Moisés Bonilla Estrada

Proportional and derivative state-feedback decoupling of linear systems

We consider the row-by-row decoupling of linear time-invariant systems by proportional and derivative state feedback. Our contribution, with respect to previous results, is that our procedure is based on simple operator (say matrices) manipulations, without any need to use a canonical form. The only assumptions for applying such a decoupling strategy are that the system is right invertible (which is a necessary condition to ensure solvability) and minimum phase. An illustrative example is proposed.

Necessary and sufficient conditions for disturbance decoupling with stability using PID control laws

The authors consider the disturbance decoupling problem with stability using PID-control laws. They give necessary and sufficient conditions in order to solve this problem with m derivators (m being a fixed integer). As an obvious by-product, these conditions characterize the minimal value of m for which such a PID-solution exists. They also propose a synthesis procedure.

Structural conditions for disturbances decoupling with stability using proportional and derivative control laws

We consider the disturbance decoupling problem with internal stability by means of generalized control laws which use not only state feedback, but also external terms coming from the disturbance and some of its time derivatives. We derive from our previous geometric condition an equivalent one in terms of some structures of the system to be controlled (zeros at infinity and unstable zeros), and no longer dependent on a particular approach (geometric, algebraic, ...).

Implicit control law for linear time varying SISO systems with bounded disturbances

We propose a linear time invariant control law for a following linear time varying SISO system. The aim of this linear time invariant control law is to obtain a linear time invariant SISO closed loop system without disturbance and with desirable dynamics. The control scheme is developed in three steps: (i) we find first a trivial control law for a controllable state realization; (ii) we find next a practical approximation of the trivial control law which guarantees internal stability and tends to the ideal behavior (obtained with the trivial control law); we assume in this second step that the state is measurable; (iii) finally we suppose that the state is not available and we thus add a state reconstructor which preserves the nice characteristics of the practical control law.

Time Domain Left Invertibility: Application to Failure Detection

Abstract We consider here the problem of recovering from the output alone, and at any time t ≥ 0, the (unknown) input, with initial conditions not necessarily equal to zero. In this case left invertibility of transfer functions is not sufficient.

ON THE CONTROL OF LINEAR SYSTEMS HAVING INTERNAL VARIATIONS, PART I—REACHABILITY

Abstract Non square implicit descriptions can be used for modelling a set of linear systems, characterized by a certain common structure. Necessary and sufficient conditions, expressed in terms of the overall implicit model, exist for controlling it so that it has a unique behaviour (whatever be the internal structure variations). We enhance from these conditions the parts which are due to the common internal dynamic equation and, respectively, to the algebraic constraints which are “controlled” (in an hidden way) by the degree of freedom.

ON THE CONTROL OF LINEAR SYSTEMS HAVING INTERNAL VARIATIONS, PART II-CONTROL

Abstract In this paper we show how to embed the variable internal structure present in square implicit descriptions inside an (A, E, B) invariant subspace contained in the kernel of the output map. Thanks to this embedding, we make unobservable the variable internal structure, obtaining in this way a proper closed loop system with a controllable pre specified structure.

Adaptive quaternion control of a 3-DOF inertial stabilised platforms

ABSTRACT Inertial stabilised platforms are increasingly popular with a large range of products available mainstream. Most items are controlled using popular algorithms that sometimes do not offer best achievable performances. Present paper proposes an advanced control which aims at improving these latter. The exposed solution is based on quaternion representation and self-adapts to the characteristics of the payload it tries to stabilise. Proposed control law ensures the stability of the system whatever the required orientation path is. Although only simulation has been performed to check the performances of such control, results look very promising compared to non-adaptive controls and may help to construct more polyvalent and efficient gimbals which would further facilitate their expansion. Proposed control law can also be applied, as is, to every system that shares the same quaternion-based rotational dynamics.

Quaternion Kalman filter for inertial measurement units

This paper presents a theoretical and practical implementation of a Kalman Filter (KF) to obtain the attitude and angular velocity from a nine degrees of freedom (DoF) inertial measurement unit (IMU). These include three DoF from an accelerometer, three from a magnetometer and the last three from a gyroscope. It differs from other attitude filters in two main aspects, the model representation and how the information is acquired from the IMU. The quaternion model presented has an analogous linear representation that can be used, in conjunction with the the an algorithm that is presented in order to extract the attitude information from the IMU, leading to a considerable lower computational cost in order to avoid the calculation of Jacobians matrices or gradients.

Cooperative control for load transportation using two PVTOL vehicles with a passivity approach

This paper presents a control strategy for two planar vertical take-off and landing (PVTOL) vehicles cooperating to transport a rigid body load without any explicit exchange of state information between them. This means that the vehicles have only access to their own state variables. The solution and stability analysis is based on a passivity approach.