Summary:
This article will introduce the functional principle design of active suspension in detail.
Active suspension is a type of automotive suspension on a vehicle. It uses an on-board system to control the vertical movement of the wheels relative to the chassis or body, rather than a passive suspension provided by big springs, whose movement is determined entirely by the road surface. Active suspensions fall into two categories: true active suspensions and adaptive or semi-active suspensions . Semi-adaptive suspensions only change the stiffness of the shock absorbers to adapt to changing road or dynamic conditions, while active suspensions use some type of actuator to independently raise and lower the chassis at each wheel. The active suspension system provides better ride comfort and vehicle stability. But compared to semi-active or passive suspension systems, its cost is too high.
However, in terms of the development of increasingly intelligent cars, active suspension is indeed an important direction for everyone's research. For example, the active suspension system of the Mercedes-Benz S-Class can detect the ups and downs of the road surface through the camera, and then let the suspension system actively adjust the wheel height to keep the body level on uneven roads. Let the driving experience feel like sitting on a magic carpet and floating on the road. Hence the name of the magic carpet hanging. This combination of intelligent perception + active suspension applied to intelligent driving can provide full-time body stabilization function, give the car a better driving experience, minimize uncomfortable body movements, and reduce body bumps and side effects. pour.
Therefore, this series of articles will explain the application theory of magic carpet active suspension in two different directions. These include the design principle of active suspension itself, the principle of intelligent perception of road surface preview and the design of performance indicators. This article will introduce the functional principle design of active suspension in detail.
1. Active suspension design principle
Active suspension systems operate between the sprung and unsprung masses of the vehicle. It minimizes vertical acceleration and vehicle vibrations caused by road and vehicle dynamics, improving vehicle handling and stability. Active suspension systems include hydraulic circuits, sensors and control systems. Most active suspensions that have reached the hardware development and production stages use some form of electrohydraulic actuators.
Figure 1 Active suspension frame
A quarter vehicle model as shown in Figure 2 below. In terms of the time to reach the steady state of driving, both active suspension and passive suspension can do it, but the impact of active suspension is obviously much smaller than that of passive suspension, which will achieve a better balance between ride comfort and vehicle stability. good compromise.
Fig. 2 Acceleration frequency response of active and passive suspensions
There are two forms of active suspension currently recognized. The first is the Rapid Active Suspension or High Bandwidth system (HB), often referred to as Full Active. The second is the slow active suspension or low bandwidth system (LB). In an active suspension, both passive dampers and springs are replaced by force actuators, as shown in Figure 3 below.
Fig. 3 Composition design principles of different active suspension systems
Fully Active Suspensions (High Bandwidth), also known as High Bandwidth, place the actuator between the sprung and unsprung masses. The main function of the high bandwidth system is to control the system within the full bandwidth of the whole system. Specifically, this means that it is designed to enhance suspension response around rattle spatial frequencies (from 10 to 12 Hz) and tire jump frequencies (from 3 to 4 Hz).
In the early stage, the active suspension system was also established by using the electro-hydraulic servo system (EHS), and the pressure control valve applied for the first time was adopted. The suspension is controlled by a microprocessor and accelerometer sensors, the system emphasizes skyhook dampers, which reduce body vibrations compared to conventional low frequency suspensions by applying active damping forces to the body relative to its absolute velocity . Hydraulic systems have passive damping characteristics that depend on the road input excitation frequency. The enhancement of these characteristics reduces vibrations generated by high-frequency road surface inputs.
The hardware used in active suspension systems can vary from simple swing dampers, semi-active dampers, low-bandwidth/soft active suspensions to high-bandwidth/stiff active suspensions. Adaptive and semi-active setups are effective means of improving straight-line travel and handling transients, although they don't provide as much improvement on the road as active suspensions.
Slow Active Suspension (Low Bandwidth) for low bandwidth operation . In this system, the actuator is placed in series with the spring and/or damper. Slow active suspension systems (operating at low bandwidths less than 3 Hz) aim to implement suspension control strategies in the lower frequency range, especially around the rattle spatial frequency. At higher frequencies, the actuator effectively locks, so wheel-hopping motion is passively controlled. Compared with high-bandwidth systems, low-bandwidth systems can achieve significant reductions in body roll and pitch during maneuvers with lower energy consumption. To provide suspension action beyond the controlled bandwidth, the actuator must be mounted in series with a conventional spring, which in turn reduces the energy requirements of the system.
There are currently two main forms of low-bandwidth systems, as shown in Figure 3(b)(c) above, one is the actuator in series with the road spring and has a separate passive damper (LB1), the other is the Actuators are in the Spring and Damper series (LB2). In slow active suspensions, passive springs provide the required isolation at high frequencies, while actuators provide vibration control at low frequencies (typically below 3 Hz).
Theoretical studies have shown that bandwidth-limited active systems perform similarly to fully active systems, but at lower cost and implementation complexity. These studies, based on a quarter-car model, show that power requirements are very modest when the components are assumed to be in an idealized state and the vehicle is operating in a straight line. Some possible practical implementations of this system have been proposed in part by using hydropneumatic elements, such as pneumatic springs with valves to control air supply and exhaust.
Since the actuators only require a narrow bandwidth of 3-4 Hz, slow active suspension systems are much less expensive than full active suspension systems that require wideband actuators. But active control still encompasses the normal range of body resonant frequencies in bounce, pitch and roll, and the frequency range of interest in terms of response to steering control. Therefore, slow active suspensions are a commercially viable alternative.
2. Main working mathematical model of active suspension system
1) Mathematical model of electro-hydraulic servo valve
Since the mathematical model of EHSV is described by 27 equations, for the sake of simplicity, the typical EHSV model is no longer used in the full active suspension system model because the calculation and iteration process takes a long time. Therefore, it is important to find the equivalent transfer function of EHSV. For this purpose, the actuator displacement is calculated to further obtain the transient response of the input current. It is found that the step response of the spool displacement behaves like an overdamped second-order system, which can be described by the following transfer function of the second-order system.
In this transfer function, coefficients k, ωn and ξ of the corresponding representative transfer function need to be calculated. The gain value (k) is the spool position removed under steady state conditions with an excitation current value of 10 mA. The values of ωn and ξ can be calculated by running the Simulink program.
2) Mathematical model of hydropneumatic suspension
The scheme of the liquid-pneumatic suspension device is shown in the figure below. A mathematical model of the system was developed by applying equations that describe the dynamic behavior of the suspension units.
The following equation describes this system.
in,
is a term that takes into account the effect of piston chamber compressibility.
Fig. 4. Schematic diagram of hydropneumatic suspension Fig. 5. Damping system valve of hydropneumatic suspension device
The variable orifice area in the compression and rebound strokes of the damping system shown in Figure 4 consists of four holes covered by a circular thin plate riveted in its centre.
3) Quarter Vehicle Suspension Parameters
The mathematical description of the quarter car model is as follows:
The damping coefficient (CS) of the shock absorber is calculated on-the-fly based on a validated damper simulation model. F(t) is the excitation acting on the wheel and caused by surface irregularities. If xo is the elevation of the surface profile, ox& represents the vertical velocity of the tire at the ground contact point, which is the slope of the road profile multiplied by the forward speed of the vehicle.
3. Active suspension system design
This article will explain in detail a typical active suspension working model as shown in the figure below, which can help readers quickly understand the working process of active suspension. The model mainly consists of electro-hydraulic servo valve, actuator, air spring, LVDT and controller. Electrohydraulic actuators are widely used in the design of active suspensions, and electrohydraulic servo systems provide good control from the point of view of precision and speed.
(1) Hydraulic pump (2) Relief valve (3) Accumulator (4) EHSV (5) Accumulator (6) Throttle valve (7) Gas spring (8) Hydraulic actuator (9) LVDT (10 ) tires (spring + shock absorber) (11) fuel tank
Figure 6 Active suspension working model
The output control variables were selected to achieve the desired dynamic response of the body, the control structure was constructed to measure the feedback values, and the measurement setup was determined. The operation of the designed active suspension system is divided into three modes; neutral mode, compression mode and rebound mode.
1) Neutral mode
When the vehicle is running on a very flat surface or the vehicle is stopped, it means that there is no input displacement from the road surface and there is no relative motion between the body and the wheel assembly. The feedback current from the LVDT and accelerometer is zero, and the error signal (ie) to the servo valve is zero. As shown in the figure (4) above, the spool of the EHSV is in the neutral position at this time.
2) Compression mode
If the vehicle encounters a bump in the road, the wheel assembly moves up and the distance between the body and the wheel decreases. The feedback current from the LVDT and accelerometer increases and the error signal to the servo valve increases accordingly. Pressure (P2) will also increase synchronously and the spool will move to the left. The piston chamber is partially connected to the fuel tank to allow oil flow movement due to the movement of the piston to be directed into the tank, keeping the body nearly on the same level in the process.
3) Rebound mode
During the pothole rebound stroke, the wheel assembly moves downward and the distance between the body and the wheel assembly increases. As a result, the feedback current increases and at the same time the negative error signal (ie) of the EHSV also increases.
The oil flow movement increases to the left spool chamber, the pressure (P1) increases, so the spool moves to the right, the cylinder chamber is connected with the pressure line, and the oil flows to the piston chamber to compensate for the outward movement of the piston, which can keep the body as much as possible on the same level.
4. Application of Pseudo Differential Feedback Control PDF in Active Suspension PID
For the adjustment of active suspension, a typical proportional-integral-derivative controller (PID controller) is usually used to control the loop feedback. The process of PID control is to calculate the "error" value as the difference between the measured output value and the desired set point, and the controller tries to minimize the error by adjusting the actual plant control input.
With a typical step input, a PID block that includes a differentiator block can cause sudden high-amplitude spikes in the system response. In order to eliminate this shortcoming, it is necessary to introduce a differential operation in the feedback path and improve the response of the system. The basic idea of PDF control (pseudo-derivative feedback control) is to avoid a large control signal inside the system (which will cause saturation). Therefore, in the PDF controller, the system response is highly acceptable, and point jumps can be set to avoid pulse shocks due to the presence of differentiators in the forward path of conventional PID controllers.
In addition, the system can guarantee low asynchronous errors. By introducing proportional and derivative control actions into the feedback path, larger values for Kp and Td can be chosen than are possible with PID control. Therefore, the PDF control system can attenuate the influence of the disturbance faster than the case of PID control. Therefore, studying the dynamic performance of the active suspension system PID and PDF controller will be beneficial to the optimization of the application strategy of the entire active suspension system.
The application of these two adjustment mechanisms in active suspension will be described in detail below to facilitate better research on the dynamic performance of vehicle active suspension systems.
This paper presents the design of a quarter vehicle equipped with an active suspension system by developing a mathematical model for the controlled system and developing a computer simulation program to evaluate the dynamic behavior of the system. The system consists of an electrohydraulic servo system controlled by a proportional-integral-derivative (PID) controller or using a pseudo-differential feedback controller (PDF). The parameters of both controllers are estimated and tuned to minimize the Integral Squared Error (ISE) and Integral Time Absolute Error (ITAE) criteria. A proportional-derivative (PD) controller provides the shortest settling time. The PDF controller shows a negligible maximum percentage overshoot, while the PID shows a maximum percentage overshoot within 5%. Proportional, Integral (PI) and PD show long settling times.
1) Design of PID controller
The PID controller calculation algorithm involves three independent constant parameters, so it is sometimes called three-term control: proportional value, integral value and differential value, respectively represented as P, I and D (as shown in the figure below). The proportional term P depends on the current error, the integral term I depends on the accumulation of past errors, and the derivative term D is a prediction of future errors based on the current rate of change. The weighted sum of these three actions is used to adjust the equipment or process by controlling elements such as the position of control valves or dampers.
2) Connection of PID controller in closed loop system
The process of selecting controller parameters to meet a given performance specification is called controller tuning. It is recommended to tune the rules of the PID controller (ie set Kp, Td and Ti values) according to the experimental step response or Ku value, which leads to marginal stability when using only proportional control action. Employing the Ziegler-Nichols rule is useful when the mathematical model is unknown. Such rules suggest a set of Kp, Td, and Ti values that will give the system stable operation. However, the final system may exhibit a large maximum overshoot in the step response, which is unacceptable. In this case, we need to do a series of fine-tuning until we get an acceptable result. In fact, the Ziegler-Nichols tuning rules give very educated guesses about parameter values and provide a starting point for fine-tuning, rather than giving final settings for Kp, Ti, and Td all at once.
Here, the first estimation of the parameters of the PID controller used in this study is carried out according to the first Ziegler-Nichols method. In addition, the subsequent manual fine-tuning process can also find the controller parameters; K, Ti and Td, which ensure the minimum value of the Integral Time Absolute Error (ITAE) performance index.
The corresponding ITAE is defined as follows:
Some applications may only need to use one or two operations to provide proper system control. This is achieved by setting other parameters to zero. Without a corresponding control action, a PID controller would be called a PI, PD, P or I controller. PI controllers are quite common because the derivative action is sensitive to measurement noise. The constants of the controller are calculated and fine-tuned. The step response of the system with a proportional controller shows that the implementation of a proper proportional controller reduces the settling time from 5.26 seconds to 0.65 seconds. However, this conclusion cannot be generalized. Proportional controllers are associated with non-negligible steady-state errors unless the device contains an integrating element.
2) Design of PDF controller
Existing theory proposes a set of formulas for estimating first approximations of the controller gain constants; Kp, KD and Ki, from which fine-tuning begins. These formulas are a combination of analytical and experimental results. These formulas are based on the largest step input that requires a substantially linear output response. Therefore, the development of a PDF controller requires an open-loop representation of the system, via a first-order or second-order transfer function. To this end, the transient response of the system to a step input current i is calculated for different magnitudes of the applied step. The step response exhibited by an active suspension system is clearly similar to that of a second-order element whose transfer function is given by:
3) Step response and equivalent representative model of active suspension system
A first order approximation of the PDF controller constants can be calculated from the above equations. The adjustment of the PDF controller is provided by finding the best combination of coefficients Kp, KD, Kin to achieve the best system response.
The following figure shows the comparison of the control results of PID and PDF for the response.
The PID controller gave the best results, mainly on the settling level time. And the PD controller gives the minimum and maximum percentage overshoot. Derivative action predicts system behavior, improving settling time and stability of the system. However, differential action is rarely used in practice because of its inherent sensitivity to measurement noise. If this noise is severe enough, the derivative action will be unstable and actually degrade control performance. Large and sudden changes in measurement error (usually occurring when the set point is changed) can cause sudden, large control actions, originating from the derivative term, which is called derivative kick. This problem can be improved to some extent if the measurement error is passed through a linear low pass filter or a nonlinear but simple median filter.
PI controllers are common because the derivative action is sensitive to measurement noise. But since an integral element is included in the studied active suspension, the function of this controller does not appear here.
Author | Jessie
Produced| Yan Zhi