Nonlinear Output Regulation Theory Research Articles

Switched Energy and Neural Network-Based Approach for Swing-Up and Tracking Control of Double Inverted Pendulum

The double inverted pendulum (DIP) system is a benchmark underactuated mechanical system. The control problem of the DIP system is challenging since it not only has high nonlinearity, but also has underactuation degree equal to two. In this article, a switched energy-based swing-up and neural network (NN) controller is proposed to solve the swing-up and tracking control problem of the DIP system when the desired position is time varying. The implementation of the proposed controller can be divided into three steps. In step one, the energy-based control method is adopted to drive the first pendulum from the downward position to the neighborhood of the upright position. In step two, the sliding mode control method is adopted to stabilize the first pendulum. Meanwhile, a method combining energy-based control and “equivalent cart” is adopted to swing up the second pendulum. In step three, on the basis of approximate nonlinear output regulation theory, the NN controller is used for achieving satisfactory position tracking performance. Finally, the effectiveness of our design is verified by experimental results.

Experimental Output Regulation of Linear Motor Driven Inverted Pendulum With Friction Compensation

Over the past few decades, the nonlinear output regulation (NOR) theory has attracted extensive attentions in control society. However, few experimental results have been reported about the NOR theory. This article first presents experimental results on discrete-time NOR problem for a linear motor driven inverted pendulum (LMDIP) system. To solve this problem, it is essential to find the solution of the complicated discrete regulator equations (DREs). Moreover, the friction force commonly exists in mechanical systems and cannot be neglected for control systems requiring high precision tracking performance. We present a novel discrete-time controller by combining neural network (NN) approach and friction-feedforward compensation mechanism. Finally, we verify the proposed control algorithm by experiment and make some comparisons with the linear controller.

Discrete-Time Neural Network Approach for Tracking Control of Spherical Inverted Pendulum

In recent years, the tracking problem of spherical inverted pendulum (SIP) system with multi-input, multi-output nature and unstable zero dynamics has been well addressed based on continuous-time nonlinear output regulation (NOR) theory. For the convenience of digital implementation, this paper further investigates the approximate NOR problem of the SIP system in discrete-time framework. The key for solving the discrete-time NOR problem lies in how to solve a set of algebraic functional equations known as discrete regulator equations (DRE). Since the equations are very complicated, the accurate solution of the DRE can not be obtained. In this paper, we first show that the DRE associated with the SIP system are solvable by center manifold theorem and then use neural network approach to tackle with the tracking problem. Finally, we compare our method with polynomial approximation method.

Station-keeping and formation flying based on nonlinear output regulation theory

Station-keeping and formation flying along a libration point orbit in the circular restricted three-body problem are considered. In order to deal with the relative motion with respect to a reference trajectory, this paper extends our previous study which derives the station-keeping controller based on the output regulation theory. First the reference orbit of the chief satellite is represented as the output of an autonomous system called exosystem, assuming the reference orbit is given by a truncated Fourier series. For the formation flying, the relative trajectory of the deputy satellite with respect to the chief satellite is also represented by the output of an exosystem. Then the reference signal to be asymptotically tracked for the formation flying is obtained by the superposition of the two exosystems. The proposed controllers are applied and verified for the station-keeping and formation flying along a periodic orbit of the Sun-Earth L2 point.

Robust output synchronization of heterogeneous nonlinear agents in uncertain networks

This paper investigates the global robust output synchronization problem for a class of nonlinear multi-agent systems. In the considered setup, the controlled agents are heterogeneous and with both dynamic and parametric uncertainties, the controllers are incapable of exchanging their internal states with the neighbors, and the communication network among agents is defined by an uncertain simple digraph. The problem is pursued via nonlinear output regulation theory and internal model based design. For each agent, the input-driven filter and the internal model compose the controller, and the decentralized dynamic output feedback control law is derived by using backstepping method and the modified dynamic high-gain technique. The theoretical result is applied to output synchronization problem for uncertain network of Lorenz-type agents.

Pilot induced oscillation suppression controller design via nonlinear optimal output regulation method

This paper proposes a controller design method for preventing pilot-induced-oscillation (PIO) based on nonlinear optimal output regulation theory and center stable manifold method. The type of PIO considered is due to actuator rate limiting and the proposed controller assures C⁎ handling quality by the optimal control when actuator works in the linear region. The simulation result shows that the proposed nonlinear controller has better tracking performance in comparison with the linear optimal output regulation controller. The robustness of the designed controller against parametrization error, noise and time-delay is also verified.

Optimal Servo Design for Lock-Up Slip Control for Torque Converter—Nonlinear Output Regulation Approach

It is well known that slip control of lock-up clutch in automatic transmission systems is a crucial technology for improving fuel economy and driving comfort. However, plant parameters rapidly vary according to turbine speed, making the slip control challenging. For this problem, we apply nonlinear output regulation theory for the system represented as a linear parameter-varying system with the turbine speed as the parameter. In this framework, it is possible to design a servo controller that is optimally scheduled according to the turbine speed. The effectiveness of the proposed method is confirmed by experiments compared with an $H_{\infty }$ controller, which is one of the most advanced methods employed in the field of lock-up clutch slip control.

Synchronised output regulation of nonlinear multi-agent systems

This paper considers a synchronised output regulation (SOR) problem of nonlinear multi-agent systems with switching graph. The SOR means that all agents have their outputs synchronised but also ultimately evolve on a manifold determined by a predefined exosystem. Each agent constructs its local copy of the predefined exosystem and exchanges the state information of the local exosystem to realise the synchronisation of local exosystem. A controller based on the nonlinear output regulation theory is then presented to force the agent's output track the output of local exosystem. It is shown that the SOR is solvable under the assumptions same as that for nonlinear output regulation of a single agent, if the switching graph satisfies the bounded interconnectivity times condition. Both state feedback and output feedback are addressed. A numerical simulation is made to show the efficacy of the analytic results.

Automatic bottom-following for underwater robotic vehicles

In this note we propose a solution for the automatic bottom-following problem for a low cost autonomous underwater vehicle. We consider the case that the seabed profile is not known in advance, and we show that it is possible to solve the bottom-following using only one echo sounder and without the need to measure the vertical velocity component (heave velocity). To this effect, we propose an output feedback controller that is obtained by first re-formulating the bottom-following into a trajectory tracking problem, then constructing a reference signal generator (the exo-system) using Fourier series theory, and finally solving the control design problem in the framework of nonlinear output regulation theory. An interesting feature of this approach is that the combination of the Fourier series with output regulation problem allows to bypass the need to compute explicitly the Fourier coefficients. To obtain an approximate solution of the resulting regulator equations we resort to pseudo-spectral methods. Stability analysis that takes explicitly into account the effects of the inner-loop autopilots, disturbances, and measurement noise is presented. Simulation results with real seabed data show the effectiveness of the proposed controller.

Experimental Output Regulation for a Nonlinear Benchmark System

Research on the nonlinear output regulation problem is mainly focused on theoretical developments and studies on simulation level. In this brief, we present experimental results on the local output regulation problem for a nonlinear benchmark mechanical system, the so-called translational oscillator with a rotational actuator system. The presented results show the effectiveness of the nonlinear output regulation theory in practice. As follows from the conducted experiments, issues such as the convergence rate, stability, and performance robustness with respect to (non) parametric uncertainties, the size of the region of attraction, and actuator saturation should be accounted for in tuning the controller gains. This design problem has not been addressed in the existing literature on the nonlinear output regulation problem and it, therefore, raises a new direction for research crucial to the future application of output regulation theory in practice.

Output tracking and synchronization of chaotic Chua’s circuit with disturbances via model predictive regulator

In this paper, we consider the output tracking and synchronization problem for a piecewise linear chaotic Chua’s circuit, which is expected to follow the reference signal generated by another autonomous chaotic Chua’s circuit. A novel model predictive regulator is proposed to guarantee the chaos synchronization in the presence of external disturbance. Moreover with this regulator, the optimal transient tracking performance for synchronization is ensured even when the piecewise autonomous and controlled Chua’s circuits switch asynchronously. The proposed approach is highly efficient in the sense that the regulation conditions can be satisfied by solving a set of linear matrix inequalities and several Sylvester equations instead of many partial differential regulator equations in the well-known nonlinear output regulation theory.

INTERNAL MODEL BASED FRAMEWORK FOR TRACKING AND FAULT TOLERANT CONTROL OF A PERMANENT MAGNET SYNCHRONOUS MOTOR

In this paper an adaptive internal model based control scheme is designed to deal with tracking and input disturbance suppression problems for a permanent magnet synchronous motor. More in detail we show how to design a controller able to guarantee the perfect asymptotic tracking of unknown exogenous trajectories belonging to a certain family, embedding in the regulator the internal model of this family; the theoretical machinery exploited in order to prove the global asymptotical stability of the solution exposed is the nonlinear output regulation theory, specialized for the energy-based port-Hamiltonian formalism.

Implicit fault-tolerant control: application to induction motors

In this paper we propose an innovative way of dealing with the design of fault-tolerant control systems. We show how the nonlinear output regulation theory can be successfully adopted in order to design a regulator able to offset the effect of all possible faults which can occur and, in doing so, also to detect and isolate the occurred fault. The regulator is designed by embedding the (possible nonlinear) internal model of the fault. This idea is applied to the design of a fault-tolerant controller for induction motors in presence of both rotor and stator mechanical faults.

Regulation and Input Disturbance Suppression for Port-Controlled Hamiltonian Systems

In this paper the output feedback regulation problem for port-controlled Hamiltonian systems (PCHS) is addressed. Following the nonlinear output regulation theory, the regulator which solves the problem is given by a parallel connection of two subcontrollers: an internal model unit and a regulator to stabilize the extended system composed by the plant and the internal model unit. The main idea is to use the PCHS theory in order to design that stabilizer controller: as in many cases the plant to be addressed is indeed a mechanical/electric system, and it is very easy to think about it as a PCHS, the paper shows the conditions to fulfill in order to design the internal model unit as a PCHS, allowing to use the powerful energy-shaping theory in order to stabilize the extended system. Moreover the same techniques are used to design an internal model based controller able to globally solve a problem of input disturbance suppression

IMPLICIT FAULT TOLERANT CONTROL: APPLICATION TO INDUCTION MOTORS

In this paper we propose an innovative way of dealing with the design of fault tolerant control systems. We show how the nonlinear output regulation theory can be successfully adopted in order to design a regulator able to offset the effect of all the possible faults which can occur and, so doing, also to detect and isolate the occurred fault. The regulator is designed by embedding the (possible nonlinear) internal model of the fault. This idea is then applied to the design of a fault tolerant controller for induction motors in presence of both electrical and mechanical faults. Copyright © IFAC 2002

Nonlinear Output Regulation with Bounded Control by Trajectory Reparameterization

This paper addresses the problem of stabilization and trajectory tracking of nonlinear systems in the presence of input saturation. The main idea consists on avoiding the input saturations by means of a time scale reparameterization of the desired trajectories. The control scheme is based on a well-known nonlinear output regulation theory, where the modification is directly performed on the evolution of the exosystem state trajectories. Finally, some illustrative examples are given.