Output Feedback Controller Reduction Of Active Suspensions And Rapid Control Prototyping

Suspension is the main part of the vehicle. It lies between body and wheels. Usually, the suspension is composed of the spring and damper elements. Performance requirements for advanced vehicle suspensions include isolating passengers from vibration and shock arising from road roughness (ride comfort), suppressing the hop of the wheels so as to maintain firm, uninterrupted contact of wheels to road (good handling or good road holding) and keeping suspension strokes within an allowable maximum. Moreover, control inputs, for example active forces that are generated by hydraulic actuators, are constrained due to actuator saturation. However, these requirements are conflicting, for example, increasing ride comfort results in larger suspension stroke and smaller damping in the wheel-hop mode.In order to manage the trade-off between conflicting requirements, many active suspension control approaches are proposed based on various control techniques, such as LQG, adaptive control, H∞control and nonlinear control. A common point of most approaches is that all requirements are weighted and formulated in a single objective functional ( H 2 or H∞), which will be minimized to find an optimal controller. One manages the trade-off between conflicting requirements by choosing appropriate weighting, possibly frequency-dependent, which is however not trivial. For the 4 DOF half-car model, in order to capture control requirements (ride comfort, good handling, limited suspension stroke and actuator saturation), one may choose a single objective by tuning 8 weights. Clearly, to do this to achieve an optimal performance is quite difficult, if not impossible in practice.Having a close insight into the control requirements for active suspensions, it is clear that requirements on good road holding, limiting suspension strokes and control inputs within bounds are in fact hard constraints in time domain. Hence, it is much nature to formulate the active suspension control problem as a disturbance attenuation problem with hard constraints.In terms of different input signals, there are two interpretations of the H 2 norm:①the square root of the total output energy in the impulse response of the system.②the asymptotic output variance when the input is white noise. In the second case, if the input signals are independent, the H 2 norm is equal to the root mean square (RMS) value of the output, too. It implies that under no matter what ground disturbances style, either normal road or pronounced bumps or potholes, H 2 performance should be appropriate. Since generalized H 2 norm is defined as a measurement from energy-bounded inputs to peak amplitudes of the outputs in time domain, we consider to capture the hard constraints by generalized H 2 performance.Thus products the strategy of H 2 /generalized H 2 mixed control active suspension. In this strategy, the H 2 norm from ground disturbances to body accelerations is minimized, while all constraint outputs is captured by generalized H 2 norm. In the framework of LMI optimization and multi-objective control, mixed control arithmetics, which combining either of the constraints control methods and H 2 performance are formulated. In the mixed control arithmetics, design of the controller is convert to a LMI based semi-definite programming problem. While only one parameter has to be determined and can be used as a freedesign parameter to manage effectively conflicting requirements. It indicates a big betterment in active suspension control.In order to validate the efficiencies of the proposed approaches, we designed output feedback controller to a real half car model based on mixed control strategy. In the later case, the design model we considered is augmented, in which the dynamics of the actuator is assumed to be a hydraulic actuator placed between the sprung and unsprung masses. Design results are analyzed and simulated in frequency responses, time property, pulse responses. Analysis results show an obvious improvement to the performance of the active suspension.As it is well known the H 2 controller design method results in a controller with the same order as the plant plus the order of the weights. This property makes the order of an H 2/generalized H 2 based controller unacceptable for half-car plants and which with hydraulic actuator. Evidently, simple controllers are normally preferred over complex ones, because there are fewer things to go wrong in the hardware or bugs to fix in the software; and the computational requirements are less. For these reasons, we scan a famous approach-balancing and truncation for controller reduction, that we have applied to active suspension system. Sometimes balancing and truncation of Moore method is applied for controller reduction but unlike the model reduction case, there is no guarantee for the stability of the closed loop system in controller reduction case and consequently error bound. In Moore method the diagonal elements of the balanced matrices are sorted in descenting order and are called Hankel singular values. If the Hankel singular values dwindle rapidly, there is a high possibility to obtain a good reduced controllers. In this case, if it fail to keep the closed loop stabile, you must add the order and do it again. And the final controller will maintains the closed loopstability and results in an acceptable error norm. The frequency domain plots show that the reduced order controller is also efficient at the frequencies of interest and there is not any perceivable degradation in the time domain plots.Finally, integrative real-time experiments of RCP(Rapid Control Prototyping) based on dSPACE were made to validate the proposed control approaches in "actual" condition. Controllers we designed were download to a hardware and run in a real-time environment. Experiment curves again reveal availability of the methods.Deeper research work need to be done since some problems is still remain to be solved, such as how to derive a solution of robust guaranteed output feedback synthesis, and how to design output feedback controller which has the highest precision in the frequency and timedomain with the lowest order, etc.