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This paper addresses the challenge of predictive control of a quarter-car nonlinear suspension and low controller-precision. This is done by designing and implementing an adaptive controller with time-delay compensation. First, a real-time control model is created. Then, time-delay compensation is realized and both frequency-domain and time-domain simulation of the controller performance are conducted. According to the simulation results, the sprung-mass acceleration of the suspension controlled by an adaptive controller with time-delay compensation is superior to that without time-delay compensation. Both the period to settle down and the peak of vibration acceleration are smaller. This means the proposed controller is capable of dealing with problems including variable time delay, nonlinear vibration and predictive control. [ABSTRACT FROM AUTHOR]