Research Article | Open Access
Vimal Rau Aparow, Khisbullah Hudha, Zulkiffli Abd Kadir, Megat Mohamad Hamdan Megat Ahmad, Shohaimi Abdullah, "Modeling, Validation, and Control of Electronically Actuated Pitman Arm Steering for Armored Vehicle", International Journal of Vehicular Technology, vol. 2016, Article ID 2175204, 12 pages, 2016. https://doi.org/10.1155/2016/2175204
Modeling, Validation, and Control of Electronically Actuated Pitman Arm Steering for Armored Vehicle
In this study, 2 DOF mathematical models of Pitman arm steering system are derived using Newton’s law of motion and modeled in MATLAB/SIMULINK software. The developed steering model is included with a DC motor model which is directly attached to the steering column. The Pitman arm steering model is then validated with actual Pitman arm steering test rig using various lateral inputs such as double lane change, step steer, and slalom test. Meanwhile, a position tracking control method has been used in order to evaluate the effectiveness of the validated model to be implemented in active safety system of a heavy vehicle. The similar method has been used to test the actual Pitman arm steering mechanism using hardware-in-the-loop simulation (HILS) technique. Additional friction compensation is added in the HILS technique in order to minimize the frictional effects that occur in the mechanical configuration of the DC motor and Pitman arm steering. The performance of the electronically actuated Pitman arm steering system can be used to develop a firing-on-the-move actuator (FOMA) for an armored vehicle. The FOMA can be used as an active safety system to reject unwanted yaw motion due to the firing force.
Recently, automotive researchers have focused their work on the advanced technology of steering system to increase the safety system of a vehicle [1–3]. However, most of the advanced researches are mainly concentrated in a passenger vehicle. A number of researches have been carried out in the development of active safety system using rack and pinion steering configuration. An active front wheel steering system using rack and pinion configuration has been developed by automotive developers, BMW . This invention allows driver-independent steering system by intervening at the front axle using the mechanical link between the steering wheel and the front axle. The system is supported with double planetary gear and an actuated DC motor. Meanwhile, other researchers also actively involved in implementation of the active front wheel steering system as a vehicle yaw stability control method . This method has been used to reject the unwanted yaw motion due to aerodynamic disturbance. The similar type of active steering has been used in the development of direct yaw moment control and also advanced driver support technology .
Steering system using rack and pinion configuration also has been used to develop electric power assisted system (EPAS) for passenger vehicle . The EPAS has been used to design an active disturbance rejection control to reduce the steering torque exerted by the driver due to external side wind force. Other automotive researchers as stated in [8, 9] focused on the safety system of steering system using steer-by-wire technology. This technology is mainly invented from an aircraft system known as fly-by-wire. Besides, there are also some studies related to hardware-in-the-loop simulation (HILS) to investigate the performance of the active front wheel steering to develop yaw rejection control system using rack and pinion test rig [10–12]. However, most of the previous work is mainly related to rack and pinion type of steering system which is basically implemented in a passenger vehicle.
Meanwhile, research works related on the Pitman arm steering system are very much limited. Commercial heavy vehicle research in California has initiated research on the safety performance of heavy vehicle system using an actual truck . The research entirely focuses on the modeling, development of heavy vehicle using ADAMS software, and validation with an actual vehicle. However, the validation on Pitman arm steering is not included in this work. Recently, an active independent front steering (AIFS) has been developed to compare with the conventional active front wheel steering system . This active system used the truck model to develop active independent front steering system but has neglected the Pitman arm steering model. Thus, it clearly shows that most of the automotive researchers have not considered the performance evaluation of the Pitman arm steering system before it can be implemented in virtual or actual heavy vehicle system.
To overcome the limitations of active safety system in heavy vehicle technology due to the steering mechanism, a detailed investigation on the Pitman arm steering system is required in this study. A detailed modeling related to the Pitman arm steering system is developed with additional DC motor. The developed model is compared using an actual Pitman arm steering system to validate the behavior of developed model. In order to evaluate the capability of the Pitman arm steering for the active safety system, position tracking response is used in this study. The position tracking response is tested using the validated Pitman arm steering model via simulation. Then, the same tracking response has been implemented in the actual Pitman steering system using hardware-in-the-loop simulation (HILS) technique with additional friction compensation using Karnopp model. The control parameters from simulation or named as software-in-the-loop simulation (SILS) is used as benchmark control parameters in HILS testing.
This paper is organized as follows: Section 1 contains introduction, review on other research works, and review on the design and performance evaluation using steering system. Section 2 introduces detailed mathematical derivation of Pitman arm steering system using MATLAB/SIMULINK software. Section 3 discusses the validation of the developed Pitman arm steering model using actual Pitman arm steering test rig. Section 4 focuses on the position tracking response of both validated and actual Pitman arm steering system. Simulation method is used to evaluate the effectiveness of the validated steering model. Meanwhile, hardware-in-the-loop simulation (HILS) technique is used to investigate the position tracking control analysis in real environment. Section 6 explains the potential applications of the active Pitman arm steering system as firing-on-the-move actuator and finally the conclusion.
2. Modeling of Pitman Arm Steering Actuated by DC Motor Model
Pitman arm steering system is commonly used in wheeled armored vehicle. Thus, a multi-DOF Pitman arm steering model is developed using Newton’s second law of motion as shown in Figure 1 which consists of steering wheel and column, Pitman arm link, hydraulic assist, steering linkage, and wheel itself.
An additional torque from DC motor is included in the steering model to improve performance of conventional Pitman arm steering mechanism for active front wheel steering (AFWS).
2.1. Steering Column Equation
By assuming the rotation of the steering wheel is equivalent to the rotational motion of the steering wheel, the following equation is formulated as follows: wherewhere and are moments of inertia of steering column and DC motor and , , and are torque due to hydraulic assisted pump, DC motor, and Pitman arm member link. Meanwhile, and are defined as viscous damping of steering column and DC motor. are known as steering column friction while , , and are angular displacement due to universal joint, steering column, and steering wheel.
2.2. Equation of DC Motor
Basically, the DC motor is modeled by considering electrical and mechanical parts as shown in Figure 2. Based on Kirchhoff Voltage Law (KVL), the total voltage for the electrical part can be obtained asThe motor torque, , can be formulated aswhere is the DC motor input voltage, is back electromagnetic force, and , , and are the resistor, inductance, and current flow of the DC motor. The terms and are defined as back electromagnetic force and motor torque constants and is defined as DC motor gear ratio. Rearrange expression (5) as a function of asBy substituting expression (6) into (3), the final equation for DC motor’s torque can be obtained aswhere is 0.1 ohm, is 0.0001 H, is 16 : 3 gear ratio, and is 0.0533 N·m/A.
2.3. Hydraulic Power Assisted Equation
The other mechanism connected to the steering column is the hydraulic power assisted unit. This unit enables elimination of extensive modifications to the existing steering system and reduces effort by the driver to rotate the steering wheel since the hydraulic power assisted unit is able to produce large steering effort using hydraulic pump, rotary spool valve, and Pitman arm:where and are right and left cylinder pressures, while is defined as length of cylinder and the piston area of the cylinder is expressed as . The detailed description can be obtained from .
2.4. Universal Joint Equation
Due to the limitation of space at the engine location of the armored vehicle, the hydraulic power assisted system cannot be located at the same axis as the steering wheel. Hence, an additional join known as universal joint is used as a solution to overcome the space constraint. The universal joint angle is used for the steering mechanism since it is a flexible coupling where it is rigid in torsion but compliant in bending. The angle of is set at 20 degrees lower than the steering column, , and described as
2.5. Description on Pitman Arm
The torque from the hydraulic power assisted model is transferred to actuate the Pitman arm member link through the worm and sector gears. The Pitman arm converts the rotational motion of the steering column into translational motion at the steering linkage. The configuration of worm gear, sector gear, and the Pitman arm member is shown in Figure 3. Based on Figure 3, the output torque of the Pitman arm link, , can be obtained by equating both worm and sector gear torque, and , aswhere ratio of sector gear is and is the angular displacement of worm gear. Since the torque created at sector gear is equal to the torque created at the end joint of Pitman arm, hence
2.6. Steering Linkage Equation
The rotational input from the sector gear is converted into translational motion to the steering linkage using Pitman arm joint link. By using the torque from Pitman arm as the input torque, the equation of motion of the steering linkage is where , , and are mass, viscous damping, and coulomb friction breakout force of steering linkage. Additionally, the terms , , and are the translational displacement, resistance at steering linkage, and radius of Pitman arm. and are the gear ratio efficiency of forward and backward transmission.
2.7. Wheel Dynamics Equation
By using (1), (7), (8), and (11), equation of motion of the wheel can be obtained. The output response of the wheel which is wheel angle, , is given by where , , and are the moment of inertia of road wheel and rotation mass about steering displacement, viscous damping of steering linkage bushing, and coulomb friction breakout force on road wheel. and are the tire alignment moment from Pacejka Magic Tire model and torque at steering linkage. , , and are rotational ratio of steering linkage, steering wheel stiffness, and steering translational stiffness due to linkage and bushing. Figure 4 shows overall configuration of the Pitman arm steering actuated by DC motor.
The state space equation is developed to summarize the final equations of the Pitman arm steering system as shown below:
For steering column,where .
For steering linkage,For wheel dynamic,
3. Validation of Pitman Arm Steering Model
In this section, the behavior of Pitman arm steering model is validated with actual Pitman arm steering system by using hardware-in-the-loop (HIL) technique. The purpose of this validation is to analyze the performance of mathematical model of Pitman arm steering model which is used in heavy vehicle such as truck, bus, or wheeled military vehicle. The parameters of the Pitman arm steering model are listed in Table 1. The performance of the model is validated using three types of lateral inputs such as double lane change, slalom, and step steer test. A detailed discussion on the performance of the Pitman arm steering model is discussed in this section.
3.1. Hardware Setup
A Pitman arm steering test rig has been prepared in Automotive Laboratory at National Defense University of Malaysia (NDUM) as shown in Figure 5. Two incremental rotary encoders are installed at the steering column and wheel chamber. Meanwhile, a DC motor has been attached to the steering column to provide steering inputs as initiated from the host PC. An ECU as shown in Figure 4 has been designed to operate the DC motor using hardware-in-the-loop (HIL) simulation [18, 19].
(a) Top part of Pitman arm steering test rig
(b) Bottom part of the Pitman arm steering test rig
3.2. Hardware-in-the-Loop Setup
HIL technique is used in this study to validate the developed mathematical model of Pitman arm steering model with the actual Pitman arm steering mechanism and to evaluate the performance of the Pitman arm steering by providing various wheel inputs. HIL can be divided into two systems which are software and hardware. Software part includes signal interface between Target PC and HOST PC, xPC Target, and Real-Time Workshop software to control DC motor and measure the signal of rotary encoder while Visual Studio 2012 Express used as a C compiler for xPC Target. MATLAB/SIMULINK software has been used as interface to interlink between the hardware and HOST PC via xPC Target. As for the hardware section, it involves with the HOST PC, Target PC, Gear box of DC motor, DC motor, Pitman arm steering test rig, rotary encoders, PCI network card, and data acquisition system, known as National Instrument (NI) board. The configuration of hardware can be observed in Figures 5 and 6 as shown below. With a host computer running xPC Target, MATLAB/SIMULINK, Real-Time Workshop, and a C compiler as the development environment, real-time Pitman arm characteristic can be generated and run on a Target PC using the xPC Target real-time kernel. After the Target PC is interlinked with hardware, the Pitman arm steering can be simulated in real time .
3.3. Validation Results
Four types of steering inputs have been used to validate the Pitman arm steering model. The inputs are known as double lane change and slalom test at 90 degrees as well as step steer at 90 and 180 degrees. The validation results are presented in Figures 7–10 which are the comparison between the measured the wheel angle and also the wheel angle from the simulated Pitman arm steering model based on the actual steering inputs. Based on the validation results, it can be concluded that the mathematical model of Pitman arm steering actuated by DC motor model is able to follow the desired response which was obtained from actual steering responses.
In order to analyze the performance of the developed Pitman arm model, the maximum error between actual and simulation results and root mean square (RMS) is analyzed in this study. The maximum error for double lane change and slalom test is 2.35% and 1.81%. Meanwhile, the maximum errors for step steer test at both 90 and 180 degrees are 3.23% and 3.07%. The maximum error range is less than 5%. Similarly, the percentages of RMS value for both simulation and actual Pitman arm steering model are compared. The percentages of differences using RMS value between simulated and actual system are not more than 2% as shown in Table 2.
4. Hardware-in-the-Loop Simulation of Pitman Arm Steering System
Before implementing steering mechanism into active safety system of a vehicle such as steer-by-wire, active front wheel steering, and electronic stability control, the mechanism should be tested using hardware-in-the-loop simulation (HILS) technique. HILS testing or commonly known as virtual testing electronic control has also become one of the repository tools for the automotive researchers and designers. HILS technique is required in testing an actuator to identify its capability and performance before it can be applied to any real automotive system.
In this study, both mathematical model and actual Pitman arm steering are tested using various wheel inputs. The mathematical model is tested via simulation known as software-in-the-loop simulation (SILS) analysis by tuning the controller parameters to its optimum value which can be used for various inputs. The parameters of PID controller are tuned by using the Ziegler-Nichols technique. The Ziegler-Nichols tuning method attempts to produce optimum values for the PID gain parameters [20, 21]. The similar control parameters are implemented while testing the actual pitman arm steering mechanism using HILS technique.
Two types of control loops are mainly focused in position tracking control of the pitman arm steering mechanism which are inner and outer loop control. The inner loop control is focused on the position control of a DC motor for both simulation and HILS technique which can be referred from . Meanwhile, the outer loop control is designed by using the Pitman arm steering model for simulation analysis and actual mechanisms for HIL analysis. A conventional PID control is used as the controller for both inner and outer loop controls.
4.1. Position Tracking Control
The position tracking control is developed by merging both inner and outer loop controls as shown in Figure 11. Two PID controllers have been used to control the DC motor shaft’s rotational angle and also the steering column of the Pitman arm steering system. The first PID controller is used to command the DC motor by varying the voltage input to the DC motor. Meanwhile, the second PID controller is used to actuate the steering column according to the desired inputs. Therefore, the validated Pitman arm steering model is used initially to evaluate position tracking control using a PID controller via SILS analysis. The control structure of the position tracking control is developed as shown in Figure 11.
Meanwhile, Figure 12 shows the control structure for position tracking control of the Pitman arm steering model using an automotive DC motor. Two rotary sensors have been used to measure the rotation angle of the DC motor which is attached to the steering column. Meanwhile, the other rotary sensor is mounted at the wheel to measure actual wheel angle. The output signal from first PID controller is sent as analogue output to the DC motor using the PCI 6221 National Instrument (DA). The signals obtained from rotary sensors which are connected through PCI 6221 National Instrument (DA) are used as feedback input to the HILS evaluation. Likewise, the position tracking of the Pitman arm steering system is validated using four different types of inputs, namely, sine, square, sawtooth, and step inputs. Similar PID control parameters from SILS are used for the HILS experiment as the benchmark point. However, there are slight changes in the control parameters due to the frictional force that occurred on the Pitman arm member link and also backlash occurred at the gear mechanism which connects the DC motor and the steering column. The control parameters are listed in Table 3 for further references.
In the HILS results, there are some disturbances that occurred due to the mechanical friction which affects the performance of the Pitman arm steering system. In order to minimize the effect, a model-based compensation approach is used in this study. Its implementation requires choice of an appropriate friction model, identification of its parameters, and finally friction compensation using the identified model. Besides, this model also assumes that the frictional force or torque of adequate bandwidth is available and stiffly coupled to the friction element. Therefore, friction compensation is implemented by adding the opposite of the predicted friction to the control signal as shown in Figure 15. To cope with the presence of actuator dynamics, one possibility is to use an inner force control loop, in addition to the position control loop. The HILS control structure with implementation of friction compensation can be minimized position steady state error and oscillation generated by unwanted friction. In this paper, the diagram in Figure 14 is used for Karnopp model-based friction compensation in the electric DC motor and Pitman steering system. Model-based friction compensation using the Karnopp model, in an electric-motor system, has been already used . This compensator gives satisfactory results when the objective is position tracking response.
The Karnopp model solves the unwanted friction problem by introducing a pseudo velocity a small neighbourhood of zero velocity, . The pseudo velocity, , which is referred from momentum, is integrated in the standard way:where is the force acting on the system while is the estimated friction force based on the system response. The velocity of the system is set according to (17) where is referred to as steering mass:The friction law is described as follows:where (19) includes static, coulomb, and viscous terms , , and .
4.2. Performance Evaluation
In this study, both SILS and HILS were performed for a period of 10 seconds using Runge-Kutta solver with a fixed step size of 0.001 seconds. The model is evaluated with various inputs with two types of frequency which are 0.5 and 1.0 hertz. The purpose of this validation is to verify the capability of the pitman arm steering to follow desired steering correction response after implementation in heavy vehicle system. Four types of desired trajectories known as sine, square, sawtooth, and step inputs have been used to verify the performance of the actual and the validated model pitman arm steering as shown in Figures 13–21.
(a) Side view of armored vehicle
(b) Top view of armored vehicle
Figures 13 and 14 show the comparison of the desired sine input wheel angle compared with the SILS and HILS results with and without friction compensation. Both SILS and HILS results are able to follow the desired wheel angle. HILS with friction compensation follow the response without any influence from hardware but HILS without friction compensation follow the desired response with minor phase shifting due to mechanical response after experiencing friction between gears. It shows that friction compensation able to minimize the effect of the frictional force occurred in the hardware. The responses of the wheel angle for square inputs are shown in Figures 15 and 16 which illustrate minor deviation using HILS without friction compensation compared with simulation and HILS with friction compensation results. There is overshoot that occurred at each change point due to the backlash between gears of the DC motors. This interaction causes delay time up to 0.4 seconds as observed in the HILS results. By implementing the frictional compensation model, the overshoot in square response has been reduced significantly. Besides, the dead time that occurred during phase change has been minimized greatly compared with HILS without friction compensation response. Meanwhile, Figures 17 and 18 show the wheel angle using sawtooth inputs. The results show deviation during the middle of each period. This deviation mainly caused by the hardware interaction causes friction between connections of the pitman arm steering system and steering column which is attached to the hydraulic assist unit . However, these minor deviations can be reduced by adding the friction compensation which estimated the friction that occurred and minimized the effects of unwanted friction.
Figures 19 and 20 represent the step response for HILS and SILS position tracking control using two desired wheel angles of 4.5° and 9°. The HILS with friction compensation results show that the rise-time of step input of wheel angle at 4.5° and 9° is 3.07 s and 3.05 s at 10% height and at 90% of height is 3.45 s and 3.48 s, while dead time occurs up to 0.08 s from rest condition in both cases. The maximum percentage of overshoot is up to 11.3% for wheel angle of 4.5° and 10.2% for wheel angle of 9° as shown in Figures 19 and 20. This minor deviation occurred due to sudden change in rotary sensors response and also because mechanical friction happened between the mounting and gear mechanism which connects DC motor and steering column. However, the HILS performance has been improved significantly by adding the friction compensation model in the HILS control structure which can be observed in Figures 19 and 20. Overall, the response of position tracking response of Pitman arm steering using automotive DC motor shows good agreement between desired trajectories, simulation, and actual response from validated and actual Pitman arm steering since the response of the actual response follows the desired input with a delay of less than 1 s.
5. Future Works
Currently, this Pitman arm steering model is used as a firing-on-the-move actuator (FOMA) in the armored vehicle model. This active system is used mainly to reject the unwanted external disturbance due to backward firing momentum from the gun turret. The dynamic performance of the vehicle model with the pitman arm actuator system is analyzed in terms of yaw rate, lateral acceleration, and also vehicle body side slip. An advance control strategy is proposed to enhance the dynamic performance of the armored vehicle in terms of the directional path and stability of the armored vehicle after firing. The configuration of FOMA in armored vehicle is shown in Figure 21.
In this study, the Pitman arm steering system is developed using Newton’s law motion to describe the working principle of the steering system. The Pitman arm steering model is then validated with an actual Pitman arm steering system in order to validate the mathematical model of the Pitman arm steering model. Four types of steering inputs in the lateral direction are used to evaluate the behavior of the developed steering model. Then, position tracking system using software-in-the-loop simulation (SILS) and hardware-in-the-loop simulation (HILS) is developed using both validated and actual pitman arm steering system. Various types of desired inputs have been used to evaluate the performance of the validated and actual pitman arm steering system. In order to improve the HILS performance, friction compensation using Karnopp model is implemented in this study to minimize the effect of mechanical friction on the system. Significant improvement is obtained for the HILS results which is able to follow the desired response with errors less than 10%. The position tracking system improved with friction compensation is used as inner loop model in the development of an active safety system in armored vehicle.
The authors declare that there are no competing interests regarding the publication of this paper.
This work is part of a research project entitled “Robust Stabilization of Armored Vehicle Firing Dynamic Using Active Front Wheel Steering System,” funded by LRGS Grant (no. LRGS/B-U/2013/UPNM/DEFENSE and SECURITY-P1) and led by Associate Professor Dr. Khisbullah Hudha. The authors would like to thank the Malaysian Ministry of Science, Technology and Innovation (MOSTI), MyPhD programme, from Minister of Education and National Defense University of Malaysia (NDUM) for their continuous support and the support is gratefully acknowledged.
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