Model Reference Approach Research Articles

Optimal Controller Identification for multivariable non-minimum phase systems

This work deals with data-driven control for non-minimum phase (NMP) systems, where the goal is to design a controller for a plant whose model is unknown by using a batch of input–output data collected from it. The approach is based on the Model Reference paradigm, where a transfer function matrix – the reference model – is used to specify the desired closed-loop performance. The NMP systems issue in Model Reference approaches is a well-known problem in control literature and it is no different in data-driven methods. This work explains how to adapt the formulation of the Optimal Controller Identification (OCI) method to cope with this class of systems. Considering a convenient parametrization of the reference model and a flexible performance criterion, it is possible to identify the NMP transmission zeros of the plant along with the optimal controller parameters, as it will be shown. Both diagonal and block-triangular reference model structures are treated in detail. Simulation examples show the effectiveness of the proposed approach.

Adaptive velocity control of an autonomous vehicle using input-error model reference approach

The input error model reference adaptive control (IE-MRAC) is employed to regulate the longitudinal velocity of an autonomous vehicle to desired values by controlling both the throttle and the braking system. The proposed method deals with matching the unknown longitudinal model of the vehicle with a predefined model in the presence of various disturbances, including road conditions and aerodynamic effects. Moreover, it is shown that the saturation on the throttle and the brake pedals are successfully handled due to the properties of the derived error equation. Besides analyzing the natural properties of IE-MRAC, a novel stability proof of the closed-loop system is presented, and a robust modification of the adaptive control law is given as well. By using the proposed control technique, higher-order tracking is captured, and the effects on enhancing the vehicle responses are investigated. The applicability of the presented theoretical results is validated via the CarSim simulator.

A New Adaptive Controller for Linear Systems: A Model Reference Approach

In this paper, a finite-time model reference adaptive controller is proposed to solve the tracking problem for a class of linear time-invariant systems with parameter uncertainties. The convergence to zero in a finite time for the tracking and parameter identification errors is ensured. The convergence proofs are developed based on Lyapunov function approach. Finally, some simulation results show the feasibility of the proposed approach.

Model reference strategy for mismatched disturbance attenuation in relative degree one and two DSMC

In this paper we propose a new model reference approach to reaching law based sliding mode control of discrete-time systems. The new approach significantly improves performance of the controlled plant by eliminating the persistent effect of past uncertainties on its sliding motion. It involves obtaining a desired state trajectory with the use of a reference model of the system and the reaching law approach, and then driving the state of the original plant alongside that trajectory. As a result, sliding motion of the system is not distorted by past uncertainties, and state trajectory more precisely follows the desired one. Furthermore, the proposed model reference approach allows one to apply strategies with arbitrary relative degree sliding variables to the reference model and successfully carry over the properties of these strategies to the original plant, even in the presence of non-matched uncertainties. This is an important advantage since such strategies without the reference model, despite their robustness with respect to matched disturbance, cannot typically be used when matching conditions are not satisfied. In particular, we have considered two reaching laws for the proposed model reference scheme, using relative degree one and two sliding variables, respectively. In both cases we have shown that system sliding motion is only affected by the single most recent disturbance, which results in increased robustness of the plant when compared to traditional reaching law approach.

Model Reference DSMC With a Relative Degree Two Switching Variable

Reaching-law-based discrete sliding mode controllers are well known to be easy to tune and robust with respect to disturbance. In recent years, it has been demonstrated that their robustness can be further enhanced with the use of arbitrary relative degree sliding variables. However, reaching laws using such variables only ensure a good sliding mode performance of the system when the perturbations affecting the plant are matched, which is a very restrictive assumption. To address this issue and to further improve robustness of the plant, in this article, we propose a new model reference approach for strategies with relative degree two sliding variables. In the proposed approach, the reaching law is first used to control the evolution of a disturbance-free model of the plant, and then, the original system state is driven toward that of the model with a secondary controller. It will be shown that the proposed approach ensures better system robustness compared to the conventional reaching law approach and that it does not require the assumption about matched uncertainties.

Optimal Nonlinear Model Reference Controller Design for Ball and Plate System

This paper presents a new design procedure of an optimal nonlinear controller using the model reference approach. The ball and plate system is used as nonlinear, uncertain, and MIMO system to verify the effectiveness of the proposed controller. The main goal of the proposed design is to assure a desirable performance despite the presence of the coupling among control loops and uncertainty. The invasive weed optimization (IWO) method, which is one of the metaheuristic optimization algorithms, is used to obtain the optimal parameters of the proposed controller. The feasibility and efficiency of the proposed nonlinear controller are illustrated experimentally using real ball and plate system.

Active Damping: An <inline-formula> <tex-math notation="LaTeX">$\mathcal {H}_\infty$</tex-math> </inline-formula> Model Reference Approach

This paper focuses on the design of an active-damping controller that shapes the dynamics of an LCL grid connected voltage source converter (VSC) to mimic an L -filter connected VSC. This makes possible to use simpler classical proportional plus resonant or proportional plus integral controllers design methods to regulate the grid current with minimum penalties in both performance and stability margins. The active-damping design follows a model-reference approach and is synthesized through a (sub)optimal $\mathcal {H}_\infty$ algorithm. The controller uses the grid current and point of common coupling voltage, although it allows the selection of a different set of measurements. Effectiveness of the method is demonstrated with time- and frequency-domain experimental results.

Adaptive synchronization of unknown heterogeneous agents: An adaptive virtual model reference approach

This work deals with state synchronization of heterogeneous linear agents with unknown dynamics. The problem is solved by formulating the synchronization problem as a special model reference adaptive control where each agent tries to converge to the model defined by its neighbors. For those agents that do not know the reference signal that drives the flock, a fictitious reference is estimated in place of the actual one: the estimation of such reference is distributed and requires measurements from neighbors. By using a matching condition assumption, which is imposed so that the agents can converge to the same behavior, the fictitious reference estimation leads to adaptive laws for the feedback and the coupling gains arising from distributed matching conditions. In addition, the coupling connection is not scalar as in most literature, but possibly vector-valued. The proposed approach is applicable to heterogeneous agents with arbitrarily large matched uncertainties. A Lyapunov-based approach is derived to show analytically asymptotic convergence of the synchronization error: robustification in the presence of bounded errors or unknown (constant) leader input is also discussed. Finally, a motivational example is presented in the context of Cooperative Adaptive Cruise Control and numerical examples are provided to demonstrate the effectiveness of the proposed method.

Containment Control of Heterogeneous Systems With Non-Autonomous Leaders: A Distributed Optimal Model Reference Approach

This paper presents a distributed optimal model reference adaptive control approach for solving containment control of heterogeneous multi-agent systems (MASs) with non-autonomous leaders. First, a fully distributed adaptive observer is designed to provide for each agent the desired reference trajectory by estimating the convex hull spanned by leaders. The distributed observer dynamics serves as a reference model for each follower to synchronize. The global communication graph information or the leader dynamics is not required to design the observer. In contrast to existing model reference adaptive controllers (MRAC) for single-agent systems and containment control solutions for MASs, the proposed MRAC approach imposes optimality and presents a distributed adaptive optimal solution to the containment control problem. To impose optimality, a performance function is defined based on the adaptive observers’ states as well as the followers’ local measurements. It is shown that considering non-autonomous leaders in this optimal control problem leads to solving inhomogeneous algebraic Riccati equations (AREs), instead of normal AREs in standard optimal control problems. To obviate the requirement of knowing the agents’ dynamics, an off-policy reinforcement learning approach implemented on an actor-critic structure is utilized for solving the inhomogeneous ARE. A simulation example is conducted to illustrate the effectiveness of the presented method.

The Scaled SLW model of gas radiation in non-uniform media based on Planck-weighted moments of gas absorption cross-section

The Scaled SLW model for prediction of radiation transfer in non-uniform gaseous media is presented. The paper considers a new approach for construction of a Scaled SLW model. In order to maintain the SLW method as a simple and computationally efficient engineering method special attention is paid to explicit non-iterative methods of calculation of the scaling coefficient. The moments of gas absorption cross-section weighted by the Planck blackbody emissive power (in particular, the first moment – Planck mean, and first inverse moment – Rosseland mean) are used as the total characteristics of the absorption spectrum to be preserved by scaling. Generalized SLW modelling using these moments including both discrete gray gases and the continuous formulation is presented. Application of line-by-line look-up table for corresponding ALBDF and inverse ALBDF distribution functions (such that no solution of implicit equations is needed) ensures that the method is flexible and efficient. Predictions for radiative transfer using the Scaled SLW model are compared to line-by-line benchmark solutions, and predictions using the Rank Correlated SLW model and SLW Reference Approach. Conclusions and recommendations regarding application of the Scaled SLW model are made.

3D cooperative control of tower cranes using robust adaptive techniques

An adaptive robust controller that simultaneously rotates the tower and moves the trolley is proposed for a tower crane. The robust behavior of the controller is derived through the sliding mode technique, and its adaptive performance is obtained based on the adaptive model-reference approach. The controller operated well regardless of the significant variation of system parameters, internal noises, and external disturbances. Specifically, the controller did not require a priori knowledge of cargo mass and friction factors because an adaptation mechanism is integrated to estimate system parameters. Emulating experimental results showed that the proposed controller consistently stabilized all system responses.

Dual-Band Digital Predistortion Using a Single Transmitter Observation Receiver and Single Training Engine

This paper tackles the hardware complexity of a digital predistortion (DPD) system used to linearize a power amplifier (PA) driven with interband carrier aggregated (CA) signals (i.e., two component carriers with different modulation bandwidths and wide frequency separations). It focuses particularly on reducing the required bandwidth, and number of channels, of the transmitter's observation receiver (TOR) as well as the specifications of the underlying building blocks (e.g., speed of the analog-to-digital converter). A novel dualband DPD system using a single TOR was devised. The training of the DPD for each band was carried out in an alternating fashion, using a single training engine following a model-reference adaptive control approach with a recursive least squares algorithm. The proposed approach was experimentally validated by successfully linearizing a 20-W Class F Doherty PA driven with different multistandard CA signals.

Robust voltage‐mode controller for DC–DC boost converter

In this study, a robust voltage-mode controller for DC–DC boost converter subject to time varying parameters is presented. The time-varying parameters of the boost converter are considered as the input voltage, the load resistance and the passive components (inductor and capacitor). The proposed controller, designed in discrete time, is based on the sliding mode control combined with the model-reference approach. In addition to this controller structure, the system dynamics are augmented by integral action to ensure zero steady-state tracking error. Experimental results, obtained from prototype operating at the fixed frequency, are provided to demonstrate the excellent robustness of the designed controller against wide input voltage variations and large load transients and also variation in passive components.

Design and implementation of adaptive PI control schemes for web tension control in roll-to-roll (R2R) manufacturing

In this paper, two adaptive Proportional-Integral (PI) control schemes are designed and discussed for control of web tension in Roll-to-Roll (R2R) manufacturing systems. R2R systems are used to transport continuous materials (called webs) on rollers from the unwind roll to the rewind roll. Maintaining web tension at the desired value is critical to many R2R processes such as printing, coating, lamination, etc. Existing fixed gain PI tension control schemes currently used in industrial practice require extensive tuning and do not provide the desired performance for changing operating conditions and material properties. The first adaptive PI scheme utilizes the model reference approach where the controller gains are estimated based on matching of the actual closed-loop tension control systems with an appropriately chosen reference model. The second adaptive PI scheme utilizes the indirect adaptive control approach together with relay feedback technique to automatically initialize the adaptive PI gains. These adaptive tension control schemes can be implemented on any R2R manufacturing system. The key features of the two adaptive schemes is that their designs are simple for practicing engineers, easy to implement in real-time, and automate the tuning process. Extensive experiments are conducted on a large experimental R2R machine which mimics many features of an industrial R2R machine. These experiments include trials with two different polymer webs and a variety of operating conditions. Implementation guidelines are provided for both adaptive schemes. Experimental results comparing the two adaptive schemes and a fixed gain PI tension control scheme used in industrial practice are provided and discussed.

Robotic hand posture and compliant grasping control using operational space and integral sliding mode control

SUMMARYThis paper establishes a novel approach of robotic hand posture and grasping control. For this purpose, the control uses the operational space approach. This permits the consideration of the shape of the object to be grasped. Thus, the control is split into a task control and a particular optimizing posture control. The task controller employs Cylindrical and Spherical coordinate systems due to their simplicity and geometric suitability. This is achieved by using an integral sliding mode controller (ISMC) as task controller. The ISMC allows us to introduce a model reference approach where a virtual mass-spring-damper system can be used to design a compliant trajectory tracking controller. The optimizing posture controller together with the task controller creates a simple approach to obtain pre-grasping/object approach hand postures. The experimental results show that target trajectories can be easily followed by the task control despite the presence of friction and stiction. When the object is grasped, the compliant control will automatically adjust to a specific compliance level due to an augmented compliance parameter adjustment algorithm. Once a specific compliance model has been achieved, the fixed compliance controller can be tested for a specific object grasp scenario. The experimental results prove that the Bristol Elumotion robot hand (BERUL) can automatically and successfully attain different compliance levels for a particular object via the ISMC.

Neural network-based motion control of an underactuated wheeled inverted pendulum model.

In this paper, automatic motion control is investigated for one of wheeled inverted pendulum (WIP) models, which have been widely applied for modeling of a large range of two wheeled modern vehicles. First, the underactuated WIP model is decomposed into a fully actuated second order subsystem Σa consisting of planar movement of vehicle forward and yaw angular motions, and a nonactuated first order subsystem Σb of pendulum motion. Due to the unknown dynamics of subsystem Σa and the universal approximation ability of neural network (NN), an adaptive NN scheme has been employed for motion control of subsystem Σa . The model reference approach has been used whereas the reference model is optimized by the finite time linear quadratic regulation technique. The pendulum motion in the passive subsystem Σb is indirectly controlled using the dynamic coupling with planar forward motion of subsystem Σa , such that satisfactory tracking of a set pendulum tilt angle can be guaranteed. Rigours theoretic analysis has been established, and simulation studies have been performed to demonstrate the developed method.

An Output-Tracking-Based Discrete PID-Sliding Mode Control for MIMO Systems

Due to its ability to reject disturbance, sliding mode control (SMC) has been widely employed in various control applications with the presence of uncertainty and/or disturbance. However, chattering, caused by the switching function used in SMC, can greatly deteriorate its performance, and thus, limit its applications. In addition to chattering, the application of SMC to a multi-input–multi-output (MIMO) system becomes more challenging due to the coupling effects between the control variables. This paper presents the development of an output-tracking-based discrete proportional-integral-derivative SMC (PID-SMC) for MIMO systems, in which the problem of output tracking is defined to the one of state tracking by using the model reference approach. The developed control scheme allows for both achieving the zero steady-state error and eliminating the chattering problem. For validation, experiments were performed on a commercially available three degrees-of-freedom nanopositioning stage with the developed control scheme, as compared to a traditional PID controller. Experimental results illustrate that with the developed control scheme, the positioning performance of the stage can be significantly improved, including the zero steady-state error and eliminated chattering.

A Model-Reference Sliding Mode for Dual-Stage Actuator Servo Control in HDD

This paper presents a method of sliding mode control (SMC) designing and developing for the servo system in a dual-stage actuator (DSA) hard disk drive. Mathematical model of hard disk drive actuators is obtained, extracted from measuring frequency response of the voice-coil motor (VCM) and micro-actuator separately. The Matlab software tools are used for mathematical model estimation and also for controller design and simulation. A model-reference approach for tracking requirement is selected as a proposed technique. The simulation results show that performance of the model-reference SMC controller in DSA servo control can be satisfied in the tracking error, as well as keeping the positioning of the head within the boundary of +/-5% of track width under the presence of disturbance. The overall results of model-reference SMC design in DSA are met per requirement specifications and significant reduction in %off track is found when compared to the single-state actuator (SSA).

Finite-time consensus for multi-agent systems via terminal feedback iterative learning

This study is devoted to the finite-time consensus problem of multi-agent systems with higher-order dynamics, and presents a framework for effectively constructing distributed protocols which incorporate iterative learning control actions into output feedbacks. Using a terminal updating law, the feedback iterative learning protocols are shown with the ability to enable all agents to achieve the consensus at a finite time that can be prescribed. Furthermore, a model reference approach is employed to improve the feedback iterative learning protocols such that all agents can be guaranteed to achieve the consensus at any given desired terminal output. In both cases, necessary and sufficient conditions are provided which can also offer design criteria for the learning gains to ensure consensus. Simulation results are included to verify the effectiveness of the proposed theoretical results.

Discrete-time minimal control synthesis adaptive algorithm

This article proposes a discrete-time Minimal Control Synthesis (MCS) algorithm for a class of single-input single-output discrete-time systems written in controllable canonical form. As it happens with the continuous-time MCS strategy, the algorithm arises from the family of hyperstability-based discrete-time model reference adaptive controllers introduced in (Landau, Y. (1979), Adaptive Control: The Model Reference Approach, New York: Marcel Dekker, Inc.) and is able to ensure tracking of the states of a given reference model with minimal knowledge about the plant. The control design shows robustness to parameter uncertainties, slow parameter variation and matched disturbances. Furthermore, it is proved that the proposed discrete-time MCS algorithm can be used to control discretised continuous-time plants with the same performance features. Contrary to previous discrete-time implementations of the continuous-time MCS algorithm, here a formal proof of asymptotic stability is given for generic n-dimensional plants in controllable canonical form. The theoretical approach is validated by means of simulation results.