Parameter dependent freeway modelling

International audience

This paper presents a controller design method for dealing with the induced ℒ 2 -norm problem for switched linear parameter-varying (LPV) systems. Considering the arbitrary switchings caused by the parameters varying, a common parameter-dependent Lyapunov function is employed to derive sufficient linear matrix inequality (LMI) conditions for the switched LPV systems. A family of LPV controllers are designed according to the LMI conditions, and each of them is suitable for the corresponding parameter region. The proposed switching LPV control method is applied to an F-16 aircraft longitudinal model and simulation results demonstrate the effectiveness of the approach.

In this paper, a linear parameter-varying (LPV) control design method is evaluated experimentally on an active magnetic bearing (AMB) system. Linear matrix inequality (LMI) conditions for control design of affine parameter-dependent systems using parameter-dependent Lyapunov functions are proposed. A speed-dependent LPV model of the AMB system is derived. Speed-dependent model uncertainties are identified using artificial neural networks (ANNs), and a parameter-dependent uncertainty weighting function is approximated for LPV control synthesis. Experiments are conducted to verify the robustness of LPV controllers for a wide range of rotor speeds. This LPV control approach eliminates the need for gain-scheduling, and provides better performance and less conservativeness over a wide range of rotational speeds than controllers designed with constant uncertainty weighting functions.

We introduce a controller design methodology for nonlinear systems via complementary Linear Parameter Varying (LPV) controller and observer structures. The recently developed method is able to control physiological systems even with complex nonlinearities — without using Linear Matrix Inequalities (LMI) or other techniques requiring iterations. The developed method is based on the classical state feedback theorems, matrix similarity theorems and supplementary controller and observer structure which efficiently uses the mathematical properties of the parameter space of the LPV system. The main benefits of the proposed method is that the controller design does not require mathematical tools needing iteration thus high computational capacity. We used a nonlinear compartmental model in order to demonstrate the application of the method. The results showed that the developed complementary LPV controller and observer structures perform well on both the LPV systems and the original nonlinear system as well.

This paper deals with the accurate and fast positioning control of a nonlinear electrostatically actuated microgripper. Considering the importance of nonlinearities, performances are achieved through the design of gain scheduled controllers. To this end, a nonlinear model of the studied system is proposed and is reformulated into a polynomial LPV (Linear Parameter Varying) model. Controllers are designed considering the particular polynomial parametric dependence of the LPV model. In a first instance, a controller is synthesized using an affine LPV descriptor representation of the system and LMI (Linear Matrix Inequality) constraints. In a second instance, to deal with real time implementation constraints, a second controller is designed based on an iterative procedure using the eigenstructure assignment methodology and a worst case analysis. For embedded applications, requiring simple controller structures, we show experimentally the interest of the iterative procedure which can achieve good results relatively with the ones obtained using recent advances of robust controllers based on LMI conditions.

This paper presents a Linear Parameter Varying (LPV) approach to model and control two-mass systems with backlash. The maximum amplitude of the backlash angle is assumed to be unknown and variable having no knowledge about the upper and lower bounds of it. Proper affine state space model together with the admissible variations of the LPV parameters is designed in order to realize a viable convex polytope. Utilizing H ∞ LPV lemmas and theories lead to a set of Linear Matrix Inequalities (LMIs). By solving these LMIs, appropriate scheduled state feedback gains are obtained. The designed robust control strategy can easily handle the variations of the backlash angle and load disturbance torque. A simulated two-mass backlash system verifies the efficiency of the designed control law.

The article presents a state-space based Fault Diagnosis (FD) method for discrete-time, affine Linear Parameter Varying (LPV) systems. The goal of the technical note is to develop a robust and dynamic inversion based technique for systems with parameter varying representations when an additive, exogenous disturbance signal perturbs the system. After applying geometric concepts for explicit fault inversion, a robust strategy is proposed to attenuate the effect of the unknown disturbance input signal on the fault estimation error. The proposed robust observer is derived as a solution of off-line Linear Matrix Inequality (LMI) conditions. The technical note demonstrates the viability of the novel methodology through a numerical example.

We propose a less conservative linear matrix inequalities (LMIs) condition for ℋ∞ performance analysis and synthesis of discrete-time linear parameter varying (LPV) systems. The time varying parameter is represented by a linear fractional form. Sufficient conditions for ℋ∞ performance and controller synthesis are given in terms of a finite number of LMIs using parameter dependent Lyapunov functions.

Trajectory tracking is extremely difficult for rotorcrafts based on the nonlinear model and taking into account all the parameters of the system and especially considering the effects of flapping and the main rotor and its control tail in all directions. This paper describes the tracking route, based on nonlinear model and velocity control and feedback mode and Polytopic linear parameter varying (LPV) modeling with the help of solving linear matrix inequalities (LMI) equations for different conditions and complex maneuvers for an unmanned rotorcraft that has been examined in all directions including, longitudinal, altitudinal, latitudinal directions. Based on the different operating points of the system and the different flight conditions, first a Polytopic modeling of the system is performed, and then the control signal is generated based on the state feedback and solution of the linear matrix inequalities (LMI) equations. The final control signal consists of feedback of changes of the state variables around the nominal trajectory under the designed feedback gains, in addition to the nominal control signal for the desired trajectory. In calculating the nominal control signal for the optimum trajectory, the Polytopic system model is used instead of the nonlinear system model. Therefore, the final control signal does not require a dynamic system model and all control calculations are performed using a Polytopic system model and have high computational speed. System simulation shows the capabilities of the proposed control system in different operating conditions.

In this paper, we consider the fault Detection and isolation (FDI) problem for faulty linear parameter-varying (LPV) systems subject to disturbances and propose a observer-based solution by using multiobjective optimization techniques. To simply the design process, a general faulty LPV system will be constructed from standard LPV description by converting actuator/system component faults into sensor faults at first. Then a bank of LPV FDI filters will be designed to identify each fault. Each FDI filter could generate a residual signal to track individual fault with minimum error and suppressing the effects of disturbances and other fault signals. The design of FDI filters will be formulated as multiobjective optimization problems in terms of linear matrix inequalities (LMIs) and can be solved efficiently. Two numerical examples are also presented to demonstrate the proposed fault detection and isolation approach on both LPV and LTI systems.

Linear Parameter Varying (LPV) system shows preferable performance in dealing with NonLinear (NL) systems and systems with time-varying parameters, based on a kind of wheel-legged robot with two-wheel and balance as Inverted Pendulum, this paper proposes a gain scheduling control method for balancing using LPV system on Equivalent model with Center Of Mass (COM). In order to ensure the stability and responsive of the system with possible values for all variable parameters, Higher Order Singular Value Decomposition (HOSVD) is used for constructing polytopic LPV system, then the robust controller is designed for the vertex systems forthputting Linear Matrix Inequality (LMI) approach, and the gain scheduling controller for global system is obtained by convex combination of vertex LTI systems. The simulation results show that the system can achieve the expected indicators.

Applications of a quadrotor with payload, particularly for chemical spraying, have increased in recent times. The variation in payload mass over time causes a change in the moments of inertia (MOI). Moreover, large tilt angles are required for fast reference tracking and external disturbance rejection. These variations in plant parameters (i.e., mass and inertia) and large tilt angles can degrade the control scheme’s performance and stability. This article proposes a linear matrix inequalities (LMIs)-based linear parameter varying (LPV) control scheme for a quadrotor subject to time-varying mass, time-varying inertia, mass flow rate, and large tilt angles. The control strategy is designed by solving LMIs derived from quadratic H∞ performance and D-stability. The robust stability and quadratic H∞ performance are assessed by LMIs. The efficacy of the proposed methodology is established using numerical simulations, and its performance is compared to the linear time-invariant (LTI) H∞ design with pole placement constraints. The results obtained show that the LPV control scheme gives better tracking performance in the presence of time-varying parameters, noise, and external disturbances without actuator saturation. In comparison to the LTI design technique, the proposed LPV scheme improves the rise time (tr), settling time (ts), and mean squared error (MSE) by up to 14%, 15%, and 30%, respectively. Moreover, smooth transitions are observed in the tilt angles and control signals with the LPV scheme, contrary to the LTI controller, which exhibits significant oscillations.

Development of an autonomous fog computing platform using control-theoretic approach for robot-vision applications

This paper considers the optimal control of polytopic, discrete-time linear parameter varying (LPV) systems with a guaranteed l2 to l∞ gain. Additionally, to guarantee robust stability of the closed-loop system under parameter variations, H∞ performance criterion is also considered as well. Controllers with a guaranteed l2 to l∞ gain and a guaranteed H∞ performance (l2 to l2 gain) are a special family of mixed H2=H∞ controllers. Normally, H2 controllers are obtained by considering a quadratic cost function that balances the output performance with the control input needed to achieve that performance. However, to obtain an optimal controller with a guaranteed l2 to l∞ gain (closely related to the physical performance constraint), the cost function used in the H2 control synthesis minimizes the control input subject to maximal singular-value performance constraints on the output. This problem can be efficiently solved by a convex optimization with linear matrix inequality (LMI) constraints. The main contribution of this paper is the characterization of the control synthesis LMIs used to obtain an LPV controller with a guaranteed l2 to l∞ gain and >H∞ performance. A numerical example is presented to demonstrate the effectiveness of the convex optimization.

Design of Observer-Structured H∞ Flight Controllers Converted from Unstructured Conventional H∞ Flight Controllers