Model Predictive Control of Double Stacked Suspension System
Authors: Batta Nathan , Doscher Daniel 
Published: February 2021

Abstract
This study examines implementation of a Model Predictive Controller (MPC) to a new concept in active suspension design. Active and passive components are placed in series to mitigate both high and low frequency disturbance inputs at the tire-road interface. This is modelled using an additional mass spring damper tuned to regulate high frequency inputs, leaving the active components to respond to low frequency inputs. A generic half car model for such a system is developed and subjected to various disturbance inputs at constant velocity and output to verify the system dynamics. Inputs include step, multimodal, and random disturbances as well as a step input that returns to zero. These trials serve as a baseline to evaluate the performance of the passive suspension as well as a Model Predictive Controller. Current research that uses MPC in active suspension design focuses heavily on the traditional half car model with 4 DOF[4]. MPC is applied to this new 6 DOF model and incorporates preview information into the controller response for each of the test cases. The cost function for the MPC places penalties on the translational and rotational position and velocity of the chassis relative to a reference state that is based on each disturbance profile. Parameters of interest are driver absorbed power due to both linear and rotational movement of the chassis. The results for each test case demonstrate the utility of MPC. For every response, there is a decrease in the absorbed power due to rotational and linear sources on the magnitude of 98–100%. The incorporation of preview information also removed the rotation of the chassis for each test case by placing a heavy weight upon its movement. For the step input, the controller reduced the peak rate of change of the chassis by 71.4%. For the multi-mode input, the low frequency sinusoidal inputs showed a dramatic reduction in vertical displacement in the steady state behavior as the MPC will produce an output that is tuned to cancel the disturbance. The high frequency effects are also effectively removed by the passive components of the suspension. This ability to mitigate both sources of disturbance is a marked advantage of the double-stacked suspension design. MPC allowed for the overall reduction of chassis movement by 54.0% with preview information. This improvement is due to the ability of the double stacked suspension with MPC to use the additional degrees of freedom to attenuate disturbances at more than one frequency. The random input demonstrates the ability of the controller to maintain a smooth chassis trajectory even with a chaotic road profile. Finally, the step up-down input demonstrates the ability of the controller to use other components of the suspension system to mitigate a disturbance in order to keep the chassis stable. These results demonstrate that preview information can be used to take full advantage of double stacked, active suspensions and further enhance mobility over different kinds of terrain. Future work includes investigating the effectiveness of other predictive control methods such as two-point boundary value problem or dynamic programming, optimizing the weights used, or adding constraints to the model.