Date of Award


Document Type


Degree Name

Master of Science (MS)

Legacy Department

Mechanical Engineering


Vahidi, Ardalan

Committee Member

Thompson , Lonny

Committee Member

Ayalew , Beshah


This thesis describes development of a real-time-implementable algorithm for simultaneous estimation of a heavy vehicle's mass and time-varying road grade and its verification with experimental data. Accurate estimate of a heavy vehicle's mass is critical in several vehicle control functions such as in transmission and stability control. The goal is to utilize the standard signals on a vehicle in a model-based estimation strategy, as opposed to a more costly sensor-based approach. The challenge is that unknown road grade complicates model-based estimation of vehicle mass and therefore the time-varying grade should be estimated simultaneously. In addition an estimate of road grade may be used as a feedforward input to transmission control and cruise control systems enhancing their responsiveness.
The vehicle longitudinal dynamics model (F=ma) forms the core of this model-based approach. Mathematically this is a single equation with one unknown parameter (mass) and one time-varying input disturbance (grade). The goal is to estimate the constant parameter and time-varying grade by using engine torque and speed, vehicle speed and transmission state. The problem is fundamentally difficult because of i) variation of grade over time ii) lack of ``rich'' data during most of vehicle's cruise time, iii) uncertainty about available traction force during gear-shift periods and braking, and iv) low signal-to-noise ratio for vehicle acceleration signal.
We have tested two independent estimation schemes using experimental data sets provided by Eaton Corporation. The first algorithm uses recursive least square with two forgetting factors for simultaneous estimation of mass and grade. The second algorithm is a two-stage scheme which cascades a Lyapunov-based nonlinear estimator next to a recursive least square scheme. These algorithms were conceived in our group in the past; however they needed modification and refinements for robust real-time implementation. After these refinements, the modified algorithms are capable of generating estimates for mass and time-varying road grade which are more accurate in realistic scenarios and for most part of the vehicle run. More specifically we are able to generate very accurate estimates of road grade, when the clutch is fully engaged and we have proposed fixes that improve the quality of estimates even during periods of gear change. Provided persistence of excitations we are able to generate accurate estimates of mass which in turn improves the quality of grade estimate. It is important to robustify initialization of algorithm 1 further which is now sensitive to an initial batch size; a task listed in the future work. Algorithm 2 does not rely on an initial batch and therefore is expected to be adopted as the preferred approach for implementation.