International Journal of Automation and Computing X(X), X X, X-X DOI: XXX Model Predictive Control of Resonant Systems using Kautz Model Shamik MISRA Rajasekhara REDDY Prabirkumar SAHA Department of Chemical Engineering, Indian Institute of Technology Guwahati, Assam 781039, India Phone: +91.361.2582257, Email: p.saha@iitg.ac.in Abstract: The scope of this paper broadly spans in two areas: system identification of resonant system and design of an efficient control scheme suitable for resonant systems. Use of filters based on orthogonal basis functions (OBF) have been advocated for modelling of resonant process. Kautz filter has been identified as best suited OBF for this purpose. A state space based system identification technique using Kautz filters, viz. Kautz model, has been demonstrated. Model based controllers are believed to be more efficient than classical controllers because explicit use of process model is essential with these modelling techniques. Extensive literature search concludes that very few reports are available which explore use of the model based control studies on resonant system. Two such model based controllers are considered in this work, viz. Model Predictive Controller and Internal Model Controller. A model predictive control algorithm has been developed using the Kautz model. The efficacy of the model and the controller has been verified by two case studies, viz. linear second order underdamped process and a mildly nonlinear magnetic ball suspension system. Comparative assessment of performances of these controllers in those case studies have been carried out. Keywords: Model Predictive Control, Resonant systems, Kautz model, orthonormal basis function, Internal Model Control. 1 Introduction There are several mechanical and electrical systems which show resonating characteristics. Existence of one or more pairs of complex poles in those systems yields oscil- latory behaviour in thier output profiles. Such kind of sys- tems require an efficient and adequate control strategy that can offer tight and stable closed loop control. Some example of such resonating systems can be found in robotics, power system electronics, mechanical systems like crane etc. Even in large scale chemical processes some oscillatory behaviour may be observed in the process outputs, especially where multiple recycle loops exist in the process network or the case of a cascade control with the primary loop cut off [1] . PID controller, the most widely used controller over the decades due to its robustness and simplicity, is however not well understood for plants with resonating response. Some tuning techniques based on heuristic knowledge have been proposed by [2], nevertheless it has been observed that such controllers seldom need human intervention [3] , and one may have to tune the PID controller manually through trial and error while implementing it in practice. One of the rea- sons of failure of PID controllers for resonating systems may be attributed to its classical design procedure where no scope exists for explicit use of exact model of the pro- cess. Model based control strategies, such as Internal Model Control (IMC) and Model Predictive Control (MPC), might be good alternatives for classical control strategies as these control systems embed the process model in the control al- gorithm. They may always not be the substitute of the conventional control schemes rather they would act as an aid to improve the traditional control strategies [4] . In fact [5] has proved that the IMC design procedure, in certain sit- uations, leads to traditional PID controller with feedback loop. Design method of IMC based PID controller is quite Manuscript received date; revised date well-established and are available even in textbooks [6] . On the other hand, though originally developed to meet the specialized control needs of power plant & petroleum re- fineries, MPC technology can now be found in a wide variety of application areas, including chemicals, food processing, automotive & aerospace applications. This work is mainly focussed on application of MPC for resonant systems. MPC uses an explicit dynamic model of the plant in or- der to predict the future output by simulating input ma- nipulation and thereby optimizes an appropriate objective function to calculate the best control action (i.e. the best set of input manipulations) for the actual process. Pro- cess/model mismatch, arising out of the actual implemen- tation of control action, is fed back to the MPC algorithm before calculating the next set of best control actions. Due to its immense prospect, researchers of both academic and industrial field show great interest in MPC that resulted in various developments in its techniques over the years [7] . Nevertheless, there hardly exists any research report that explores the applicability of MPC on resonant systems. As the name suggests, modeling is a very important part of a model predictive control scheme. It is perhaps the absence of appropriate modelling techniques for resonant systems, that has barred the researchers to study MPC for resonant systems. Modeling of a process consists of formulating a set of mathematical equations which describes dynamic in- put/output behavior of the process [8] . Modeling can ei- ther be knowledge based (mechanistic modelling) or expe- rience based (black-box modelling). A mechanistic model needs physical insight of the system that includes differ- ential eqautions of balance of states (mass, energy or mo- mentum) and algebraic equations of thermodynamic and/or chemical equilibrium of a process. However, (as in most of the real cases) if obtaining complete knowledge of the sys- tem is very difficult, people resort to black-box model which