Controller Parameters Tuning Based on Transfer Matrix Method for Multibody Systems

Hossam Hendy,Xiaoting Rui,Mostafa Khalil,Qinbo Zhou

doi:10.1155/2014/957684

Hossam Hendy, Xiaoting Rui + Show 2 more

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https://doi.org/10.1155/2014/957684

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Abstract

Transfer matrix method for multibody systems (MS-TMM) is a rife method to multi-rigid-flexible-body systems dynamics model deduction due to that there are no needs to establish the global dynamics equations of the system. Its basic idea is transferring a state vector between the body input(s) and output(s); this idea is close to the linear theories in control analysis and design. In this paper, three controllers’ parameters tuning techniques for the proposed system model using MS-TMM are utilized; one technique is applied to get the stability regions via the frequency response of MS-TMM derived model. Another technique considers a classical PID controller design through the analysis of step input response of the system, and the last technique can be applied in both time and frequency domains if the model has a known mathematical model. A car suspension system is considered to represent modeling and tuning problems. In-depth study of MS-TMM with control techniques and defining the controllers’ parameters stability regions provide an opportunity to formulate a relationship between MS-TMM and control design for novel control applications due to the powerful strength of MS-TMM dealing with more complex problems of the controlled multibody systems.

Highlights

With the increments of complexity of multibody systems and the development of their design and control methods, the need for more elegant formulations of the equations of motion becomes an issue of paramount importance
In transfer matrix method for multibody systems (MS-TMM) there are two cases to deal with control element, one is to express the control force with state of system of previous time such as the delay control, and the second is that the control force is relative to present state of system, such as real-time control systems
50 km/hr; the results show the effectiveness of the used controllers to reduce the displacement motion as shown in Figure 11 and zoomed in Figure 12, results illustrated that different control techniques can be applied to MS-TMM, results of the passive suspension response are plotted in blue solid line, Zeigler-Nichols result is plotted in blue dot plot, Shamsuzzohas’ result is plotted in green dash-dot plot, and the PI controls’ result is plotted in red dash plot

Summary

Introduction

With the increments of complexity of multibody systems and the development of their design and control methods, the need for more elegant formulations of the equations of motion becomes an issue of paramount importance. Many methods and theories for developing the model of the multibody system dynamics and control are presented for such reasons. Rui et al have trials to develop new controlled systems depending on deriving the dynamics equations using MS-TMM [1, 2]. Shamsuzzoha and Skogestad (2010) developed a new procedure for PI/PID tuning method in closed-loop mode, only one closed-loop step test is required to deduce PI controller values. In this method it is simple to obtain the PID tuning parameters in one step [11, 12].

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