Position‐heading quadrotor control using LPV techniques

International audience

This paper proposes a shifting feedback linearization controller for nonlinear systems under input saturation. The suggested approach for determining a linear parameter‐varying (LPV) state‐feedback controller is based on employing a linear matrix inequality (LMI)‐based methodology, the input‐output feedback linearization approach, and the shifting paradigm concept. The resultant controller deals with a full linearized version of the nonlinear system under state‐dependent input constraints, and it modifies the closed‐loop convergence speed of the system in accordance with changes in the system's region of linearity. The proposed approach is validated by means of an experimental example.

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.

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 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.

A direct drive variable reluctance motor for robotic applications is considered. A cascade control structure is adopted, with an inner torque loop and an outer velocity loop. The inner loop consists of a static torque precompensator transforming the torque control problem into a current or flux control one. Optimization techniques that minimize power dissipation under the voltage limit imposed by the power amplifier are used to define an optimal ripple-free flux profile. Sliding mode implementation of the inner controller is considered, while the outer loop is designed using binary control techniques to achieve insensitivity to load and inertia variations. The drive is simulated for a single-link robotic arm, showing good performances in terms of residual torque ripple and velocity-tracking capability.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

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.

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.

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.

Two freedom linear parameter varying μ synthesis control for flight environment testbed

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.

In this paper, a class of nonlinear controllers is proposed for rotational maneuvers of spacecraft with a pair of flexible appendages attached. With the application of proposed nonlinear feedback torque, dynamic equations of the flexible spacecrafts are converted into the linear parameter-varying (LPV) form. Regional pole assignment for the resultant LPV system is performed via secondary linear state feedback, and the feedback gain is computed through convex optimization constrained by linear matrix inequalities (LMI). It is shown that exponential closed-loop stability of the original spacecraft system can be achieved. Numerical simulations show that the rotational maneuvers can be performed precisely and the vibration is suppressed as well.

In the entry/reentry operation of the flexible marine riser, the operators are required to connect its lower end to the blowout preventer at the seabed quickly with both its top connected angle and its deformation controlled. Because of the hydrodynamical force and the flexibility of the riser, it is very difficult for them to operate it correctly. In the paper, we consider the entry/reentry control problem of the flexible marine riser. Firstly, the governing equation of the flexible marine riser is formulated and transformed to the finite dimensional equation by the mode expansion method. Secondly, for the control problem, we apply LPV (Linear Parameter Varying) technique taking the varying parameter as its upper end velocity which determines the hydrodynamical damping force. Finally, the effectiveness of the LPV technique is shown by numerical simulations, compared with the results by the LTI (Linear Time Invariant) H∞ control