Abstract
A refined approach for the implementation of preview control in discrete time based on methods from earlier work is given. This allows the use of multiple preview inputs and reduces the system order of a discrete-time preview system significantly with respect to former methods, while describing the dynamic system in an exact form and yielding an equivalent control law. This method is applied to a limited-bandwidth quarter-car system, which incorporates an actuator in series with a passive spring, the combination being in parallel with a passive damper. Control design is carried out using discrete-time linear quadratic regulator (LQR) theory with tyre deflection, suspension working space, vertical body acceleration and control demand. How the optimal preview control law works in a physical sense is worked out regarding the feedforward gain matrix. It is shown that, as a part of the optimal control strategy, the preview controller "concentrates" in some sense on what it can do best for any amount of preview time. The conclusions from that are backed up considering performance indices and their components for variation of preview time, actuator bandwidth and the constraints in the cost function. Emphasis is put on the investigation of how the actuator bandwidth influences the performance capabilities of the system. General relationships between cast reduction, cost-component reduction, preview time and system bandwidth are exposed. By increasing preview time, the cost function can be reduced until it reaches a saturation value, which depends on the actuator bandwidth chosen. Increasing the actuator bandwidth beyond a certain value has only a small influence on the preview time needed for the diminishing returns to set in. Improving the road holding requires fast actuators, but comparatively short preview distances. Ride comfort can be influenced by a rather slow controller, but requires a long preview time.
Published Version
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