The aim of suspension systems in vehicles is to provide the best balance between ride and handling depending on the operating conditions of a vehicle. Active suspensions are far more effective over a variety of different road conditions compared to passive suspension systems. This is because of their ability to store and dissipate energy at different rates. Additionally, they can even provide energy of their own into the rest of the system. This makes active suspension systems an important topic of research in suspension systems. The biggest benefit of having an active suspension system is to be able to provide energy into the system that can minimize the response of the sprung mass. This is done using actuators. Actuator design in vehicle suspension system is an important research topic and a lot of work has been done in the field but little work has been done to estimate the peak control force and bandwidth required to minimize the response of the sprung mass. These two are very important requirements for actuator design in active suspensions. The aim of this study is estimate the peak control force and bandwidth to minimize the acceleration of the sprung mass of a vehicle while it is moving on a compliant surface. This makes the road surface a bi-lateral boundary and hence, the total system is a combination of the vehicle and the compliant road. Generalized vehicle and compliant road models are created so that parameters can be easily changed for different types of vehicles and different road conditions. The peak control force is estimated using adaptive filtering. A least mean squares (LMS) algorithm is used in the process. A case study with fixed parameters is used to show the results of the estimation process. The results show the effectiveness of an adaptive LMS algorithm for such an application. The peak control force and the bandwidth that are obtained from this process can then be used in actuator design. / Master of Science / Active suspension systems have been proven to be a better option compared to passive suspension systems for a wide variety of operating conditions. Active suspensions typically have an actuator system that produces a force which can reduce the disturbance caused by road inputs in the suspension. The sprung mass of a vehicle is the mass of the body and other components supported by the suspension system and the un-sprung mass is the total mass of the components which are not supported by the suspension or are part of the suspension system. The actuator is typically between the sprung mass and the un-sprung mass. When there is a single event disturbance from the road, the energy is transferred to the sprung mass, which contains the occupants, through the un-sprung mass. The actuator produces a force that reduces this acceleration in the sprung mass and hence improves ride comfort for the occupants of the vehicle. In this thesis, the single event disturbance that has been considered is a compliant road surface. This is a bi-lateral boundary since the vehicle interacts with the compliant elements under the surface of the ground. The aim of this thesis is to develop and implement a method to estimate the peak control force and bandwidth that the actuator needs to produce to eliminate or reduce the acceleration of the sprung mass which is caused by the compliant surface single event disturbance.