Sky-Hook Control for a Regenerative Suspension System Chen-Yu Hsieh
Bo Huang
Farid Golnaraghi
Mehrdad Moallem
[email protected] [email protected] [email protected] [email protected] School of Mechatronic Systems Engineering, Simon Fraser University, Surrey, BC V3T 0A3. Abstract— This paper proposes a mechatronic suspension system with capabilities of energy regeneration and sky-hook (SK) control incorporated into the mechanism. The system overcomes the tradeoffs between energy consumption and ride comfort in an active suspension system. Central to the concept is development of a coupled switched-mode rectifier (SMR) capable of providing either a positive or negative damping ratio by alternating between regenerative and motoring modes. Using the proposed circuit, an active sky-hook control strategy is utilized to offer continuous damping force that improves the vibration isolation significantly. Simulation results presented demonstrate the directions of power flow in both regenerating and motoring modes to verify performance of the SMR. Keywords— Regenerative suspension, switched-mode rectifier, energy-efficiency
I.
sky-hook
control,
INTRODUCTION
The suspension system in a vehicle is used to suppress undesirable vibration from road roughness. The system not only provides ride comfort but also safety, by maintaining good road contact. A conventional suspension system consists of a spring and viscous shock absorber. The shock absorber dissipates vibration energy into wasted heat. A fully active suspension system provides better isolation and improves control performance. However, it has a main disadvantage of high power consumption. In addition to passive and fully active suspension systems, semi-active suspension systems have been proposed to provide a compromise between isolation control and energy saving. To this end, Karnopp et al. [1], proposed a semi-active sky-hook control scheme that can maintain the reliability of passive control using an acceptable amount of energy. Semi-active control strategies utilizing innovative magnetorheological (MR) fluid damper designs have been proposed by several researchers (see e.g. [2]). Rakheja and Sankar [3] proposed an R-S control method to minimize the damping force when the spring force and damping force have the same direction. Shen et al. [4] investigated three semi-active control methods, i.e., limited relative displacement (LRD), modified R-S, and modified skyhook (MSK), and verified their performance by experimental tests. Although the “on-off” semi-active methods are efficient in suspension control, they result in uncomfortable jumps when switching between on and off modes. Hence, there would be a sacrifice in the control performance when compared with the continuously variable type. Bolandhemat et al.[5- 6] utilized a modified Skyhook fuzzy controller in the design of a semiactive suspension system for a Cadillac SRX 2005 is
demonstrated with road tests results. Their real-time experiments confirmed that the use of this design method reduces the required time and effort in real industrial problems. Conventionally, concepts of recharging the wasted kinetic energy are widely implemented on not only hybrid electric vehicle (HEV) powertrains, but also on railroad vehicles [7][10]. In this work, a new method of regenerating kinetic suspension energy is presented by employing an active control strategy for a vehicle suspension system by using the sky-hook control method. To this end, a mechanism that transforms kinetic energy into rotary motion is presented. By studying requirements for the sky-hook detection method, a bidirectional SMR control method is presented using a doubleband hysteresis current controller (DB- HCC). The circuit is capable of regenerating/supplying energy from/to the suspension system, based on the direction of power flow. The outline of the paper is as follows. Section II discusses modeling of the proposed regenerative suspension system along with the algebraic screw mechanism. Section III focuses on the sky-hook detection method and its extension to the proposed system. Section IV addresses the mechanicalelectrical analogy to ease the analysis of the proposed mechatronics system. Section V defines the power flow direction for both regenerating and motoring modes. Section VI demonstrates the operation of power stage and control algorithm along with the simulation results, indicating positive and negative damping provided by the SMR. II.
SYSTEM DESCRIPTION AND MODELING
The proposed regenerative suspension system can be simplified by a quarter-car model, which is shown in Fig 1. The model consists of a sprung mass, a DC motor/generator (DCMG), a planetary gearbox, an algebraic screw mechanism [11], a physical spring, and a load resistor representing the load.
Fig 1. : Base excitation model of the regenerative suspension system.
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A. DC motor and generator In the proposed regenerative suspension depicted in Fig. 1, the permanent magnet DC motor acts as a motor/generator depending on the mode of operation. Using proper power electronics circuitry and controller the load on the DC motor can be considered to be purely resistive. Fig. 2 shows a model of a generator connected to a load resistor (Rload). Following KVL as shown in (1), the current (I) flowing in the circuit is written as follows:
(7)
C. Dynamics of the quarter-car suspension system The whole system can be modeled as a quarter-car suspension system, as shown in Fig 1. The dynamic equations of the sprung mass can be derived as follows (8) (9) where x is the motion of the sprung mass with the base excitation motion usually considered as cos . Hence, the dynamic equation of the system is derived as
Fig. 2: Circuit diagram of motor/generator.
(10)
(1) (2) Therefore, the output torque of the motor is expressed as (3) where ke, kt are the motor torque and angular velocity constants, respectively. The output torque of the motor will be used to derive the output force of the regenerative damper as discussed in the following section. B. Output force of the regenerative damper The entire damping mechanism consists of the dc motor/generator with a gearbox and the algebraic screw. The gearbox amplifies the rotation of the motor by gear ratio , and attenuates the torque to the motor by . Therefore, the equation of the rotor dynamics are described as follows
cos
.
where m is the sprung mass, ma and Ja are algebraic linear and translational mass, respectively; and Jm and Jg are the motor and gearbox inertia respectively. The physical friction is indicated by cf. The physical spring coefficient is indicated by k. DCMG emf and torque constants are indicated by ke and kt, respectively. The planetary gear ratio is represented by kg. d is the linear- rotational ratio. Hence, (10) can be simplified as follows cos
.
(11)
The equivalent mass, damping coefficient, and excitation amplitude in terms of other physical parameters values are listed in Table I. TABLE I.
EQUIVALENT MASS, DAMPING COEFFICIENT AND EXCITATION AMPLITUDE.
Symbol
Description
(4)
(5)
The algebraic screw is a mechanism used to convert the translational motion due to the vibration into rotary motion proposed in [11]. Following [11], the relationships between the torque τb, force Fb, angular motion θ , and stroke motion z are
/
(6)
Consequently, the equivalent output force, as a function of relative velocity z and acceleration z , is obtained as follows
III.
ACTIVE SKY-HOOK CONTROL STRATEGY
The damping force for a 1-DOF system with a sky-hook damper can be written as (12) . Using a semi-active damper, the sky-hook damping force must be realized in terms of the relative velocity . Therefore, the conventional semi-active sky-hook control algorithm is given by 0 (13) 0 0 According to the limitation of semi-active damper, when and have opposite signs, the damper cannot provide a force
opposite to . As a result, it is better to supply no force in that situation. As for the proposed active sky-hook control strategy, the damper can supply a negative force from a negative damping . So the active sky-hook control algorithm can be ratio written as 0 (14) 0. The desired positive and negative damping ratios can be realized by switch-mode power electronics converter by synthesizing a tunable load resistance . Specifically, when the positive damping ratio is desirable, the load resistance can be calculated as (15)
.
Similarly, when a negative damping ratio is desirable, the load resistance can be calculated as follows (16)
.
By actively tuning the value of load resistance, both positive and negative damping ratios are realizable and the corresponding continuous damping force can be generated. IV.
SUSPENSION ELECTRICAL ANALOGY
The purpose of emulating variable damping through variable resistor synthesis is explained by transforming mechanical elements of the regenerative suspension system into equivalent electrical elements, as shown in Fig. 3.
iin
L
iL
Rd
iR
C
Vemf
iC
power) to the power electronics circuit according to the relative velocity (i.e., voltage.) of the suspension system. Referring to the electrical side of the equivalent suspension system, the main objectives of power electronics circuitry are to provide variable bipolar electrical damping and capture vibrational energy provided by road force. As explained previously, the variable electrical damper is modeled as a variable synthesized resistor, Rload. In order to correctly supply the desired damping, the desired terminal current it should be given by −1 (17) it = Vemf ( Z s + Rload ) where Vemf is the back EMF, and Zs =Rs+ jωLs is the source impedance. V.
REGENERATION AND MOTORING MODES
The operation of the switch-mode damping synthesizer allows bi-directional flow of load (i.e., battery) energy. There exits tradeoffs in the implementation of the sky-hook semiactive control law, where suspension control performance and energy harvesting objectives should be met as outlined in the following. A. Regenerating mode The purpose of operating in the regenerative mode is to harvest energy from the suspension mechanism through the electric machine while providing positive damping force to the suspension system. In the regenerative mode, during positive cycle of Vin, positive source power contributes to storing energy into the DC bus (i.e., battery). This condition indicates a charging operation.
Rload
it CCCS
VCVS
Fig. 4: Motoring and regenerating states by direction of current. Fig. 3: Electrical analogue of proposed regenerative suspension model.
The sprung mass, physical stiffness, and damper are transformed into the capacitor, inductor and resistor, respectively. Moreover, the force provided by road input through base excitation is represented by a current source. For the shock absorber, we model it as a current controlled current sink (CCCS) and a voltage controlled voltage source (VCVS). Since part of the current (i.e., force) provided by the current source (i.e., base excitation) will flow into the shock absorber, the current (i.e. force) provided by the power electronics on the electrical side will actuate the dynamics of the suspension model (e.g. relative displacement) through the DC motor. The shock absorber is thus modeled as a voltage controlled voltage source, since the DC motor provides voltage (or available
B. Motoring mode The purpose of motoring mode is to provide negative damping force (i.e. Rload < 0) to the regenerative suspension, according to outcome of sky-hook control detection method. In the motoring mode and during a positive cycle of Vin, negative load power results in supplying power to the source (i.e., motor EMF). This results in discharging the battery, which is shown by the direction of current flowing to the source.
VI.
PRINCIPLE AND REALIZATION OF VARIABLE DAMPING IN ELECTRICAL DOMAIN
∆I = iref - it), defined as the difference between reference current iref and measured current it.
A. Switch- Mode Rectifier for Variable Resistance Synthesis The bi- directional power converter for variable resistor synthesizing is shown in Fig. 5. The synthesizer is essentially a switch-mode rectifier (SMR) operating in CCM with a variable switching frequency double-band 3-level hysteresis current control (DB- HCC).
Fig. 5: Configuration of switch- mode rectifier.
The power stage consists of a physical power inductor and a single phase Voltage Source Inverter (VSI) providing the desired vc through the corresponding PWM pulses driving the power MOSFETs. B. Controlling of SMR with Double-band Hysteresis Current Control The controller implemented consists of hysteresis comparators with two different sizes of error-bands as shown in Fig. 6. The additional digital logic circuits were introduced in [12]- [13] for MOSFETs switching frequency reduction and equalization, synonymous to carrier- based PWM modulation, in order to reduce switching power losses.
Fig. 6: Double-band 3-level HCC.
The current ripple is primarily determined by smaller error-band hysteresis comparator while the large error-band hysteresis comparator is implemented to reverse the polarity of average DC voltage, vDC, when the smaller error-band comparator is unable to regulate the current error. Under this condition, the larger error-band comparator will be activated to accomplish polarity reversal. Referring to the controller state machine shown in Fig. 7, let us assume that the converter initially operates in the regenerating state with sign(vin) >0. The smaller error-band comparator acts as a single-band hysteresis comparator, which switches on either Q1 or 2 according to the error current (i.e.,
Fig. 7: State diagram of DB- HCC.
When |it-iref|< ∆I, Q2/4 are switched on, connecting vin to La, which charges it at the rate of ∆it = Vx/La. When |it-iref|> ∆I, Q1/4 are switched on thus it into battery at the rate of ∆it = (vxVDC)/La. Subsequently, when sign(vin) 0 and sign(vinit)> 0, SMR alternates between Mode 1 and 2, as shown previously in Fig. 7. After entering the Motoring mode, where sign(vin)< 0 and sign(vinit)< 0, the alternation between Mode 3 and 4 takes place. 1 0 -1 0.3 20
0.35
0.4
0.45
0.5
0.55
0.6
-10 0.3
0.35
0.4
0.45
0.5
0.55
0.6
40 20 0 -20 0.3
0.35
0.4
0.45
0.5
0.55
0.6
10 0
Fig. 10: (a) Sky-hook detection outcome. (b) Instantaneous input power. (c) Instantaneous output power in motoring and regenerating modes.
According to the sky-hook detection outcome in Fig. 10(a), both input and output power shown in Fig. 10(b) and Fig. 10(c), respectively, indicate regenerating and motoring modes taking place according to their instantaneous polarities. Again, while synthesizing negative damping, it implies transferring negative source power; therefore, in the motoring mode the power is transferred from battery to source. Thus, energy
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