Control Engineering Practice 13 (2005) 1439–1451 Experimental validation of different MIMO-feedback controller design methods D. Vaes à , J. Swevers, P. Sas KULeuven, Department of Mechanical Engineering, Division PMA (Production engineering, Machine design and Automation), Celestijnenlaan 300B, B-3001 Leuven, Belgium Received 15 March 2004; accepted 23 December 2004 Available online 5 February 2005 Abstract The multivariable tracking performance of an automotive vibration test rig can be improved by extending the current industrial off-line iterative feedforward procedure with a real-time feedback controller. This paper tests and validates three different MIMO- controlschemesonanindustrialtestrig.Firstlydecentralized(ordiagonal)controlisused,whichisacombinationofindependently designedSISO-controllersbasedonthediagonalelementsoftheMIMO-systemmodel.SecondlyfullMIMO H 1 -control,basedon aMIMO-modelistested.Finallyinverse-basedcontrolisappliedtothetestrig,thisisacombinationofapre-compensatordealing with the interaction in the system and a decentralized controller, designed for the compensated system. The performance of these controllers is compared experimentally, and the best controller is combined with the off-line feedforward control, showing a significant reduction of the tracking error. r 2005 Elsevier Ltd. All rights reserved. Keywords: MIMO-control; Robust control; Tracking applications; Inverse-based control; H 1 -control 1. Introduction During the design of a new car, vibration tests on hydraulic test rigs (comfort evaluation and durability analysis) are important to adjust comfort and durability properties of the car. Comfort evaluation tests are performed by measuring acceleration levels on specific pointsofthecarlikethewheelaxles,theseat,thesteering wheel, etc. Durability tests investigate whether the vehicle or one of its components endure a long sequence of repeatedcyclicloadingonthehydraulictestrig.Tomake the vibration tests on the hydraulic test rig representative for the further lifetime of the vehicle, it is necessary to subject the vehicle on the rig to the correct loading. A general practice is to measure reference signals (accelera- tions or forces) during a test drive on a test track. These reference signals are reproduced on the test rig. The calculation of the control signals for the hydraulic actuators of the vibration test rig, such that the measured signals on the test rig match the reference signals, is a multivariable tracking problem. Current industry practice to solve this multivariable tracking problem is to use an off-line iterative process (De Cuyper and Coppens, 1999). Many iterations are often requiredbeforeaccuratetrackingisobtained,duetothe system nonlinearities. In the off-line iterative process, the control signals u ðj Þ ff ðtÞ are updated in the next iteration based on the inverse of the measured frequency response function matrix (FRF-matrix) G m ðf Þ and the tracking errors in the previous iteration: u ðj þ1Þ ff ðtÞ¼ u ðj Þ ff ðtÞþ Q j ðG m Þ 1 ðrðtÞ y ðj Þ ðtÞÞ (1) with rðtÞ being the reference signal, y ðj Þ ðtÞ the measured output in the previous iteration and Q j a parameter, chosen between 0 and 1 to guarantee convergence. ARTICLE IN PRESS www.elsevier.com/locate/conengprac 0967-0661/$-see front matter r 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.conengprac.2004.12.013 à Correspondingauthor.Tel.:+3216322833;fax:+3216322987. E-mail address: david.vaes@mech.kuleuven.ac.be (D. Vaes).