+6,  6RSRW 3RODQG -XQH   978-1-4673-5637-4/13/$31.00 '2013 IEEE Abstract. This paper proposes the data-driven performance improvement of low-cost control systems (CSs) for vertical three-tank systems. The MIMO CSs dedicated to two tanks of the three-tank systems consist of two SISO control loops with separately tuned PI controllers. The Modulus Optimum method is applied to initially tune the PI controllers. Optimization problems are defined on the basis of an original objective function which depends on the controller tuning parameters and is expressed as the sum of squared output errors multiplied by variable weights. The performance improvement is achieved by a new convergent Iterative Feedback Tuning (IFT) algorithm which aims the parameter tuning of PI controllers by the experiment-based solving of the optimization problems. The convergence is ensured by the formulation of the parameter update laws in the IFT algorithm as a nonlinear dynamical feedback system in the parameter space and iteration domain and by setting the step sizes to fulfill inequality-type convergence conditions derived from Popov!s hyperstability theory. The experimental results for a laboratory vertical three-tank system show the convincing CS performance improvement by few experiments. Keywords: Iterative Feedback Tuning, Modulus Optimum method, Popov!s hyperstability theory, proportional-integral controllers, vertical three-tank systems. I. INTRODUCTION HE data-driven techniques for controller optimization and tuning offer the performance improvement of control systems (CSs) by the minimization of objective functions (o.f.s) in the framework of appropriately defined optimization problems using no a priori information about This work was supported by a grant in the framework of the Partnerships in priority areas - PN II program of the Romanian National Authority for Scientific Research ANCS, CNDI - UEFISCDI, project number PN-II-PT-PCCA-2011-3.2-0732, by a grant of the Romanian National Authority for Scientific Research, CNCS - UEFISCDI, project number PN-II-ID-PCE-2011-3-0109, and by a grant from the NSERC of Canada. R.-E. Precup, M.-B. Rădac, C.-A. Dragoú, S. Preitl and A.-I. Stnean are with the !Politehnica" University of Timisoara, Department of Automation and Applied Informatics, Bd. V. Parvan 2, RO-300223 Timisoara, Romania (phone: +40 2564032-29, -24; fax: +40 2564032-14; e-mail: radu.precup@aut.upt.ro). E. M. Petriu is with the University of Ottawa, School of Electrical Engineering and Computer Science, 800 King Edward, Ottawa, ON, K1N 6N5 Canada. the controlled process or little such information [1]. The main data-driven techniques that carry out the iterative experiment-based performance improvement of CSs are Iterative Feedback Tuning (IFT) [2#4], Correlation-based Tuning (CbT) [5], Frequency Domain Tuning (FDT) [6], Iterative Regression Tuning (IRT) [7], Simultaneous Perturbation Stochastic Approximation (SPSA) [8#9], and data-driven predictive control [10#11]. IFT uses the input-output data measured during the CS operation to calculate the estimates of the gradients and eventually Hessians of o.f.s. Several experiments are conducted per iteration and the updated controller parameters are obtained on the basis of input-output data and off-line calculated estimates as well. The three-tank systems are nonlinear Multi Input-Multi Output (MIMO) benchmarks which illustrate control design, fault detection and diagnosis problems. Some current approaches to the optimal level control in three-tank systems include neural networks [12#13], IFT-based linear and fuzzy control [14#15], qualitative feedback theory [16] and switched model predictive control [17]. This paper is built upon the low-cost CS structures dedicated to the level control of the first two tanks in horizontal [14#15] or vertical three-tank systems [18]. This MIMO CS consists of two Singe Input-Single Output (SISO) control loops with separately tuned proportional- integral (PI) controllers for each level. The two PI controllers are initially tuned in terms of the Modulus Optimum (MO) method. A new IFT algorithm is next suggested and implemented in order to ensure the parameter tuning of PI controllers for CS performance improvement. This paper belongs to the state-of-the-art research on stable and convergent data-driven techniques briefly pointed out as follows. The convergence assurance of CSs based on data-driven techniques by means of stability analysis is suggested in [19] by the frequency domain characterization of the o.f. The need to calculate the generalized stability margin is outlined in [20]. A relaxed sufficient condition compared to [19] is offered in [21] by the estimation, via spectral analysis, of the frequency domain magnitudes of two transfer functions (t.f.s) of the CS. A stability test for data-driven controllers tuned by the Virtual Reference Feedback Tuning technique is given in Data-Driven Performance Improvement of Control Systems for Three-Tank Systems Radu-Emil Precup 1 , Mircea-Bogdan Rădac 1 , Emil M. Petriu 2 , Claudia-Adina Dragoú 1 , Stefan Preitl 1 , and Alexandra-Iulia Stnean 1 1 !Politehnica" University of Timisoara, Romania, 2 University of Ottawa, Canada, radu.precup@aut.upt.ro, mircea.radac@aut.upt.ro, petriu@eecs.uottawa.ca, claudia.dragos@aut.upt.ro, stefan.preitl@aut.upt.ro, alexandra-iulia.stinean@aut.upt.ro T 306