Closed-loop Properties Research Articles

Variable-Performance Servo System Design Without Actuator Current and Angle Measurement for Rover Vehicles

This study devises a variable-performance control law for rover vehicles servoing velocity and pitch angle commands. This considers both vehicle and actuator dynamics as well as load and parameter variations. The main merits are summarized as follows. First, the proposed auto-tuning law magnifies the feedback gain for desired systems to achieve transient performance improvement with the convergence property guarantee. Second, the collaboration of pole-zero cancellation controller and disturbance observers eliminates over/undershoots through closed-loop order reduction by a special form of feedback gain. Beneficial closed-loop properties are also derived from the closed-loop analysis. The prototype rover vehicle built with TETRIX and MyRIO-1900 experimentally validates the closed-loop performance and robustness improvement.

Modular Model Predictive Control upon an Existing Controller

The availability of predictions of future system inputs has motivated research into preview control to improve set-point tracking and disturbance rejection beyond that achievable via conventional feedback control. The design of preview controllers, typically based upon model predictive control (MPC) for its constraint handling properties, is often performed in a monolithic nature, coupling the feedback and feed-forward problems. This can create problems, such as: (i) an additional feedback loop is introduced by MPC, which alters the closed-loop dynamics of the existing feedback compensator, potentially resulting in a deterioration of the nominal sensitivities and robustness properties of an existing closed-loop and (ii) the default preview action from MPC can be poor, degrading the original feedback control performance. In our previous work, the former problem is addressed by presenting a modular MPC design on top of a given output-feedback controller, which retains the nominal closed-loop robustness and frequency-domain properties of the latter, despite the addition of the preview design. In this paper, we address the second problem; the preview compensator design in the modular MPC formulation. Specifically, we derive the key conditions that ensure, under a given closed-loop tuning, the preview compensator within the modular MPC formulation is systematic and well-designed in a sense that the preview control actions complement the existing feedback control law rather than opposing it. In addition, we also derive some important results, showing that the modular MPC can be implemented in a cascade over any given linear controllers and the proposed conditions hold, regardless of the observer design for the modular MPC. The key benefit of the modular MPC is that the preview control with constraint handling can be implemented without replacing the existing feedback controller. This is illustrated through some numerical examples.

Switching Perfect Control Algorithm

The application of the switching control framework to the perfect control algorithm is presented in this paper. Employing the nonunique matrix inverses, the different closed-loop properties are obtained and further enhanced with possible switching methodology implementation. Simulation examples performed in the MATLAB/Simulink environment clearly show that the new framework can lead to benefits in terms of the control energy, speed, and robustness of the perfect control law. The possibility of transferring the new obtained results to the symmetrical nonlinear plants seems to be immediate.

Energy-Shaping Speed Controller With Time-Varying Damping Injection for Permanent-Magnet Synchronous Motors

This brief presents a novel energy-shaping technique-based speed controller for permanent-magnet synchronous motors (PMSMs) considering machine nonlinearities and load and parameter changes. There are three features: The time-varying damping term is injected into the speed loop, which is automatically updated by the proposed self-tuner. The disturbance observers are designed for both the speed and current loops to achieve better disturbance rejection performance with removal of offset errors without the use of tracking error integral actions. Furthermore, the closed-loop analysis result is provided to demonstrate its beneficial closed-loop properties. The practical advantages are experimentally verified in several convincing scenarios with a prototype 500-W PMSM driven by a three-phase inverter.

Explicit Construction of Stabilizing Robust Avoidance Controllers for Linear Systems With Drift

We propose a constructive design method for linear systems with a nontrivial drift term, guaranteeing robust global asymptotic stability of the origin of the closed-loop system, as well as robust obstacle avoidance. To obtain discontinuous input actions, our controller is designed in the framework of hybrid systems. Using our proposed hybrid controller, we demonstrate that solutions do not enter a sphere, which we term an avoidance neighborhood, around specified isolated points. The constructive controller design methodology, as well as the closed-loop properties, is investigated via numerical examples.

Dissipativity properties in constrained optimal control: A computational approach

In this paper, we consider discrete-time nonlinear optimal control problems with possibly non-convex cost subject to constraints on states and inputs. For these problems, we present a computational approach for the verification of strict dissipativity properties, which have recently been employed to study optimal system operation, turnpike phenomena, and closed-loop properties of economic model predictive control schemes. Based on a non-strict dissipation inequality, we provide necessary and sufficient conditions for strict dissipativity by explicitly computing the set w.r.t. which the system is strictly dissipative as well as the corresponding storage function. We focus on strict dissipativity w.r.t. periodic orbits and steady-states, being the most relevant cases of strict dissipativity, although our approach can be directly extended to strict dissipativity w.r.t. more general sets. For polynomial optimal control problems, the presented approach leads to a polynomial optimization problem, which is solved via sum-of-squares programming. The optimal periodic orbit can then be constructed, without a priori knowledge of its period length, as the set of points for which a suitable non-strict dissipation inequality holds with equality. In addition, we consider the important special case of indefinite linear quadratic optimal control problems subject to quadratic constraints, for which an optimal periodic orbit resulting from our construction is always located on the boundary of the constraint set.

A Graphical Design Approach for Two-Input Single-Output Systems Exploiting Plant/Controller Alignment: Design and Application

Abstract Due to the unique structure of two-input single-output (TISO) feedback systems, several closed-loop properties can be characterized using the concepts of plant and controller “directions” and “alignment.” Poor plant/controller alignment indicates significant limitations in terms of closed-loop performance. In general, it is desirable to design a controller that is well aligned with the plant in order to minimize the size of the closed-loop sensitivity functions and closed-loop interactions. Although the concept of alignment can be a useful analysis tool for a given plant/controller pair, it is not obvious how a controller should be designed to achieve good alignment. We present a new controller design approach, based on the PQ method (Schroeck et al., 2001, “On Compensator Design for Linear Time invariant Dual-Input Single-Output Systems,” IEEE/ASME Trans. Mechatronics, 6(1), pp. 50–57), which explicitly incorporates knowledge of alignment into the design process. This is accomplished by providing graphical information about the alignment angle on the Bode plot of the PQ frequency response. We show the utility of this approach through a design example.

Economic Model Predictive Control for Time-Varying Cost and Peak Demand Charge Optimization

With the increasing prevalence of variable-supply electricity production, dynamic market structures, including time-varying prices and/or peak demand charges are becoming more common for electricity consumers. This framework requires consumers to consider both the time-varying amount of electricity (i.e., energy) consumed throughout the day as well as the maximum rate of electricity purchase (i.e., power) over a given period, typically a month. Because of this complexity, online optimization techniques such as economic model predictive control (MPC) are a natural tool for consumers to use to minimize cost. However, while closed-loop optimization of these pricing structures is already being proposed for various applications, little has been established about stability or performance properties of the closed-loop system. Due in particular to the peak penalty (which violates the principle of optimality if naively included in the objective function), this theoretical gap leaves the potential for pathological closed-loop behavior despite high-quality open-loop solutions. In this paper, we derive asymptotic performance and stability results for general time-varying economic MPC. We then present a novel extended-state formulation to convert peak demand charges into a time-varying stage cost that can be optimized using economic MPC. In addition, we give a terminal cost and constraint for the augmented system that avoids reducing the feasible set in the original space. Finally, we demonstrate these structures and the closed-loop properties that they satisfy via two illustrative examples.

Data-Driven Model Predictive Control With Stability and Robustness Guarantees

We propose a robust data-driven model predictive control (MPC) scheme to control linear time-invariant (LTI) systems. The scheme uses an implicit model description based on behavioral systems theory and past measured trajectories. In particular, it does not require any prior identification step, but only an initially measured input-output trajectory as well as an upper bound on the order of the unknown system. First, we prove exponential stability of a nominal data-driven MPC scheme with terminal equality constraints in the case of no measurement noise. For bounded additive output measurement noise, we propose a robust modification of the scheme, including a slack variable with regularization in the cost. We prove that the application of this robust MPC scheme in a multi-step fashion leads to practical exponential stability of the closed loop w.r.t. the noise level. The presented results provide the first (theoretical) analysis of closed-loop properties, resulting from a simple, purely data-driven MPC scheme.

Disturbance Observer-based Proportional-type Position Tracking Controller for DC Motor

This article exhibits a nonlinear proportional-type position tracking controller for DC motors, taking the parameter and load variations into account. The proposed method makes two contributions. First, a first-order disturbance observer (DOB) is devised in order to exponentially estimate the disturbances caused by parameter and load uncertainties. Secondly, a proportional-type nonlinear position tracking controller is constructed by incorporating the resulting DOB in order to ensure two useful closed-loop properties; namely, performance recovery and offset-free properties without the tracking error integral actions. The experimental result confirms the efficacy of the proposed method where a 30-W DC motor is used with an half bridge inverter.

Passivity-Based Robust Output Voltage Tracking Control of DC/DC Boost Converter for Wind Power Systems

This paper exhibits a passivity-based robust output voltage controller for DC/DC boost converters for wind power system applications. The proposed technique has two features. The first one is to introduce a nonlinear disturbance observer for estimating the disturbances arising from the load and parameter variations. The second one is to derive a proportional-type passivity-based output voltage tracking controller incorporating the disturbance observer output, which simplifies the control algorithm by removing the use of tracking error integrators and an anti-windup algorithm. These two features constitute the useful closed-loop properties called the performance recovery and offset-free properties. Numerical simulation results confirm the efficacy of the proposed scheme, where a wind power system including the proposed controller is emulated using the PowerSIM software.

Robust speed control algorithm with disturbance observer for uncertain PMSM

ABSTRACTThis article suggests a robust cascade speed control algorithm for a permanent magnet synchronous motor (PMSM) combining the classical feedback linearising (FL) method and the disturbance observers (DOBs) without the integrators. The contributions of this method are twofold. The first one is to provide the simple DOBs for not only guaranteeing the closed-loop performance recovery property but also removing the steady-state errors without the integrators with respect to the tracking errors. The second one is to prove that the inner and outer loops are stabilised by the proposed cascade-type controller, simultaneously. The simulation and experimental results reveal that the proposed method maintains the speed tracking performance to be satisfactory for a wide operating region with the fixed control gain despite a plant-model mismatch where a 3-kW interior PMSM is utilised.

Adaptive thermal control for PEMFC systems with guaranteed performance

Proton exchange membrane fuel cell (PEMFC) s are faced with dynamical load scenario in practical applications, and the resulting temperature variation will decrease the performance and consequently shorten the fuel cell lifetime. To address this problem, a control strategy for regulating the stack temperature is proposed in this paper. Firstly, a thermal management-oriented dynamic model of a water-cooled PEMFC system is built to facilitate the control design. Secondly, considering that the stack temperature should be maintained in a certain range regardless of the dynamical changing current demand, a Barrier Lyapunov function is employed to construct a feedback error of the stack temperature. Thirdly, a set of adaptation laws is designed to estimate the unknown parameters related to the gas flow rates in the flow fields. Particularly, a dynamic inversion tracking methodology is applied to design the non-affine input. A Lyapunov method based analysis demonstrates the stability and convergence of the closed-loop properties. Simulation results are provided to show that the proposed control strategy can satisfy all the control objectives and enhance the control performance compared to the proportional-integral controlled case.

Fractional PID controller design for nonlinear systems based on singular perturbation technique

This paper deals with the output regulation of nonlinear control systems in order to guarantee desired performances in the presence of plant parameters variations and external disturbances. The proposed control law structures are based on the fractional order PI (FOPI) and PID (FOPID) control schemes. By introducing the two-time-scale notions in the closed-loop system, the presented design methodology of fractional PID control guarantees desired transients. Then, the singular perturbations technique is used to analyse the closed-loop system properties and to get explicit expressions for evaluation of the controller parameters. The tuning of the controller parameters is based on a constrained optimisation algorithm. Simulation examples are presented to show the effectiveness of the proposed method.

A robust predictor for dead-time systems based on the Kalman filter

Abstract Dead time processes are common in the industry and represent a challenge for control. One way to avoid (or attenuate) the problem is to use a predictor structure alongside the controller. In this paper, an observer-predictor structure based on a steady-state Kalman filter is explored. It is shown that this structure is equivalent to the Filtered Smith Predictor (FSP) for linear systems, hence, all the tools used to analyze the closed-loop properties of the FSP can also be used in the proposed predictor, specially the frequency domain ones. With the results of this analysis, tuning guidelines for the predictor are given to achieve different closed-loop characteristics, e.g., better disturbance rejection or better robustness. Furthermore, the proposed predictor can easily be used with all kind of systems, including unstable and non-minimum phase systems.

Stochastic economic model predictive control for Markovian switching systems

The optimization of process economics within the model predictive control (MPC) formulation has given rise to a new control paradigm known as economic MPC (EMPC). Several authors have discussed the closed-loop properties of EMPC-controlled deterministic systems, however, little have uncertain systems been studied. In this paper we propose EMPC formulations for nonlinear Markovian switching systems which guarantee recursive feasibility, asymptotic performance bounds and constrained mean square (MS) stability.

Real-Time Adaptive Control of a Fuel Cell/Battery Hybrid Power System With Guaranteed Stability

This paper studies a real-time control problem for a hybrid power system consisting of a proton exchange membrane fuel cell (FC), a unidirectional boost converter, and a lithium-ion battery. An adaptive control strategy is proposed to manage the power sharing in this hybrid power system. System constraints, including the slow dynamics of the FC and the state of charge of the battery, are explicitly considered. The controller achieves tracking a dynamically changing load demand while satisfying the system constraints based on parameter estimations. The main contribution is that, compared with the previous control methods, the proposed control design for hybrid power systems has provable stability and convergence closed-loop properties. Simulation and experimental results are provided to validate the control design.

Stability and performance verification of optimization-based controllers

This paper presents a method to verify closed-loop properties of optimization-based controllers for deterministic and stochastic constrained polynomial discrete-time dynamical systems. The closed-loop properties amenable to the proposed technique include global and local stability, performance with respect to a given cost function (both in a deterministic and stochastic setting) and the L2 gain. The method applies to a wide range of practical control problems: For instance, a dynamical controller (e.g., a PID) plus input saturation, model predictive control with state estimation, inexact model and soft constraints, or a general optimization-based controller where the underlying problem is solved with a fixed number of iterations of a first-order method are all amenable to the proposed approach.The approach is based on the observation that the control input generated by an optimization-based controller satisfies the associated Karush–Kuhn–Tucker (KKT) conditions which, provided all data is polynomial, are a system of polynomial equalities and inequalities. The closed-loop properties can then be analyzed using sum-of-squares (SOS) programming.

Output feedback MPC with send-on-delta measurements for uncertain systems

Abstract: In many applications, it is desired to reduce the communications between sensors and the controller for example to reduce the network load or to improve battery lifetime. We present an output feedback model predictive control approach for uncertain systems subject to measurement noise that utilizes the event driven-so called send-on-delta strategy Based on the change of the measurement, the sensor decides, if it sends data to the controller. The controller combines a linear state estimator with a predictive control law. It employs an online approach to improve the error bounds and thus the control performance. Conditions that guarantee closed loop properties are presented. We illustrate the results by an example.

Separated Design of Encoder and Controller for Networked Linear Quadratic Optimal Control

For a networked control system, we consider the problem of encoder and controller design. We study a discrete-time linear plant with a finite horizon performance cost, comprising a quadratic function of the states and controls, and an additive communication cost. We study separation in design of the encoder and controller, along with related closed-loop properties such as the dual effect and certainty equivalence. The encoder outputs are quantized samples, but our results also apply to two other formats for encoder outputs: real-valued samples at event-triggered times, and real-valued samples over additive noise channels. If the controller and encoder are dynamic, then we show that the performance cost is minimized by a separated design: the controls are updated at each time instant as per a certainty equivalence law, and the encoder is chosen to minimize an aggregate quadratic distortion of the estimation error. This separation is shown to hold even though a dual effect is present in the closed-loop syst...