Fixed-structure LPV discrete-time controller design with induced l(2)-norm and H-2 performance

A new method for the design of fixed-structure dynamic output-feedback linear parameter-varying (LPV) controllers for discrete-time LPV systems with bounded scheduling parameter variations is presented. Sufficient conditions for the stability, H-2 and induced l(2)-norm performance of a given LPV system are represented through a set of linear matrix inequalities (LMIs). These LMIs are used in an iterative algorithm with monotonic convergence for LPV controller design. Extension to the case of uncertain scheduling parameter value is considered as well. Controller parameters appear directly as decision variables in the optimisation program, which enables preserving a desired controller structure in addition to the low order. Efficiency of the proposed method is illustrated on a simulation example, with an iterative convex optimisation scheme used for the improvement of the control system performance.

Fixed-order Discrete-time LPV Controller Design

Zlatko Emedi, Alireza Karimi

A new method for the design of fixed-order dynamic output-feedback Linear Parameter Varying (LPV) controllers for discrete-time LPV systems with bounded scheduling parameter variations is presented in this paper. Sufficient conditions for the stability, H2 and induced L2 performance of a given LPV system are given through a set of Linear Matrix Inequalities (LMIs) and exploited for design. Controller parameters appear directly as decision variables in the convex optimisation program, which enables preserving a desired controller structure in addition to the low order. Efficiency of the proposed method is illustrated on a simulation example, with an iterative convex optimisation scheme used for the improvement of the control system performance.

2014

Fixed-structure LPV Discrete-time Controller Design with Induced l2-Norm and H2 Performance

Zlatko Emedi, Alireza Karimi

A new method for the design of fixed-structure dynamic output-feedback Linear Parameter Varying (LPV) controllers for discrete-time LPV systems with bounded scheduling parameter variations is presented. Sufficient conditions for the stability,

\mathscr{H}_2

and induced

l_2

-norm performance of a given LPV system are represented through a set of Linear Matrix Inequalities (LMIs). These LMIs are used in an iterative algorithm with monotonic convergence for LPV controller design. Extension to the case of uncertain scheduling parameter value is considered as well. Controller parameters appear directly as decision variables in the optimization program, which enables preserving a desired controller structure in addition to the low order. Efficiency of the proposed method is illustrated on a simulation example, with an iterative convex optimization scheme used for the improvement of the control system performance.

2015

From Fixed-Order Gain-Scheduling to Fixed-Structure LPV Controller Design

Zlatko Emedi

This thesis focuses on the development of some fixed-order controller design methods in the gain-scheduling/Linear Parameter Varying (LPV) framework. Gain-scheduled controllers designed using frequency-domain Single Input Single Output (SISO) models are considered first, followed by LPV controller design in the SISO transfer function setting and, finally, by Multiple Input Multiple Output (MIMO) LPV controller design in the state-space setting. In addition to the guarantee of closed-loop stability, each of the methods optimizes some classical performance measure, such as the

\mathscr{H}_\infty

\mathscr{H}_2

performance metrics. In the LPV state-space setting, the practical assumption of bounded scheduling parameter variations is taken into account in order to allow a higher performance level to be achieved. The fixed-order gain-scheduled controller design method is based on frequency-domain models dependent on the scheduling parameters. Based on the linearly parameterized gain-scheduled controllers and desired open-loop transfer functions, the

\mathscr{H}_\infty

performance of the weighted closed-loop transfer functions is presented in the Nyquist diagram as a set of convex constraints. No a posteriori interpolation is needed, so the stability and performance level are guaranteed for all values of scheduling parameters considered in the design. Controllers designed with this method are successfully applied to the international benchmark in adaptive regulation. These low-order controllers ensure good rejection of the multisinusoidal disturbance with time-varying frequencies on the active suspension testbed. One issue related to the gain-scheduled controller design using the frequency response model is the computational burden due to the constraint sampling in the frequency domain. The other is a guarantee of stability and performance for all the values of scheduling parameters, not just those treated in design. To overcome these issues, a method for the design of fixed-order LPV controllers with the transfer function representation is proposed. The LPV controller parameterization considered in this approach leads to design variables in both the numerator and denominator of the controller. Stability and

\mathscr{H}_\infty

performance conditions for all fixed values of scheduling parameters are presented in terms of Linear Matrix Inequalities (LMIs). With a problem of rejection of a multisinusoidal disturbance with time-varying frequencies in mind, LPV controller is designed for an LTI plant with a transfer function model. The extension of these methods from SISO to MIMO systems is far from trivial. The state-space setting is used for this reason, as there the transition from SISO to MIMO systems is natural. A method for fixed-order output-feedback LPV controller design for continuous-time state-space LPV plants with affine dependence on scheduling parameters is proposed. Bounds on the scheduling parameters and their variation rates are exploited in design through the use of affine Parameter Dependent Lyapunov Functions (PDLFs). The exponential decay rate, induced

\mathscr{L}_2

-norm and

\mathscr{H}_2

performance constraints are expressed through a set of LMIs. The proposed method is applied to the 2DOF gyroscope experimental setup. In practice control is performed using digital computers, so some effort needs to be put into the LPV controller discretization. If the discrete-time LPV model of the system is available [...]

EPFL2014

From Fixed-Order Gain-Scheduling to Fixed-Structure LPV Controller Design

Zlatko Emedi

\mathscr{H}_\infty

\mathscr{H}_2

\mathscr{H}_\infty

\mathscr{H}_\infty

\mathscr{L}_2

-norm and

\mathscr{H}_2

EPFL2014

Fixed-structure LPV Discrete-time Controller Design with Induced l2-Norm and H2 Performance

Zlatko Emedi, Alireza Karimi

\mathscr{H}_2

and induced

l_2

2015