Trajectory robust control of autonomous quadcopters based on model decoupling and disturbance estimation

In this article, a systematic procedure is given for determining a robust motion control law for autonomous quadcopters, starting from an input–output linearizable model. In particular, the suggested technique can be considered as a robust feedback linearization (FL), where the nonlinear state-feedback terms, which contain the aerodynamic forces and moments and other unknown disturbances, are estimated online by means of extended state observers. Therefore, the control system is made robust against unmodelled dynamics and endogenous as well as exogenous disturbances. The desired closed-loop dynamics is obtained by means of pole assignment. To have a feasible control action, that is, the forces produced by the motors belong to an admissible set of forces, suitable reference signals are generated by means of differentiators supplied by the desired trajectory. The proposed control algorithm is tested by means of simulation experiments on a Raspberry-PI board by means of the hardware-in-the-loop method, showing the effectiveness of the proposed approach. Moreover, it is compared with the standard FL control method, where the above nonlinear terms are computed using nominal parameters and the aerodynamical disturbances are neglected. The comparison shows that the control algorithm based on the online estimation of the above nonlinear state-feedback terms gives better static and dynamic behaviour over the standard FL control method

Observation and control of a ball on a tilting

The ball and plate system is a nonlinear MIMO system that has interesting characteristics which are also present in aerospace and industrial systems, such as: instability, subactuation, nonlinearities such as friction, backlash, and delays in the measurements. In this work, the modeling of the system is based on the Lagrange approach. Then it is represented in the state-space form with plate accelerations as inputs to the system. These have a similar effect as applying torques. In addition, the use of an internal loop of the servo system is considered. From the obtained model, we proceed to carry out the analysis of controllability and observability resulting in that the system is globally weak observable and locally controllable in the operating range. Then, the Jacobi linearization is performed to use the linearized model in the design of linear controllers for stabilization. On the other hand, analyzing the internal dynamics of the ball and plate system turns out to be a non-minimum phase system, which makes it difficult to design the tracking control using the exact model. This is the reason why we proceed to make approximations. Using the approximate model, nonlinear controllers are designed for tracking using different approaches as: feedback linearization for tracking with and without integral action, backstepping and sliding mode. In addition, linear and nonlinear observers are designed to provide full state information to the controller. Simulation tests are performed comparing the different control and observation approaches. Moreover, the effect of the delay in the measurement is analyzed, where it is seen that the greater the frequency of the reference signal the more the error is increased. Then, adding the Smith predictor compensates the delay and reduces the tracking error. Finally, tests performed with the real system. The system was successfully controlled for stabilization and tracking using the designed controllers. However, it is noticed that the effect of the friction, the spring oscillation and other non-modeled characteristics significantly affect the performance of the control.Tesi

Unknown dynamics estimator-based output-feedback control for nonlinear pure-feedback systems

Most existing adaptive control designs for nonlinear pure-feedback systems have been derived based on backstepping or dynamic surface control (DSC) methods, requiring full system states to be measurable. The neural networks (NNs) or fuzzy logic systems (FLSs) used to accommodate uncertainties also impose demanding computational cost and sluggish convergence. To address these issues, this paper proposes a new output-feedback control for uncertain pure-feedback systems without using backstepping and function approximator. A coordinate transform is first used to represent the pure-feedback system in a canonical form to evade using the backstepping or DSC scheme. Then the Levant's differentiator is used to reconstruct the unknown states of the derived canonical system. Finally, a new unknown system dynamics estimator with only one tuning parameter is developed to compensate for the lumped unknown dynamics in the feedback control. This leads to an alternative, simple approximation-free control method for pure-feedback systems, where only the system output needs to be measured. The stability of the closed-loop control system, including the unknown dynamics estimator and the feedback control is proved. Comparative simulations and experiments based on a PMSM test-rig are carried out to test and validate the effectiveness of the proposed method

Robust Output Feedback of Minimum Phase Nonlinear Systems

A robust output feedback controller is synthesized for minimum phase multivariable nonlinear systems based on thedifferential geometry approach. Using the internal model control structure within the input-output (I/O) linearizationframework, the controller is combined with a closed-loop observer to estimate transformed states in the outer-loop. It isshown that the controller-observer combination achieves robust tracking and estimation using simple tuningparameters. The effectiveness of the proposed system is illustrated by a simulation example for control of concentrationin a chemical reactor

Disturbance observer design for nonlinear systems represented by input-output models

A new approach to the design of nonlinear disturbance observers for a class of nonlinear systems described by inputoutput differential equations is presented in this paper. In contrast with established forms of nonlinear disturbance observers, the most important feature of this new type of disturbance observer is that only measurement of the output variable is required, rather than the state variables. An inverse simulation model is first constructed based on knowledge of the structure and parameters of a conventional model of the system. The disturbance can then be estimated by comparing the output of the inverse model and the input of the original nonlinear system. Mathematical analysis demonstrates the convergence of this new form of nonlinear disturbance observer. The approach has been applied to disturbance estimation for a linear system and a new form of linear disturbance observer has been developed. The differences between the proposed linear disturbance observer and the conventional form of frequency-domain disturbance observer are discussed through a numerical example. Finally, the nonlinear disturbance observer design method is illustrated through an application involving a simulation of a jacketed continuous stirred tank reactor syste

A Geometric Control System with Applications to Helicopters

This thesis introduces an Automatic Flight Control System for single rotor helicopters which gives a new relevance to the traditional techniques based on the Linear Control Theory. This design was obtained by applying concepts of differential geometry tailored for engineering purposes through the Nonlinear System Theory. The development of this thesis follows the traditional path of applied sciences. First the need to establish techniques for theoretical analysis of flight machanics, where the small disturbance methods are no longer valid, is reviewed. This is followed by a presentation of the nonlinear problem and a survey of the development of the theoretical tools available. At this stage the process, a single rotor helicopter, is modelled. The model is then cast in a form suitable for Nonlinear System Theory techniques. Next, the mathematical theory to be applied is fully developed. It consists of finding the conditions required by a nonlinear system to be transformable under state feedback to a linear canonical form; the construction of the feedback is also presented. A Flight Control System is designed by applying this theory to the helicopter model previously formulated. The above application requires the development of Symbolic Algebraic Manipulation programmes, which are also included. Finally, a set of simulation studies demonstrate the performance of the design

Advanced Control of Small-Scale Power Systems with Penetration of Renewable Energy Sources

Stability, protection, and operational restrictions are important factors to be taken into account in a proper integration of distributed energy. The objective of this research is presenting advanced controllers for small-scale power systems with penetration of renewable energy sources resources to ensure stable operation after the network disturbances. Power systems with distributed energy resources are modeled and controlled through applying nonlinear control methods to their power electronic interfaces in this research. The stability and control of both ac and dc systems have been studied in a multi-source framework. The dc distribution system is represented as a class of interconnected, nonlinear discrete-time systems with unknown dynamics. It comprises several dc sources, here called subsystems, along with resistive and constant-power loads (which exhibit negative resistance characteristics and reduce the system stability margins.) Each subsystem includes a dc-dc converter (DDC) and exploits distributed energy resources (DERs) such as photovoltaic, wind, etc. Due to the power system frequent disturbances this system is prone to instability in the presence of the DDC dynamical components and constant-power loads. On the other hand, designing a centralized controller may not be viable due to the distance between the subsystems (dc sources.) In this research it is shown that the stability of an interconnected dc distribution system is enhanced through decentralized discrete-time adaptive nonlinear controller design that employs neural networks (NNs) to mitigate voltage and power oscillations after disturbances have occurred. The ac power system model is comprised of conventional synchronous generators (SGs) and renewable energy sources, here, called renewable generators (RGs,) via grid-tie inverters (GTI.) A novel decentralized adaptive neural network (NN) controller is proposed for the GTI that makes the device behave as a conventional synchronous generator. The advantage of this modeling is that all available damping controllers for synchronous generator, such as AVR (Automatic Voltage Regulator) + PSS (Power System Stabilizer), can be applied to the renewable generator. Simulation results on both types of grids show that the proposed nonlinear controllers are able to mitigate the oscillations in the presence of disturbances and adjust the renewable source power to maintain the grid voltage close to its reference value. The stability of the interconnected grids has been enhanced in comparison to the conventional methods

Intelligent control of nonlinear systems with actuator saturation using neural networks

Common actuator nonlinearities such as saturation, deadzone, backlash, and hysteresis are unavoidable in practical industrial control systems, such as computer numerical control (CNC) machines, xy-positioning tables, robot manipulators, overhead crane mechanisms, and more. When the actuator nonlinearities exist in control systems, they may exhibit relatively large steady-state tracking error or even oscillations, cause the closed-loop system instability, and degrade the overall system performance. Proportional-derivative (PD) controller has observed limit cycles if the actuator nonlinearity is not compensated well. The problems are particularly exacerbated when the required accuracy is high, as in micropositioning devices. Due to the non-analytic nature of the actuator nonlinear dynamics and the fact that the exact actuator nonlinear functions, namely operation uncertainty, are unknown, the saturation compensation research is a challenging and important topic with both theoretical and practical significance. Adaptive control can accommodate the system modeling, parametric, and environmental structural uncertainties. With the universal approximating property and learning capability of neural network (NN), it is appealing to develop adaptive NN-based saturation compensation scheme without explicit knowledge of actuator saturation nonlinearity. In this dissertation, intelligent anti-windup saturation compensation schemes in several scenarios of nonlinear systems are investigated. The nonlinear systems studied within this dissertation include the general nonlinear system in Brunovsky canonical form, a second order multi-input multi-output (MIMO) nonlinear system such as a robot manipulator, and an underactuated system-flexible robot system. The abovementioned methods assume the full states information is measurable and completely known. During the NN-based control law development, the imposed actuator saturation is assumed to be unknown and treated as the system input disturbance. The schemes that lead to stability, command following and disturbance rejection is rigorously proved, and verified using the nonlinear system models. On-line NN weights tuning law, the overall closed-loop performance, and the boundedness of the NN weights are rigorously derived and guaranteed based on Lyapunov approach. The NN saturation compensator is inserted into a feedforward path. The simulation conducted indicates that the proposed schemes can effectively compensate for the saturation nonlinearity in the presence of system uncertainty

Robust structural feedback linearization based on the nonlinearities rejection

International audienceIn this paper, we consider a class of affine control systems and propose a new structural feedback linearization technique. This relatively simple approach involves a generic linear-type control scheme and follows the classic failure detection methodology. The robust linearization idea proposed in this contribution makes it possible an effective rejection of nonlinearities that belong to a specific class of functions. The nonlinearities under consideration are interpreted here as specific signals that affect the initially given systems dynamics. The implementability and efficiency of the proposed robust control methodology is illustrated via the attitude control of a PVTOL