ) a ( Fy, RR + Fy, LR) b M RF M LF M RR M LR RF LF Tf 2 + Yaw Rate Error Model r err= r r ref = k( r, β, δ) r ref + M ISM + M dist Jz J z 1 1 Unknown part: 1 M h = k( r, β, δ) + dist Jz Known part: r ref 8/20

9 Outline Introduction and Motivation Vehicle Model for Control System Design The Yaw Rate Controller Results 9/20

10 Overall Closed-Loop Control Scheme T M * w, tot ISM T w, LF / RF = τ T, F τ M, F 2 Tf T M * w, tot T w, LR / RR = 1, 2 Tr R ISM ( 1 τ T, F ) ( τ M F ) R l l T p T w, i = min ; T m, i,max sign ( Tw, ) τ transm m, i i b, i = T m, i τ transm K b, i T w, i 10/20

11 Integral Sliding Mode Control (I) M ISM = M PID + M SM, fil M SM = J z K SM sign ( s) τ SM M SM, fil + M SM, fil = M SM s = s 0 + z s ( ) 0 1 Where z = r ref + M ISM M SM with the initial condition z( 0) = s0( rerr ( 0) ) ( rerr ) J z The sliding mode starts from the first sampling instant, without any reaching-phase transient 11/20

12 Controller Parameters Design Only two parameters needs to be tuned: K SM and τ SM η-reaching condition ssɺ < η s fulfilled for any value K SM > J z hmax +η a sequence of step steer maneuvers at v=90 km/h (high critical situation) has provided the upper bound J z hmax 9, 000Nm a conservative value has been chosen: K SM = 15, 000Nm τ SM = 0. 05s The value has been selected in order to avoid the chattering effect, so that the yaw moment generated by the high-level controller does not induce vibrations perceivable by the passengers. 12/20

13 Outline Introduction and Motivation Vehicle Model for Control System Design The Yaw Rate Controller Results 13/20

14 The Case Study The performance assessment has been carried out using an accurate IPG CarMaker model of the vehicle (validated on the basis of experimental tests at the Lommel proving ground in Belgium) Two conventional test maneuvers have been considered: - Ramp Steer Meneuver - Step Steer Maneuver The controlled vehicle ( Sport Mode ) has been compared with the passive vehicle ( Baseline Mode )

15 Ramp Steer Maneuver (I) Benefits of the adoption of the ISM yaw rate controller: lower value of the understeer gradient; extension of the linear region of the vehicle understeer characteristic; higher values of lateral acceleration. 14/20

16 Ramp Steer Maneuver (II) Reference yaw rate tracking performance at different speeds. The reference (dashed dark line) and the yaw rate of the controlled vehicle (blue line) are practically overlapped. The red line is the yaw rate of the passive vehicle 15/20

17 Step Steer Maneuver Evident degradation of the passive vehicle tracking performance at increasing speeds Good tracking of the yaw rate reference exhibited by the controlled vehicle, with very short rise-time and negligible overshoot. Obtained by means of a control signal perfectly acceptable in an automotive application. 16/20

18 Summary Results RMSE = t end 1 t in t t end in ( r ) err 2 dt BLUE: Controlled veh. RED: Passive veh. RMSEBaseline RMSEControlled ν % = 100 RMSE Baseline v=70 km/h v=100 km/h v=130 km/h Ramp Steer 94.14% 90.96% 88.25% Step Steer 73.87% 81.22% 88.13% 17/20

19 Video 18/20

20 Conclusions The torque-vectoring control of a four-wheel-drive fully electric vehicle with in-wheel drivetrains has been discussed, and an ISM control based solution has be presented. The ISM controller is easy to tune and robust with respect to a significant set of uncertainties and disturbances. Its low complexity and other positive features make it appropriate for practical implementations. The vehicle equipped with the ISM controller, compared with the non controlled vehicle, shows better tracking performance in both ramp steer and step steer maneuvers at different speeds, preventing unstable behaviours even in critical situations. 19/20

21 The research leading to these results has received funding from the European Union's Seventh Framework Programme FP7/ under grant agreement n Thanks!