Model Predictive Control (MPC) is often tuned by trial and error. When a baseline linear controller exists that is already well tuned in the absence of constraints and MPC is introduced to enforce them, one would like to avoid altering the original linear feedback law whenever they are not active. We formulate this problem as a controller matching similar to [1]-[3], which we extend to a more general framework. We prove that a positive-definite stage cost matrix yielding this matching property can be computed for all stabilizing linear controllers. Additionally, we prove that the constrained estimation problem can also be solved similarly, by matching a linear observer with a Moving Horizon Estimator (MHE). Finally, we discuss various aspects of the practical implementation of the proposed technique in some examples.
This paper proposes a novel unit-quaternion observer-based controller for attitude tracking (attitude and angular velocity) with guaranteed transient and steady-state performance. The proposed approach is computationally cheap and can operate based on measurements provided, for instance by a typical low-cost inertial measurement unit (IMU) or magnetic, angular rate, and gravity (MARG) sensor without the knowledge of angular velocity. First, an observer evolved on $\mathbb{S}^{3}\times\mathbb{R}^{3}$ is developed guaranteeing asymptotic stability of the closed loop error signals starting from a…
The design of an observer-based state feedback (OBSF) controller with guaranteed passivity properties for port-Hamiltonian systems (PHS) is addressed using linear matrix inequalities (LMIs). The observer gain is freely chosen and the LMIs conditions such that the state feedback is equivalent to control by interconnection with an input strictly passive (ISP) and/or an output strictly passive (OSP) and zero state detectable (ZSD) port-Hamiltonian controller are established. It is shown that the proposed controller exponentially stabilizes a class of infinite-dimensional PHS and asymptotically st…
This paper proposes a new fraction-order active disturbance rejection controller based on an improved fraction-order extended state observer (IFESO) for a class of fraction-order systems. Applying the IFESO, the fraction-order system can be approximated as an integer-order integrator (1/s). The parameters that ensure the stability of the IFESO and closed-loop system are provided. The frequency-domain analysis shows that the IFADRC has a stronger disturbance estimation performance for the fraction-order system than an integer-order active disturbance rejection controller (IADRC). The simulation…
This paper addresses the synthesis of safety-critical controllers using estimate feedback. We propose an observer-controller interconnection to ensure that the nonlinear system remains safe despite bounded disturbances on the system dynamics and measurements that correspond to partial state information. The co-design of observers and controllers is critical, since even in undisturbed cases, observers and controllers designed independently may not render the system safe. We propose two approaches to synthesize observer-controller interconnections. The first approach utilizes Input-to-State Stab…
Steam turbine generator is an electromechanical system which converts heat energy to electrical energy. In this paper, the modeling, design and analysis of a simple steam turbine generator have done using Matlab/Simulink Toolbox. The open loop system have been analyzed to have an efficiency of 76.92 %. Observer based & linear quadratic regulator (LQR) controllers have been designed to improve the generating voltage. Comparison of this two proposed controllers have been done for increasing the performance improvement to generate a 220 Dc volt. The simulation result shows that the steam turbine …
Disturbance observer is an inner-loop output-feedback controller whose role is to reject external disturbances and to make the outer-loop baseline controller robust against plant's uncertainties. Therefore, the closed-loop system with the DOB approximates the nominal closed-loop by the baseline controller and the nominal plant model with no disturbances. This article presents how the disturbance observer works under what conditions, and how one can design a disturbance observer to guarantee robust stability and to recover the nominal performance not only in the steady-state but also for the tr…
A Generic Formation Controller and State Observer for Multiple Unmanned Systems
Indian Institute of Science（印度科学学院）；University of Texas at San Antonio（圣安东尼奥德克萨斯大学）；New Mexico State University（新墨西哥州立大学）；University of Tennessee at Chattanooga（查塔努加田纳西大学）
In this work, we present a mixed sensorless strategy for Permanent Magnets Synchronous Machines, combining a torque/current controller and an observer for position, speed, flux and stator resistance. The proposed co-design is motivated by the need of an appropriate signal injection technique, in order to guarantee full state observability. Neither the typical constant or slowly-varying speed assumptions, nor a priori mechanical model information are used in the observer design. Instead, the rotor speed is modeled as an unknown input disturbance with constant (unknown) sign and uniformly non-ze…
An observer-based boundary controller for infinite-dimensional port-Hamiltonian systems defined on 1D spatial domains is proposed. The design is based on an early-lumping approach in which a finite-dimensional approximation of the infinite-dimensional system derived by spatial discretization is used to design the observer and the controller. As long as the finite-dimensional approximation approaches the infinite-dimensional model, the performances also do. The main contribution is a constructive method which guarantees that the interconnection between the controller and the infinite-dimensiona…
Frequency control (FC) enables utility-scale grid-connected hybrid power plants (HPPs) to operate in compliance with grid code requirements while to capture value streams from provision of frequency control services (FCSs). In this paper, a novel hierarchical FC approach is proposed to allow HPPs to provide three types of FCSs, namely fast frequency response (FFR), frequency containment response (FCR) and frequency restoration response (FRR). To accommodate state-of-the-art fast FC, controllers for fast FCSs, such as FFR and FCR, are implemented at asset controllers, while controllers for slow…
This paper investigates the design of reduced-order observers for robotic manipulators. Observer stability conditions are obtained based on a Lyapunov analysis and the proposed observer is enhanced with a hybrid scheme that may adjust the gains to cope with possible unbounded velocities of the robot joints. Thanks to such hybrid strategy, the observer works accurately both for robots driven by open-loop controllers and by output feedback controllers. Numerical simulations illustrate the efficacy of the reduced-order observer in several scenarios, including a comparison with the performances of…
While the Artificial Pancreas is effective in regulating the blood glucose in the safe range of 70-180 mg/dl in type 1 diabetic patients, the high intra-patient variability, as well as exogenous meal disturbances, poses a serious challenge. The existing control algorithms thus require additional safety algorithms and feed-forward actions. Moreover, the unavailability of insulin sensors in Artificial Pancreas makes this task more difficult. In the present work, a subcutaneous model of type 1 diabetes (T1D) is considered for observer-based controller design in the framework of contraction analys…
This paper analyses and synthesises the Disturbance Observer (DOb) based motion control systems in the discrete-time domain. By employing Bode Integral Theorem, it is shown that continuous-time analysis methods fall-short in explaining the dynamic behaviours of the DOb-based robust motion controllers implemented by computers and microcontrollers. For example, continuous-time analysis methods cannot explain why the robust stability and performance of the digital motion controller deteriorate as the bandwidth of the DOb increases. Therefore, unexpected dynamic responses (e.g., poor stability and…
In this paper we propose a PI passivity-based controller, applicable to a large class of switched power converters, that ensures global state regulation to a desired equilibrium point. A solution to this problem was reported in \cite{HERetal} but it requires full state-feedback, which makes it practically unfeasible. To overcome this limitation we construct a state observer that is implementable with measurements that are available in practical applications. The observer reconstructs the state in finite-time, ensuring global convergence of the PI. The excitation requirement for the observer is…
This paper proposes a new stability analysis for the Reaction Torque Observer (RTOb) based robust force control systems in the discrete-time domain. The robust force controller is implemented by employing a Disturbance Observer (DOb) to suppress disturbances, such as friction and hysteresis, in an inner-loop and another disturbance observer, viz RTOb, to estimate contact forces without using a force sensor. Since the RTOb-based robust force controllers are always implemented using computers and/or microcontrollers, this paper proposes a stability analysis in the discrete-time domain. It is sho…
The rigid-body attitude tracking using vector and biased gyro measurements with unknown inertia matrix is studied in this note. First, a gyro-bias observer with global exponential stability is designed. Then, an attitude tracking controller based on this observer is devised, ensuring almost global asymptotic stability and almost semiglobal exponential stability. A separation property of the combined observer-controller is proved. Lastly, an adaptive attitude tracking controller relying on a modified gyro-bias observer and with no over-parametrization is developed to deal with the unknown inert…
On the Optimization Landscape of Observer-based Dynamic Linear Quadratic Control
University of Science and Technology Beijing（北京科技大学）；Chongqing University（重庆大学）；Johns Hopkins University（约翰斯·霍普金斯大学）；Tsinghua University（清华大学）；National University of Singapore（新加坡国立大学）
This work provides formal safety guarantees for control systems with disturbance. A disturbance observer-based robust safety-critical controller is proposed, that estimates the effect of the disturbance on safety and utilizes this estimate with control barrier functions to attain provably safe dynamic behavior. The observer error bound - which consists of transient and steady-state parts - is quantified, and the system is endowed with robustness against this error via the proposed controller. An adaptive cruise control problem is used as illustrative example through simulations including real …
Output Feedback Control of Inhomogeneous Parabolic PDEs with Point Actuation and Point Measurement using SOS and Semi-Separable Kernels
Illinois Institute of Technology（伊利诺伊理工学院）；Grenoble Image Parole Signal Automatique Lab., Université Joseph Fourier/Centre National de la Recherche Scientifique（格勒诺布尔图像语音信号自动实验室，约瑟夫·傅立叶大学/法国国家科学研究中心）；School of Engineering of Matter, Transport and Energy at Arizona State University（亚利桑那州立大学物质、运输与能源工程学院）
Introductory state-space linear control courses focus on linear, time-invariant systems and spend intense efforts by introducing system realizations that allow the student to grasp fundamental concepts, among which controllability, observability, and controller and observer design. This note describes a graphical mechanism to transform a system expressed in observability form into its observer form based on elementary block diagram manipulations, a technique whose pedagogical usefulness tends to be overlooked. Given the well-known duality principle in linear systems with respect to controllabi…
We investigate the impact of packet dropouts due to non-idealities in communication networks on the performance of optimally derived controllers and observers in a minimax sense. These packet dropouts are modeled by discrete constrained switching signals via directed graphs. We consider time optimal control and estimation, minimum energy and fuel optimization and LQR problems for systems subject to packet dropouts which turn out to be combinatorial; and compute algorithmically the worst case performance of these optimization problems. To reduce the computational burden in solving these combina…
In this technical note we analyse the performance improvement and optimality properties of the Learning Model Predictive Control (LMPC) strategy for linear deterministic systems. The LMPC framework is a policy iteration scheme where closed-loop trajectories are used to update the control policy for the next execution of the control task. We show that, when a Linear Independence Constraint Qualification (LICQ) condition holds, the LMPC scheme guarantees strict iterative performance improvement and optimality, meaning that the closed-loop cost evaluated over the entire task converges asymptotica…
An Improved ESO-Based Line-of-Sight Guidance Law for Path Following of Underactuated Autonomous Underwater Helicopter With Nonlinear Tracking Differentiator and Anti-saturation Controller
In this paper, we study the application of switched systems stability criteria to derive delay-dependent conditions for systems affected by both a constant and a time-varying delay. The main novelty of our approach lies on the use of path-complete Lyapunov techniques along with the proposition of a new modified functional to obtain convex analysis conditions while avoiding the need of computing a dwell time for each mode in a switched system representation, as usual in the \textit{switched approach} for time-delay systems. Furthermore, we leverage the developed analysis to obtain LMIs for the …
In this paper, we incorporate velocity observer design into the virtual decomposition control (VDC) strategy of an $n$-DoF open chain robotic manipulator. Descending from the VDC strategy, the proposed design is based on decomposing the $n$-DoF manipulator into subsystems, i.e., rigid links and joints, for which the decentralized controller-observer implementation can be done locally. Similar to VDC, the combined controller-observer design is passivity-based, and we show that it achieves semiglobal exponential convergence of the tracking error. The convergence analysis is carried out using Lya…
Proper operation of the Active Disturbance Rejection (ADR) controller requires a precise determination of the so-called total disturbance affecting the considered dynamical system, usually estimated by the Extended State Observer (ESO). The observation quality of total disturbance has a significant impact on the control error values, making room for a potential improvement of control system performance using different structures of ESO. In this article, we provide a quantitative comparison between the Luenberger and Astolfi/Marconi (AM) observers designed for three different extended state rep…
