Parameter convergence and minimal internal model with an adaptive output regulation problem

The parameter convergence of nonlinear adaptive control systems is an important yet not well addressed issue. In this paper, using the global robust output regulation problem of output feedback systems with unknown exosystems as a platform, we will show that the well known persistency of excitation (PE) condition still guarantees the convergence of the estimated parameter vector to the true parameter vector. Moreover, the PE condition will be satisfied if the internal model is minimal in certain sense.     

Optimal preview-based stable-inversion for output tracking of nonminimum-phase linear systems

In this article, a new approach to output tracking of nonminimum-phase systems is proposed. The proposed technique extends the preview-based stable-inversion method to optimally utilize finite-preview (in time) of the future desired output trajectory to find the feedforward input (called the inverse input) for achieving precision output tracking for nonminimum-phase systems. It has been shown that having a large enough preview time is critical to ensure the precision in the preview-based output tracking. The available preview time, however, can be limited due to the physical constraints, and more generally, the associated cost and/or hardware limits. Therefore, we propose obtaining the optimal preview-based inverse input by minimizing, within the preview time window, the predicted tracking error (under the preview-based inverse input) relative to the input energy. A simulation study on a piezoelectric actuator model is used to illustrate the proposed technique.     

Robust output feedback model predictive control of constrained linear systems: Time varying case

The problem of output feedback model predictive control of discrete time systems in the presence of additive but bounded state and output disturbances is considered. The overall controller consists of two components, a stable state estimator and a tube based, robustly stabilizing model predictive controller. Earlier results are extended by allowing the estimator to be time varying. The proposed robust output feedback controller requires the online solution of a standard quadratic program. The closed loop system renders a specified invariant set robustly exponentially stable.     

Robust output regulation of a class of smart actuators described by a minimum phase LPV dynamics

This paper presents a new control strategy for a class of minimum phase linear parameter-varying (LPV) systems representative of smart material actuators. In position control applications of such devices, one is typically interested in achieving output regulation with an arbitrary exponential decay rate. In principle, this problem can be tackled by assigning an exponential decay rate to the full system state, by means of well-established linear matrix inequalities (LMI) methods. For the class of systems under investigation, however, this approach leads to excessively large controller gains in case the desired decay rate is faster than the open-loop zero dynamics. In addition, the existence of unmeasurable state variables related to the material microstructure makes it not possible to directly implement full state feedback laws which are commonly adopted in LPV theory. To overcome these issues, a new design strategy is proposed. The key idea relies on arbitrarily shaping the output exponential decay rate without requiring fast convergence of the full state vector. This goal is achieved by means of a partial state feedback control law which solely depends on the measurable system states. A LMI algorithm is also developed to systematically address the design of the partial state feedback controller. The method is validated by means of simulations on generic examples, as well as via experiments on a mechatronic positioning system based on a dielectric elastomer membrane. In case the desired output convergence speed is faster than the open-loop zero dynamics, it is shown that the new approach leads to better transient behaviors and significantly smaller controller gains than standard LPV design techniques.     

Time-delay based output feedback control of fourth-order oscillatory systems

We consider stabilization of the fourth-order oscillatory systems with non-collocated output sensing. Worth recalling is that the fourth-order systems are relatively common in mechatronics as soon as there are two-mass or more generally two-inertia dynamics with significant elasticities in between. A novel yet simple control method is introduced based on the time-delayed output feedback. The delayed output feedback requires only the oscillation frequency to be known and allows for a robust control design that leads to cancelation of the resonance peak. We use the stability margins to justify the transfer characteristics and robustness of the time-delay control in frequency domain. The main advantage of the proposed method over the other possible lead-based loop-shaping strategies is that neither time derivatives of the noisy output nor the implementation of transfer functions with a numerator degree greater than zero are required to deploy the controller. This comes in favor of practical applications. An otherwise inherently instable proportional-integral (PI) feedback of the non-collocated output is shown to be stabilized by the proposed method. The control developed and associated analysis are also confirmed by the experimental results shown for the low damped two-mass oscillator system with uncertainties.     

Output tracking control for generalised high-order nonlinear system with serious uncertainties

This paper focuses on the problem of output tracking control for a class of generalised high-order uncertain nonlinear systems. Serious uncertainties are composed of unknown high-order terms, unknown nonlinear functions and the signal to be tracked. The new feedback scheme guarantees that the tracking error belongs to a prescribed small neighbourhood of the origin in finite time. Design procedures are presented by combining improved adding a power integrator method with the recursive construction. As an application, the control methodology is used in the tracking control of the mass-spring mechanical system.     

A robust control scheme for nonlinear non-isothermal uncertain jacketed continuous stirred tank reactor

A Non-isothermal Jacketed Continuous Stirred Tank Reactor (CSTR) is extensively used in chemical as well as in other process industries to manufacture different products. The dynamics of non-isothermal CSTR are highly nonlinear and open-loop unstable in nature. Moreover, it may have parametric uncertainties, disturbances and un-modeled side reactions which may cause the reactor temperature to deviate from the reference value. This deviation may degrade quality of the product because the chemical reaction inside the CSTR depends on reactor temperature. For such a nonlinear, unstable and uncertain process, designing a control scheme with the ability to reject the effects of disturbances along with a good reference tracking capability is a challenging control engineering problem. In this work, a novel robust sliding mode control technique named as Improved Integral Sliding Mode Control (IISMC) has been presented for uncertain non-isothermal jacketed CSTR process. Moreover, a variety of recently developed sliding mode control techniques such as Classical Integral Sliding Mode Control (CISMC) and Super Twisted Algorithm based Sliding Mode Control (STA-SMC) have also been devised and compared with the proposed approach in order to investigate the effectiveness of the proposed scheme. A Lyapunov based analysis has also been provided to assure the robust stability of the closed loop process. Furthermore, in order to extend the state feedback approach to the output feedback scheme, two robust observers; High Gain Observer (HGO) and Extended High Gain Observer (EHGO), are also designed for the very process. They have also been compared with each other and have been investigated for robust stability using Lyapunov based approach. Finally, an output feedback control scheme using IISMC and EHGO has been presented and its performance has been examined and compared with the IISMC based state feedback approach. The simulation results show that the proposed control scheme effectively rejects the uncertainties and disturbances without leading the process to instability and offers good reference tracking capabilities.     

Algebraic conditions for state equivalence to a discrete-time nonlinear observer canonical form

Algebraic necessary and sufficient conditions for a single output discrete-time system to be state equivalent to a (generalized) nonlinear observer canonical form with (or without) output transformation are derived. Our algebraic conditions are easier to verify for researchers unaccustomed to differential geometry. In addition, our proofs are constructive and contain the state and output transformations for (generalized) nonlinear observer canonical forms.     

Discrete-time controllability for feedback quantum dynamics

Controllability properties for discrete-time, Markovian quantum dynamics are investigated. We find that, while in general the controlled system is not finite-time controllable, feedback control allows for arbitrary asymptotic state-to-state transitions. Under further assumptions on the form of the measurement, we show that finite-time controllability can be achieved in a time that is twice the dimension of the system, and we provide an iterative procedure to design the unitary control actions.