Design of active and energy-regenerative controllers for DC-motor-based suspension

doi:10.1016/j.mechatronics.2012.09.007

Mechatronics

Volume 22, Issue 8, December 2012, Pages 1124-1134

https://doi.org/10.1016/j.mechatronics.2012.09.007 Get rights and content

Abstract

In this paper, active and energy-regenerative controllers are designed for the DC-motor-based suspension, which is able to operate in two modes: active control for ride comfort promotion and energy-regenerative control for energy harvesting. In order to achieve these two modes, the main/torque-tracking loop control structure is presented in this paper. Then by simplifying torque-tracking loop, working areas of the DC-motor actuator are analyzed. As for main loop controller design, H∞ robust control is investigated for the active suspension based on a full-car suspension model. The restricted H∞ controller, which is the combination of proposed H∞ controller and a restriction strategy that confines the motor to the working areas of energy regeneration, is employed as the main controller to realize energy regeneration. Simulations are carried out with random uneven road inputs and the results demonstrate that better ride comfort can be achieved by proposed active suspension and energy-regenerative (ER) suspension compared with passive counterpart. Moreover, effects of uncertainties are also investigated under several cases, indicating good robustness of designed suspension systems. Meanwhile, capacity of energy regeneration is also ensured by the ER suspension.

Introduction

Vehicle active or semi-active suspension technology has been studied for decades by many researchers but still not widely applied in practice for its high energy consumption, though they can remarkably improve vehicle dynamical performances. As is widely known, the vibration excited by uneven roads has negative effects on ride comfort and its reduction is certainly one of the main targets for vehicle suspension design. On the other hand, the vibration can also be a kind of energy source, which is commonly dissipated by passive viscous dampers. If proper measures can be done to recycle and store it, not only the energy cost for active suspension control can be reduced, but the whole energy demand for vehicle may be downsized. In recent years, electromagnetic suspension has been put forward and is becoming increasingly attractive owing to its high efficiency, quick response, strong controllability and capability in energy recovery. Some researches on electromagnetic suspension have been carried out. They are reviewed as follows.

A kind of energy-regenerative suspension using a rotary DC-motor as actuator was proposed by Suda and Shiiba [1], among which the rack and pinion mechanism was applied to convert rotary motion of DC-motor into the linear motion of suspension. Subsequently, an electromagnetic damper with additional planetary gears adding to the former structure was presented in Ref. [2]. This configuration could provide nonlinear damping force by the power electronic circuits and its applicability of application to vehicle was also verified by experiments. Equipping with this prototype, the suspension of a truck cabin was able to harvest vibration energy from the truck chassis as well as store it for vibration elimination afterwards [3]. In fact, its principle was similar to which was stated in Ref. [4]. Furthermore, in depth research about the frequency characteristics of energy balance of the above electromagnetic damper can be referred to Kawamoto et al. [5], whose results proved that energy was consumed to isolate the vibration of sprung mass below 2 Hz, while regenerated above 2 Hz. As was stated by Ref. [1], the external resistance affects both damping coefficient and regenerative efficiency. As a result, reducing the external resistance can increase the damping coefficient and improve the ride performance at the sacrifice of regeneration capability, making the external resistance be the key factor to adjust the coordination.

The self-powered active vibration control by using a single actuator was presented in Ref. [6]. According to its properties, when the speed of the armature was high the actuator was able to generate power, which in return would be utilized if the speed of the armature was low. The fact was verified by experimental results that the goal of energy harvesting of proposed regenerative suspension could be achieved under specific conditions that were derived from the energy balance analysis. Effect of equivalent damping ratio on the performances of isolation and regeneration was analyzed by Okada and Harada [7], showing that larger damping ratio led to both better vibration isolation and more regenerated energy of high-frequency vibration as well.

Recently, the prototype of energy-regenerative damper for rail car was investigated by Nagode [8], which could fit inside a typical suspension spring. During laboratory tests, this system was capable of efficiently generating up to 80 W of power on quasi-continuous basis with a sinusoidal input of 3/8 inch at 2 Hz. In addition, vibration-based electromechanical energy harvesting systems presented by Nagode was presented in Ref. [9]. With size and shape similar to conventional shock absorbers, these devices were designed to be placed in parallel with the suspension elements. The result that it is capable of providing up to 75 W of power is proved by lab tests.

In 2011, Zuo [10] studied the influence of road roughness, vehicle speed, suspension stiffness, shock absorber damping, tire stiffness, wheel and chasses masses to the vehicle performances and harvestable power. In that study, experiments suggested that suspension stiffness, road roughness and vehicle speed exert great influence to power regeneration potential. In addition, 100–400 W of power is available at 60 mph for a middle-size vehicle.

According to the review above, admittedly, certain amounts of studies of electromagnetic suspension had been carried out, which provide us profound knowledge about the potential of energy regeneration of suspension. However, several issues, which are listed below, are lacking of researching:

1.
The impact that the motor servo-loop has on the overall control performance of suspension. In existing researches, most just treated the servo-loop as a linear gain, i.e., the control force of motor being proportion to the motor current, without any consideration of the force tracking performance of the motor. In fact, the effectiveness of the motor servo-loop plays an important role in realizing the commands of suspension controller.
2.
The relationship between motor working states and suspension control. In order to precisely design suspension controller to realize active control or energy regeneration, the relationship between motor working states and suspension control is the key factor. After getting knowledge about this connection, it is readily available to realize active control or energy regeneration by designing controllers to ensure motor working in respective areas, which will definitely provides great convenience in designing controllers for specific goals. Unfortunately, existing studies rarely paid attention to this point, only proposing controllers for active control and afterward analyzing their performances of energy regeneration.

These two points are what we need to address in this paper. In our pervious works, the feasibility of energy regeneration potential of active suspension using DC-motor actuator had been studied [11] and additionally, a novel DC-motor actuator for vehicle suspension was proposed [12], which was an integration of permanent-magnet DC-motor and a ball screw mechanism. Its characteristics tests were carried out and the feasibility of regeneration was verified preliminarily [13]. Based on these studies, the working states, especially the energy regenerative states, of DC-motor are analyzed in this paper. Then H∞ control is applied for active control of DC-motor-based suspension. Furthermore, a restriction strategy is embraced with the H∞ controller to form a restricted H∞ controller to realize energy regeneration.

The rest of this paper is organized as follows. Section 2 presents the model of the DC-motor actuator. Section 3 addresses the main/torque-tracking loop structure used in this paper and the analysis of motor working states are presented in Section 4. In Section 5, two kinds of main controllers (i.e., H∞ controller and restricted H∞ controller) are designed for purposes of active control or energy regeneration, respectively. Simulation results of suspension performances are shown in Section 6 and the proposed controllers are compared with passive counterpart. At last, the effects of uncertainties are investigated through several cases.

Section snippets

Modeling of the DC-motor actuator

The developed DC-motor actuator is comprised of a brushless DC-motor and a ball-screw mechanism as shown in Fig. 1. In this paper, the vibration of the ball-screw mechanism is not considered.

The ball-screw mechanism, as is depicted in Fig. 2, converts the motor torque T_e into vertical force f_d $f_{d} = \frac{\cot φ}{r} \cdot T_{e}$ and the gear ratio of ω to suspension stroke speed v is 2π/P_h, which can be expressed as: $ω = - \frac{2 π}{P_{h}} \cdot v$ where r is the effective radius for force conversion, φ is screw lead angle and P_h is the lead

Control structure

The block diagram of the main/torque-tracking loop control structure for the control of DC-motor-based suspension is shown in Fig. 6. It is divided into two loops, in which the main loop is consisted of a full-car suspension model and a main controller, calculating the reference torque T_ref for DC-motor, and the torque-tracking loop applies hysteresis current control method for control of a three-phase motor to track the reference torque calculated by the main loop. The following are the design

Torque-tracking loop controller design

The torque-tracking loop, which is shown in Fig. 7, consists of a motor, a three-phase inverter, a rotor position detector, current sensors and a DC power supply that includes a battery and a capacitor connected in parallel. A hysteresis current controller [15] is applied to track the desired control current. By comparing current error e_r with hysteresis band h_t, the controller can track reference control current i_r by changing the states of three-phase inverter, which connects two of the three

Modeling of active suspension

A full-car vehicle model, which is shown in Fig. 9, is employed in this paper. It comprises five parts: the sprung mass and four unsprung masses. The sprung mass is denoted by m_b and unsprung masses by m_fl, m_fr, m_rl, and m_rr, which represent the front left, front right, rear left and rear right wheel masses, respectively. Let the front and rear suspension stiffness, the front and rear tire stiffness be denoted by K_sf, K_sr, and K_tf, K_tr. x_gfl, x_gfr, x_grl, and x_grr are the disturbances of four

Random road excitation

In order to examine the effects of the designed controllers, simulations are carried out in MATLAB®/Simulink® software with random road inputs. The results are compared with a passive counterpart, the damping ratio of which is C_p=1500 N s/m. In the simulations, the battery nominal voltage U_B is set at 42 V, the total storage of the battery is 10 A h and the initial storage is 80%. Other parameters used are listed in Table 3.

It is assumed that the vehicle is driven on the B-class road whose roughness

Conclusion

The DC-motor-based suspension has been proved to be in high efficiency, rapid response and good controllability. Its operating states are analyzed through simplifying the three-phase motor control system into an equivalent control circuit. To achieve good performance, the main/torque-tracking approach, which is divided into main loop and torque-tracking loop, is applied. The main loop deals with control targets, such as active control or energy regeneration, and the torque-tracking loop that

Acknowledgements

This work was supported by Science Fund of Key Laboratory of Vehicles Detection, Diagnosis & Maintenance technology and National Natural Science Foundation of China (Grant Nos. 50575141 and 50875163). The authors express gratitude for the financial support.

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Design of active and energy-regenerative controllers for DC-motor-based suspension

Abstract

Introduction

Section snippets

Modeling of the DC-motor actuator

Control structure

Torque-tracking loop controller design

Modeling of active suspension

Random road excitation

Conclusion

Acknowledgements

JSAE Rev

J Sound Vib

Contr Eng Pract

Contr Eng Pract

A new hybrid suspension system with active control and energy regeneration

Veh Syst Dyn

Study on electromagnetic damper for automobiles with nonlinear damping force characteristics (road test and theoretical analysis)

Veh Syst Dyn

Combined type self-powered active vibration control of truck cabins

Veh Syst Dyn

Modeling of electromagnetic damper for automobile suspension

J Syst Des Dyn

Regenerative control of active vibration damper and suspension systems