Intelligent Backstepping System to Increase Input Shaping Performance in Suppressing Residual Vibration of a Flexible-Joint Robot Manipulator

Input shaping technique can be used to suppress residual vibration, occurring from moving rapidly a flexible system from one point to another point. An input shaping filter produces a shaped input signal that avoids exciting the flexible modes of the flexible system. The technique requires accurate knowledge of mode parameters. When the plant model is not accurate, performance of the input shaper degrades. Several robust input shapers were proposed to handle this inaccuracy at the expense of longer move time. The purpose of this paper is, for the first time, to present an application of an intelligent backstepping system to matching of the resulting closed-loop system with a reference model. The input shaper can then be designed from the mode parameters of the reference model. Because the reference model is accurate even when the plant model is not, the input shaper needs not be robust, resulting in shorter move time. The intelligent backstepping system consists of a three-layer neural network, a variable structure controller, and a backstepping controller. The neural network is used as a black-box model in case when the plant model is unknown, making the proposed system model-independent. The adaptive property of the neural network also makes the proposed system suitable for nonlinear, time-varying, or configuration-dependent systems. The variable structure controller handles the uncertainty arisen in the system. The backstepping controller, through its virtual controls, provides a means for the control authority to reach the unmatched uncertainty in the system. This study contains simulation and experimental results on a flexible-joint robot manipulator. The results showed that this proposed intelligent input shaping system outperformed previously proposed robust input shapers in terms of allowable uncertainty amount and move time. The proposed system is also relatively easy to apply because it does not require the plant model

Aspects of bond graph modelling in control

Abstract available: p. i

Energy shaping control of underactuated mechanical systems with fluidic actuation

Energy shaping is a remarkably effective control strategy which can be applied to a wide range of systems, including underactuated mechanical systems. However, research in this area has generally neglected actuator dynamics. While this is often appropriate, it might result in degraded performance in the case of fluidic actuation. In this work we present some new results on energy shaping control for underactuated mechanical systems for which the control action is mediated by a pressurized ideal fluid. In particular, we introduce an extended multi-step energy shaping and damping-assignment controller design procedure that builds upon the Interconnection-and-damping-assignment Passivity-based-control methodology in a modular fashion to account for the pressure dynamics of the fluid. Stability conditions are assessed with a Lyapunov approach, the effect of disturbances is discussed, and the case of redundant actuators is illustrated. The proposed approach is demonstrated with numerical simulations for a modified version of the classical ball-on-beam example, which employs two identical cylinders, either hydraulic or pneumatic, to actuate the beam

Design, Implementation and Testing of Advanced Control Laws for Fixed-wing UAVs

The present PhD thesis addresses the problem of the control of small fixed-wing Unmanned Aerial Vehicles (UAVs). In the scientific community much research is dedicated to the study of suitable control laws for this category of aircraft. This interest is motivated by the several applications that these platforms can perform and by their peculiarities as dynamical systems. In fact, small UAVs are characterized by highly nonlinear behavior, strong coupling between longitudinal and latero-directional planes, and high sensitivity to external disturbances and to parametric uncertainties. Furthermore, the challenge is increased by the limited space and weight available for the onboard electronics. The aim of this PhD thesis is to provide a valid confrontation among three different control techniques and to introduce an innovative autopilot configuration suitable for the unmanned aircraft field. Three advanced controllers for fixed-wing unmanned aircraft vehicles are designed and implemented: PID with H1 robust approach, L1 adaptive controller and nonlinear backstepping controller. All of them are analyzed from the theoretical point of view and validated through numerical simulations with a mathematical UAV model. One is implemented on a microcontroller board, validated through hardware simulations and tested in flight. The PID with H1 robust approach is used for the definition of the gains of a commercial autopilot. The proposed technique combines traditional PID control with an H1 loop shaping method to assess the robustness characteristics achievable with simple PID gains. It is demonstrated that this hybrid approach provides a promising solution to the problem of tuning commercial autopilots for UAVs. Nevertheless, it is clear that a tradeoff between robustness and performance is necessary when dealing with this standard control technique. The robustness problem is effectively solved by the adoption of an L1 adaptive controller for complete aircraft control. In particular, the L1 logic here adopted is based on piecewise constant adaptive laws with an adaptation rate compatible with the sampling rate of an autopilot board CPU. The control scheme includes an L1 adaptive controller for the inner loop, while PID gains take care of the outer loop. The global controller is tuned on a linear decoupled aircraft model. It is demonstrated that the achieved configuration guarantees satisfying performance also when applied to a complete nonlinear model affected by uncertainties and parametric perturbations. The third controller implemented is based on an existing nonlinear backstepping technique. A scheme for longitudinal and latero-directional control based on the combination of PID for the outer loop and backstepping for the inner loop is proposed. Satisfying results are achieved also when the nonlinear aircraft model is perturbed by parametric uncertainties. A confrontation among the three controllers shows that L1 and backstepping are comparable in terms of nominal and robust performance, with an advantage for L1, while the PID is always inferior. The backstepping controller is chosen for being implemented and tested on a real fixed-wing RC aircraft. Hardware-in-the-loop simulations validate its real-time control capability on the complete nonlinear model of the aircraft adopted for the tests, inclusive of sensors noise. An innovative microcontroller technology is employed as core of the autopilot system, it interfaces with sensors and servos in order to handle input/output operations and it performs the control law computation. Preliminary ground tests validate the suitability of the autopilot configuration. A limited number of flight tests is performed. Promising results are obtained for the control of longitudinal states, while latero-directional control still needs major improvements

Robust Control Methods for Nonlinear Systems with Uncertain Dynamics and Unknown Control Direction

Robust nonlinear control design strategies using sliding mode control (SMC) and integral SMC (ISMC) are developed, which are capable of achieving reliable and accurate tracking control for systems containing dynamic uncertainty, unmodeled disturbances, and actuator anomalies that result in an unknown and time-varying control direction. In order to ease readability of this dissertation, detailed explanations of the relevant mathematical tools is provided, including stability denitions, Lyapunov-based stability analysis methods, SMC and ISMC fundamentals, and other basic nonlinear control tools. The contributions of the dissertation are three novel control algorithms for three different classes of nonlinear systems: single-input multipleoutput (SIMO) systems, systems with model uncertainty and bounded disturbances, and systems with unknown control direction. Control design for SIMO systems is challenging due to the fact that such systems have fewer actuators than degrees of freedom to control (i.e., they are underactuated systems). While traditional nonlinear control methods can be utilized to design controllers for certain classes of cascaded underactuated systems, more advanced methods are required to develop controllers for parallel systems, which are not in a cascade structure. A novel control technique is proposed in this dissertation, which is shown to achieve asymptotic tracking for dual parallel systems, where a single scalar control input directly affects two subsystems. The result is achieved through an innovative sequential control design algorithm, whereby one of the subsystems is indirectly stabilized via the desired state trajectory that is commanded to the other subsystem. The SIMO system under consideration does not contain uncertainty or disturbances. In dealing with systems containing uncertainty in the dynamic model, a particularly challenging situation occurs when uncertainty exists in the input-multiplicative gain matrix. Moreover, special consideration is required in control design for systems that also include unknown bounded disturbances. To cope with these challenges, a robust continuous controller is developed using an ISMC technique, which achieves asymptotic trajectory tracking for systems with unknown bounded disturbances, while simultaneously compensating for parametric uncertainty in the input gain matrix. The ISMC design is rigorously proven to achieve asymptotic trajectory tracking for a quadrotor system and a synthetic jet actuator (SJA)-based aircraft system. In the ISMC designs, it is assumed that the signs in the uncertain input-multiplicative gain matrix (i.e., the actuator control directions) are known. A much more challenging scenario is encountered in designing controllers for classes of systems, where the uncertainty in the input gain matrix is extreme enough to result in an a priori-unknown control direction. Such a scenario can result when dealing with highly inaccurate dynamic models, unmodeled parameter variations, actuator anomalies, unknown external or internal disturbances, and/or other adversarial operating conditions. To address this challenge, a SMCbased self-recongurable control algorithm is presented, which automatically adjusts for unknown control direction via periodic switching between sliding manifolds that ultimately forces the state to a converging manifold. Rigorous mathematical analyses are presented to prove the theoretical results, and simulation results are provided to demonstrate the effectiveness of the three proposed control algorithms

Decentralized Control for Large-Scale Interconnected Nonlinear Systems Based on Barrier Lyapunov Function

We present a novel decentralized tracking control scheme for a class of large-scale nonlinear systems with partial state constraints. For the first time, backstepping design with the newly proposed BLF is incorporated to effectively deal with the control problem of nonlinear systems with interconnected constraints. To prevent the states of each subsystem from violating the constraints, we employ a special barrier Lyapunov function (BLF), which grows to infinity whenever its argument approaches some finite limits. By ensuring boundedness of the barrier Lyapunov function in the closed loop, we ensure that those limits are not transgressed. Asymptotic tracking is achieved without violation of the constraints, and all closed-loop signals remain bounded. In the end, an illustrative example is presented to demonstrate the performance of the proposed control

Quaternion-Based Attitude Stabilization via Discrete-Time IDA-PBC

In this letter, we propose a new sampled-data controller for stabilization of the attitude dynamics at a desired constant configuration. The design is based on discrete-time interconnection and damping assignment (IDA) passivity-based control (PBC) and the recently proposed Hamiltonian representation of discrete-time nonlinear dynamics. Approximate solutions are provided with simulations illustrating performances