Cycle-to-Cycle Control of Multivariable Manufacturing Processes With Process Model Uncertainty

Abstract

In-process closed-loop control of many manufacturing processes is often impractical owing to the impossibility or the prohibitively high cost of placing sensors and actuators necessary for in-process control. Such processes are usually left to statistical process control methods, which only identify problems without specifying solutions. Cycle-to-cycle control is a method for using feedback to improve product quality for processes that are inaccessible within a single processing cycle but can be changed between cycles. This type of control has the same objectives as run-by-run control. However, it is developed from a different point of view allowing easy analysis of the process’ transient closed-loop behavior due to changes in the target value or to output disturbances. Our previous work introduced cycle-to-cycle control for single input-single output processes and here it is extended to multiple input-multiple output processes. Gain selection, stability, and process variance amplification results are developed and compared with those obtained by previous researchers, showing good agreement. Then, the limitation of imperfect knowledge of the plant model is imposed. This is consistent with manufacturing environments that require minimal cost and number of tests in determining a valid process model. The effects of this limitation on system performance and stability are discussed. The theoretical results are applied to a novel, discrete-die sheet metal stretch-forming process. The classical, monolithic tool is replaced by a large number of small, separate pieces that can be reconfigured between cycles to approximate continuous shapes. Thus, each forming cycle can use a new input shape. The experimental system is an ideal candidate for the application of cycle-to-cycle control in a multivariable fashion. A linear process model is presented that includes the effects of single input-multiple output coupling. Experimental validation of variance amplification results for a sheet metal forming processes is presented with hundreds of inputs and outputs. While many controller designs could be considered a purely diagonal (decoupled) and a Linear Quadratic Regulator design are presented and discussed. Comparison between theory and experiments is provided, showing good agreement.