Transmission Clutch Fill Control Using a Customized Dynamic Programming Method

2008 ◽  
Author(s):  
Xingyong Song ◽  
Mohd Azrin Mohd Zulkefli ◽  
Zongxuan Sun ◽  
Hsu-Chiang Miao
Keyword(s):  
Dynamic Programming ◽  
Control Problem ◽  
Systematic Approach ◽  
Traditional Approach ◽  
Pressure Profile ◽  
Dynamic Programming Method ◽  
Transmission Performance ◽  
Automotive Transmission ◽  
Flow Demand ◽  
Numerical Dynamic Programming

Clutch fill control is critical for automotive transmission performance and fuel economy, including both automatic and hybrid transmissions. The traditional approach, by which the clutch fill pressure command is manually calibrated, has a couple of limitations. First, the pressure profile is not optimized to reduce the peak clutch fill flow demand. Moreover, it is not systematically designed to account for uncertainties in the system, such as variations of solenoid valve time delay and parameters of the clutch assembly. In this paper, we present a systematic approach to evaluate the clutch fill dynamics and synthesize the optimal pressure profile. First, a clutch fill dynamic model is constructed and analyzed. Second, the applicability of the conventional numerical Dynamic Programming (DP) algorithm to the clutch fill control problem is explored and shown to be ineffective. Thus we developed a new customized DP method to obtain the optimal and robust pressure profile subject to specified constraints. After a series of simulations and case studies, the new customized DP approach is demonstrated to be effective, efficient, and robust for solving the clutch fill optimal control problem.

Automotive Transmission Clutch Fill Control Using a Customized Dynamic Programming Method

2011 ◽  
Vol 133 (5) ◽  
Author(s):  
Xingyong Song ◽  
Mohd Azrin Mohd Zulkefli ◽  
Zongxuan Sun ◽  
Hsu-Chiang Miao
Keyword(s):  
Dynamic Programming ◽  
Control Problem ◽  
Dynamic Model ◽  
Low Cost ◽  
Pressure Profile ◽  
Open Loop ◽  
Dynamic Programming Method ◽  
Flow Demand ◽  
Compact Design ◽  
Numerical Dynamic Programming

Clutch to clutch shift control technology, which is the key enabler for a compact and low cost transmission design, is important for both automatic and hybrid transmissions. To ensure a smooth clutch to clutch shift, precise synchronization between the on-coming and off-going clutches is critical. This further requires the on-coming clutch to be filled and ready for engagement at the predetermined time. Due to the compact design, currently there is no pressure sensor inside the clutch chamber, and therefore the clutch fill can only be controlled in an open loop fashion. The traditional clutch fill approach, by which the clutch fill input pressure command is manually calibrated, has a couple of limitations. First, the pressure profile is not optimized to reduce the peak flow demand during clutch fill. Moreover, it is not systematically designed to account for uncertainties in the system, such as variations of solenoid valve delay and parameters of the clutch assembly. In this paper, we present a systematic approach to evaluate the clutch fill dynamics and synthesize the optimal pressure profile. First, a clutch fill dynamic model, which captures the key dynamics in the clutch fill process, is constructed and analyzed. Second, the applicability of the conventional numerical dynamic programming (DP) method to the clutch fill control problem, which has a stiff dynamic model, is explored and shown to be ineffective. Thus, we proposed a customized DP method to obtain the optimal and robust pressure profile subject to specified constraints. The customized DP method not only reduces the computational burden significantly, but also improves the accuracy of the result by eliminating the interpolation errors. To validate the proposed method, a transmission clutch fixture has been designed and built in the laboratory. Both simulation and experimental results demonstrate that the proposed customized DP approach is effective, efficient and robust for solving the clutch fill optimal control problem.

scholarly journals Single-Manufacturer Multi-Retailer Supply Chain Models with Discrete Stochastic Demand

2021 ◽  
Vol 13 (15) ◽  
pp. 8271
Author(s):  
Yaqing Xu ◽  
Jiang Zhang ◽  
Zihao Chen ◽  
Yihua Wei
Keyword(s):  
Dynamic Programming ◽  
Supply Chain ◽  
Computational Complexity ◽  
Stackelberg Game ◽  
Programming Model ◽  
Dynamic Programming Method ◽  
Game Model ◽  
Chain Model ◽  
Stochastic Demands ◽  
Demand Models

Although there are highly discrete stochastic demands in practical supply chain problems, they are seldom considered in the research on supply chain systems, especially the single-manufacturer multi-retailer supply chain systems. There are no significant differences between continuous and discrete demand supply chain models, but the solutions for discrete random demand models are more challenging and difficult. This paper studies a supply chain system of a single manufacturer and multiple retailers with discrete stochastic demands. Each retailer faces a random discrete demand, and the manufacturer utilizes different wholesale prices to influence each retailer’s ordering decision. Both Make-To-Order and Make-To-Stock scenarios are considered. For each scenario, the corresponding Stackelberg game model is constructed respectively. By proving a series of theorems, we transfer the solution of the game model into non-linear integer programming model, which can be easily solved by a dynamic programming method. However, with the increase in the number of retailers and the production capacity of manufacturers, the computational complexity of dynamic programming drastically increases due to the Dimension Barrier. Therefore, the Fast Fourier Transform (FFT) approach is introduced, which significantly reduces the computational complexity of solving the supply chain model.

scholarly journals UAV Formation Shape Control via Decentralized Markov Decision Processes

Algorithms ◽  
2021 ◽  
Vol 14 (3) ◽  
pp. 91
Author(s):  
Md Ali Azam ◽  
Hans D. Mittelmann ◽  
Shankarachary Ragi
Keyword(s):  
Control Problem ◽  
Shape Control ◽  
Formation Control ◽  
Three Dimensional ◽  
Geographical Region ◽  
Dynamic Programming Method ◽  
Theoretic Approach ◽  
Control Approach ◽  
Uav Swarm ◽  
Markov Decision

In this paper, we present a decentralized unmanned aerial vehicle (UAV) swarm formation control approach based on a decision theoretic approach. Specifically, we pose the UAV swarm motion control problem as a decentralized Markov decision process (Dec-MDP). Here, the goal is to drive the UAV swarm from an initial geographical region to another geographical region where the swarm must form a three-dimensional shape (e.g., surface of a sphere). As most decision-theoretic formulations suffer from the curse of dimensionality, we adapt an existing fast approximate dynamic programming method called nominal belief-state optimization (NBO) to approximately solve the formation control problem. We perform numerical studies in MATLAB to validate the performance of the above control algorithms.

scholarly journals Initializing the EM Algorithm for Univariate Gaussian, Multi-Component, Heteroscedastic Mixture Models by Dynamic Programming Partitions

2018 ◽  
Vol 15 (03) ◽  
pp. 1850012 ◽  
Author(s):  
Andrzej Polanski ◽  
Michal Marczyk ◽  
Monika Pietrowska ◽  
Piotr Widlak ◽  
Joanna Polanska
Keyword(s):  
Dynamic Programming ◽  
Mixture Models ◽  
Recursive Algorithm ◽  
Dynamic Programming Method ◽  
Mixture Distributions ◽  
Gaussian Mixtures ◽  
Scoring Functions ◽  
Initial Values ◽  
The Em Algorithm

Setting initial values of parameters of mixture distributions estimated by using the EM recursive algorithm is very important to the overall quality of estimation. None of the existing methods are suitable for heteroscedastic mixtures with a large number of components. We present relevant novel methodology of estimating the initial values of parameters of univariate, heteroscedastic Gaussian mixtures, on the basis of dynamic programming partitioning of the range of observations into bins. We evaluate variants of the dynamic programming method corresponding to different scoring functions for partitioning. We demonstrate the superior efficiency of the proposed method compared to existing techniques for both simulated and real datasets.

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