Controlador por realimentación del vector de estados mediante asignación de polos

The two configurations of the idealised vehicle were subjected to the various experimental methods currently used to estimate the dynamic characteristics of vehicles. The two categories of experimental approaches that were evaluated are the response-only (transient) and excitation- response methods.

6.1.1 Idealised Vehicle Development and Configuration

In order to undertake the critical evaluation and the in-service experiments, an idealised quarter car vehicle, known as the Single-Wheeled Experimental Vehicle (SWEV), was designed and commissioned to test and validate the currently available methods and the proposed methods using in-service response data. Constructed from a demonstration model Honda CBR 125R, the rear section was adapted to maintain the original factory-fitted shock absorber, spring and wheel and was fitted with a custom-designed tow bar. The SWEV is a towable system which has a frame located above the fairings to support dead weights, allowing the dynamic characteristics of the vehicle to be varied by adjusting the (sprung) mass loading. A conceptual illustration and photograph of the SWEV is presented in Figure 6-1.

Figure 6-1: Conceptual illustration (top) and photograph (below) of the idealised physical quarter car (SWEV).

Another consideration made prior to the commissioning of the SWEV was for the ability to change the components of the suspension system due to the notoriously nonlinear nature of automotive shock absorbers. A preliminary investigation revealed that the original factory-fitted shock absorber exhibited significant nonlinear characteristics, and so an alternative shock absorber with nominally linear characteristics was commissioned. This resulted in two configurations of the SWEV; the first configuration is known as the SWEV-A and has the original factory-fitted shock absorber. The second configuration, the SWEV-B, has the custom- designed shock absorber with a nominally constant damping coefficient of 2,000 Ns/m that is intended to be velocity-invariant.

The spring remains the same between the two configurations and is mounted onto the shock absorber, so it was important to ensure that the second shock absorber has the same geometrical specifications as those of the factory-fitted shock absorber in order to fit to the original spring and vehicle mounts. For the series of critical evaluation experiments presented in this Chapter, both configurations of the SWEV were loaded with 100 kg of dead weight at the sprung mass.

6.1.2 Response-Only (Transient) Methods

The response-only (transient) methods all attempt to induce the vehicle with a transient excitation in order to measure the free-response vibration for analysis. This is achieved by applying and swiftly releasing a load to the vehicle, or driving over a suitable geometric obstacle. Both configurations of the SWEV were subjected to the three methods outlined by the CEU (1996). These methods are specifically designed for heavy vehicles, and so two of the tests required modification due to the physical limitations of the SWEV. The SWEV was instrumented with an accelerometer to measure the acceleration response of the sprung mass with a sampling frequency of 1,000 Hz. Each of the three test methods were repeated three times to investigate the consistency of the estimates of the dynamic characteristics.

1) Push and Release Test.

CEU Method: The push and release test requires the application of one-and-a-half times the vehicle’s maximum static load before immediate release.

Adapted Approach: Because the method is suited to heavy vehicles, it is not applicable to the SWEV, requiring the applied load to be modified. Suitably large static loads were applied in order to induce the vehicle to vibrate upon release (300 N and 600 N).

2) Lift and Release Test.

CEU Method: The lift and release test requires the body of the vehicle to be raised 80 mm above the chassis and then swiftly released.

Adapted Approach: The sprung mass of the SWEV was not able to be raised 80 mm above the chassis; instead the vehicle was raised to its maximum allowable height of 25 mm without causing the tyre to leave the ground.

3) Ramp Test.

CEU Method: The vehicle is driven at a speed of 5 ± 1 km/h over a ramp as per the dimensions specified in the CEU directive (80 mm drop at the end of the ramp). The ramp is designed to have a relatively long lead up to minimise any vibration generated in the vehicle prior to the step down off the ramp.

Adapted Approach: The ramp test was undertaken using the exact specifications outlined under the CEU directive (80 mm drop).

Once the subsequent decaying free vibration of the SWEV’s sprung mass was measured, they were analysed to establish the sprung mass dynamic characteristics. The response data was filtered to isolate the sprung mass mode (Low-Pass Filter: Butterworth 5th order, cut-off frequency of 5 Hz). The filtered response data was then analysed using the FFT (with zero- padding of sixteen-times the sub-record length) to estimate the damped natural frequency, while the instantaneous magnitude envelope was established (using the Hilbert Transform) to estimate the damping ratio of the suspension system. When using the Hilbert Transform to estimate the damping ratio, there is a level of subjectivity on the operator to select the appropriate section of the envelope for analysis and so three independent estimates of the curve-fit bandwidth were obtained for each test run.

6.1.3 Excitation-Response Methods

The excitation-response experiments use a suitable vibration table to subject the vehicle to a predefined excitation spectrum (inducing vertical motion at the wheels) whilst simultaneously measuring the excitation and response, from which the vehicle’s FRF is established. This experimental method was achieved through the use of an in-ground servo-hydraulic vibration test system driven by a programmable vibration controller. The SWEV was placed onto a vibration table and the tow bar was mounted onto a stand fixed to the ground. Two accelerometers were used to measure the excitation (at the table) and the response of the sprung mass. The experimental arrangement of the excitation-response experiments using the SWEV is shown in Figure 6-2.

The excitation of the table and the response of the sprung mass for each experiment were simultaneously measured with a sampling rate of 1,000 Hz for a duration of 410 seconds (where possible) to provide a sufficient number of independent averages of the FRF. The first spectral function used was acceleration band-limited white noise (frequency range: 0.7 – 50 Hz) at three rms intensities of 1.00, 2.00 and 3.00 m/s2. The second PSD function used was acceleration band-limited violet noise, which corresponds to the ISO 8608 spectral model (frequency range: 0.5 – 50 Hz), at three rms intensities of 3.00, 6.00 and 9.00 m/s2. The vibration controller was set with a crest factor limit of four (producing normally-distributed vibration limited to ± 4 standard deviations). Before and after each experiment, the temperature of the shock absorber was measured and no significant change in temperature was encountered (less than 1 °C).

Figure 6-2: The experimental arrangement of the excitation-response experiments. The measured excitation and response data were analysed using the FFT with a sub-record length of 10 seconds (frequency resolution, ∆𝑓𝑓 = 0.10 Hz) and 41 independent averages, unless stated otherwise, to establish the transmissibility FRF, 𝐻𝐻₁(𝑓𝑓) (Equation 3-45). A Hanning window was also applied, along with 50 % overlapping of averages. It is important to note that since windowing is used, a loss in power occurs and so a correction factor was applied to compensate. Once the transmissibility FRF of the vehicle was established, the sprung mass' natural frequency and damping ratio were extracted using a least-squares regression curve-fit to the magnitude transmissibility FRF of an SDoF system (Equation 3-53).

In addition, the statistical distribution (PDF) of the excitation and response for each experiment were determined. As modern vibration controllers produce stationary, Gaussian random vibration, if the vehicle is linear, the statistical distribution of the response will also be Gaussian. This may be used to provide further indication of any nonlinear characteristic in either configuration of the SWEV. Prior to establishing the PDF of the normalised acceleration rms of the excitation and response data, a low-pass filter was applied to remove the influence of noise outside of the relevant frequency bandwidth (Low-Pass Filter: Butterworth 4th order, cut- off frequency of 60 Hz) and a total of 100 bins were used to calculate the PDFs.