Hierarchical optimal force-position control of complex manufacturing processes Hesam Zomorodi Moghadam, Robert G. Landers n , S.N. Balakrishnan Department of Mechanical and Aerospace Engineering, Missouri University of Science and Technology, Rolla, MO 65409-0050, USA article info Article history: Received 1 December 2012 Accepted 14 December 2013 Available online 23 January 2014 Keywords: Hierarchical control Optimal control Internal model principle abstract A hierarchical optimal controller is developed in this paper to regulate the machining force and axis positions, simultaneously, in a micro end milling process. The process is divided into two levels of decision making. The bottom level includes the measurable states, which in this work comprises the axis positions. The top level includes the higher order objectives, which can be derived from the bottom level objectives by an aggregation relationship. In this work, the top level 0 s objective is to regulate the machining force. A series of simulations were conducted in which the weighting between the top and the bottom level objectives is adjusted within the feasible range. The results demonstrated that excellent tracking of both axis positions and machining force are achieved during the steady state regardless of the weighting. However, the transient performance of the system could be systematically shaped to achieve better performance of either objective. For the purpose of comparison a decentralized optimal controller was constructed and simulated for the feasible range of controller weights. When the axis position errors were weighted heavily, both controllers were able to regulate the axis errors well, while the hierarchical controller had smaller machining force errors. When the machining force errors were weighted heavily, although the machining force error decreased for the decentralized controller the axis position errors increased significantly. However, with heavy machining force weighting, the hierarchical controller was able to manipulate the axial errors in a way that while the machining force error was reduced, the contour error (i.e., smallest deviation from the tool tip to the desired contour) remained small. & 2013 Elsevier Ltd. All rights reserved. 1. Introduction The demand for higher productivity in todays 0 manufacturing plants has resulted in a need for lower machining process time that leads to higher machining forces. Excessive machining forces can cause tool breakage, low surface quality, spindle stall, and other undesirable effects. In addition, due to changes in cutting geometry, tool wear, etc., the machining force constantly changes throughout the operation. As a result of machining uncertainties and process variations, adaptive approaches have been utilized extensively in the machin- ing force control literature. In these methods model parameters are estimated online and no prior knowledge of the system is required (Harder, 1995; Landers & Ulsoy, 2000). In these techni- ques stability is maintained over a wide range of parameter variations by adjusting the controller gains based upon online measurements. However, implementation, analysis, and develop- ment of adaptive methods are difficult, making them less desirable in industry. Where the development of a model was feasible, different model based approaches have been utilized to robustly control machining forces. Some examples for adaptive approaches are model reference control (Landers & Ulsoy, 2000), linearized force process control (Harder, 1995), and robust machining force control (Kim, Landers, & Ulsoy, 2003). Landers, Ulsoy, and Ma (2004) compared four model based approaches with an adaptive approach. The derived models can also aid in process planning, monitoring, and analysis, making them useful beyond machining force control (Landers & Ulsoy, 2000). Other machining force control methods adopted in the literature utilized artificial intelligence techniques such as neural networks (Luo, Lu, Krishnamurthy, & McMillin, 1998) and fuzzy logic (Kim & Jeon, 2011). Integration of force control and position control is a well- developed area in robotics. A survey on some of the studies of a class of parallel force/position control schemes can be found in a work by Siciliano (2000). Generally two types of force/position control schemes are used in literature (Siciliano, 2000). The first general category is open loop force control which is controlling the motion and force by developing a relationship (i.e., mechanical impedance) between external forces and end-effector position (Khayati, Bigras, & Dessaint, 2006). The main group in this Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/conengprac Control Engineering Practice 0967-0661/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.conengprac.2013.12.008 n Corresponding author. E-mail addresses: hzt42@mst.edu (H. Zomorodi Moghadam), landersr@mst.edu (R.G. Landers), bala@mst.edu (S.N. Balakrishnan). Control Engineering Practice 25 (2014) 75–84