Linear adaptive structure for control of a nonlinear MIMO dynamic plant

Abstract

In the paper an adaptive linear control system structure with modal controllers for a MIMO nonlinear dynamic process is presented and various methods for synthesis of those controllers are analyzed. The problems under study are exemplified by the synthesis of a position and yaw angle control system for a drillship described by a 3DOF nonlinear mathematical model of low-frequency motions made by the drillship over the drilling point. In the proposed control system, use is made of a set of (stable) linear modal controllers that create a linear adaptive controller with variable parameters tuned appropriately to operation conditions chosen on the basis of two measured auxiliary signals. These are the ship's current forward speed measured in reference to the water and the systematically calculated difference between the course angle and the sea current (yaw angle). The system synthesis is carried out by means of four different methods for system pole placement after having linearized the model of low-frequency motions made by the vessel at its nominal "operating points" in steady states that are dependent on the specified yaw angle and the sea current velocity. The final part of the paper includes simulation results of system operation with an adaptive controller of (stepwise) varying parameters along with conclusions and final remarks.

Design of a multivariable neural controller for control of a nonlinear MIMO plant

“…1 (Åström and Wittenmark, 1995) that adaptation of control systems can be implemented directly or indirectly (through identification of parameters of the plant model), as well as by on-line tuning the values of controller parameters using the above-mentioned auxiliary measured signals x am (t). As has been observed (Bańka, 2010a;2010b;2013), it can also be realized as a single adaptive controller with stepwise tuned parameter values or as a set of controllers with a common input e(t) and switchable outputsũ(t). The above control system for the nonlinear MIMO plant with specified set points y ref consists of a neural controller designed on the basis of a bank of multivariable linear modal controllers synthesized for possibly all operating points of the plant.…”

“…The designed modal controllers were calculated using the following methods: the eigenvalues method, the eigenvectors method, the polynomial method and the polynomial matrix equations method (Bańka, 2012;Bańka et al, 2013). As might be expected, the use of different synthesis methods for modal controllers yielded different results for the same data taken for calculations.…”

“…Such a neural controller could be seen as a solution that consists of only one controller with internal functionality of continuously changing parameters. The neural networks could be designed using parameter values of modal controllers (based on the Luenberger observer or the Kalman filter) obtained by four different methods of the "linear" approach (Bańka, 2007;2012;Bańka et al, 2013).…”

“…The adaptive control system structure considered is studied by means of a 3DOF nonlinear mathematical model of a ship's slow-varying motions described in detail by Bańka and Latawiec (2009) as well as Bańka (2010a;2010b;2013). The yaw angle and the ship's position in DSP are defined in an Earth-based fixed reference system whose axes are directed Northwards (N) and Eastwards (E), and whose origin is located over the drilling point on the seabed.…”

Evolutionary optimization of interval mathematics-based design of a TSK fuzzy controller for anti-sway crane control

“…Numerous authors, frequently inspired by Kharitonov's theorem (Kharitonov, 1978), studied the problem of robust controller design in the presence of system parameter variations (Dahleh et al, 1993;Chapellat et al, 1994;Mallan et al, 1997). Some practical techniques of designing robust control schemes are based on iterative methods (McNichols and Fadali, 2003), modal controllers synthesis (Bańka et al, 2013), methods derived based on Lyapunov stability theory (Zubowicz and Brdyś, 2013), as well as soft computing techniques, e.g., Genetic Algorithms (GAs) (Hsu et al, 2007) and artificial neural networks (Lee et al, 2002) applied to tune linear controller parameters in terms of acceptable ranges for phase and gain margins. In this paper, EA-based synthesis of a robust TSK (Takagi and Sugeno, 1985;Sugeno and Kang, 1988) fuzzy controller which places the coefficients of a closed-loop characteristic polynomial within desired intervals is proposed and addressed to the problem of an anti-sway crane control.…”