Adaptive Pole Placement Control Research Articles

Retrospective‐cost‐based model reference adaptive control of nonminimum‐phase systems

AbstractThis paper presents a novel approach to model reference adaptive control inspired by the adaptive pole‐placement controller (APPC) of Elliot and based on retrospective cost optimization. Retrospective cost model reference adaptive control (RC‐MRAC) is applicable to nonminimum‐phase (NMP) systems assuming that the NMP zeros are known. Under this assumption, the advantage of RC‐MRAC is a reduced need for persistency. The present paper compares APPC and RC‐MRAC under various levels of persistency in the command for minimum‐phase and NMP systems. It is shown numerically that the model‐following performance of RC‐MRAC is less sensitive to the persistency of the command compared to APPC at the cost of knowledge of the NMP zeros. RC‐MRAC is also shown to be applicable for disturbance rejection under unknown harmonic disturbances.

Robust consensus of unknown heterogeneous non‐minimum phase multi‐agent systems with unmodeled dynamics and disturbances

SummaryIn this paper, the robust leader‐following output consensus problem is addressed for unknown heterogeneous non‐minimum phase linear multi‐agent systems with unmodeled dynamics and external disturbances under directed graphs. The system matrix of the leader and the parameters of the nominal dynamics of the followers are assumed to be unknown. A novel distributed robust adaptive pole placement control scheme consisting of an adaptive distributed observer and a robust adaptive pole placement controller is developed. It is shown that the robust leader‐following output consensus problem of the concerned multi‐agent system can be solved by the proposed distributed robust adaptive control scheme under some sufficient conditions. It is also shown that the exact output consensus can be achieved if the unmodeled dynamics and external disturbances vanish as time goes to infinity. Two examples are used to demonstrate the effectiveness of the proposed control approach.

Adaptive Two-Degrees-of-Freedom Current Control for Solenoids: Theoretical Investigation and Practical Application

In this article, an adaptive two-degrees-of-freedom current control algorithm for solenoids is presented comprising an adaptive pole placement controller in combination with a regularized least-squares parameter estimation law. An additional adaptive feedforward controller takes advantage of the estimated plant parameters to further enhance the tracking performance. The stability of the overall closed-loop system is rigorously proven. The proposed solution differs from existing approaches by the adaptive feedforward controller and the way the parameter estimation is performed. The control concept is applied with the same controller parametrization to three solenoids from different applications, with substantially differing parameters. The experimental results show high tracking performance and fast parameter convergence even with poor initial estimates and despite the nonlinear dependence of the inductance on the current and position. The experimental results are also compared to two benchmark control design paradigms known from the literature, i.e. a second-order sliding mode controller and a nonlinear model reference adaptive control solution, which are both outperformed by the proposed controller.

Distributed Adaptive Output Consensus of Unknown Heterogeneous Non-Minimum Phase Multi-Agent Systems

This article addresses the leader-following output consensus problem of heterogeneous linear multi-agent systems with unknown agent parameters under directed graphs. The dynamics of followers are allowed to be non-minimum phase with unknown arbitrary individual relative degrees. This is contrary to many existing works on distributed adaptive control schemes where agent dynamics are required to be minimum phase and often of the same relative degree. A distributed adaptive pole placement control scheme is developed, which consists of a distributed observer and an adaptive pole placement control law. It is shown that under the proposed distributed adaptive control scheme, all signals in the closed-loop system are bounded and the outputs of all the followers track the output of the leader asymptotically. The effectiveness of the proposed scheme is demonstrated by one practical example and one numerical example.

Exponentially Convergent Direct Adaptive Pole Placement Control of Plants With Unmatched Uncertainty Under FE Condition

A new method of direct adaptive pole placement control (APPC) is developed for plants with unmatched uncertainty, which linearly depends on a state vector. It guarantees the exponential stability of a control system and exponential convergence of control law adjustable parameters to their true values when the regressor is finitely exciting. Considering the known classical APPC schemes and adaptive methods with exponential regulation, the advantages of the proposed one are that it does not require a priori information on a control input matrix and ensures the monotonic transient behavior of each adjustable parameter of the control law. The theoretical results are supported by the numerical experiments.

Parameter estimation and control of an unmanned aircraft‐based transportation system for variable‐mass payloads

AbstractThis paper deals with the development of an adaptive robust controller for an Unmanned Aircraft System with variable mass. The goal is to improve trajectory tracking and energy performance while the aircraft mass is gradually reducing due to payload release. To improve the trajectory tracking performance, we propose an algorithm that merges the concepts of least squares method and sliding mode observer for the estimation of the vehicle mass. The nonlinear observer estimates the linear velocities and accelerations, which are further used to obtain the vehicle mass. A robust adaptive pole placement controller based on the Attractive Ellipsoid Method uses this estimation to update the controllers gains due to the mass variation. To validate the effectiveness of the proposed algorithm for performing aerial transportation and deployment of payloads, we present a numerical example comparing the performance of the proposed method with respect to using Proportional Derivative controllers as well as Robust Controllers.

Robust Adaptive Control of a Quadruple Tank Process with Sliding Mode and Pole Placement Control Strategies

Many industrial processes have challenging issues such as complex nonlinear nature, high sensitivity to disturbances and existence of parametric uncertainties. A Quadruple Tank Process (QTP) is used in the laboratory as a scaled representation of many industrial processes involving liquid level control problems. Conventional controllers are relatively slow in tracking the reference inputs and in reacting to disturbances, and they tend to lack the ability in dealing with parametric changes in the QTP. The aim of this paper is to design and test an Adaptive Pole Placement Controller (APPC) and a robust Adaptive Sliding Mode Controller (ASMC) with the purpose of high-efficacy control of a minimum phase QTP. The controllers are tested via simulations and performance indices resulting from the simulation of these controllers are compared with a PID controller in terms of the three cases of robustness to set point variations, rejection of disturbance inputs, and robustness to parametric uncertainties. Simulation results reveal that the proposed adaptive control configurations perform better than the PID controller with lower performance indices and faster settling times due to the paramater estimation method used in the design processes. ASMC outperforms APPC in different variations of inputs and in regulation performances due to the invariant nature of the Sliding Mode Control (SMC). The results show that a decentralized ASMC can be used to improve the rapidity and robustness of many multivariable industrial process control systems.

Adaptive control designs for control-based continuation in a class of uncertain discrete-time dynamical systems

This article proposes a methodology for integrating adaptive control with the control-based continuation paradigm for a class of uncertain, linear, discrete-time systems. The proposed adaptive control strategies aim to stabilize the closed-loop dynamics with convergence toward a known reference input, such that the dynamics approach the open-loop fixed point if the reference input is chosen to make the steady-state control input equal 0. This enables the tracking of a parameterized branch of open-loop fixed points using methods of numerical continuation without specific knowledge about the system. We implement two different adaptive control strategies: model-reference adaptive control and pole-placement adaptive control. Both implementations achieve the desired objectives for the closed-loop dynamics and support parameter continuation. These properties, as well as the boundedness of system states and control inputs, are guaranteed provided that certain stability conditions are satisfied. Besides, the tuning effort is significantly reduced in the adaptive control schemes compared with traditional proportional–derivative controllers and linear state-space feedback controllers.

Semi-Adaptive Closed-Loop Control for Infusion of Medications With Transport Delay in Clinical Effects

Abstract This paper presents a semi-adaptive closed-loop control approach to autonomous infusion of medications exhibiting significant transport delay in clinical effects. The basic idea of the approach is to enable stable adaptive control of medication infusion by (1) incorporating transport delay explicitly into control design by way of a Padé approximation while (2) facilitating linear parameterization of control design model by desensitization of nonlinearly parameterized cooperativity constant associated with pharmacodynamics (PD). A novel dynamic dose–response model for control design is presented, in which the cooperativity constant exerts zero influence on the model output in the steady-state. Then, an adaptive pole placement control (APPC) technique was employed to fulfill adaptive control design in the presence of nonminimum phase dynamics associated with the Padé approximation of transport delay. The controller was evaluated in silico using a case study of regulating a cardiovascular variable with a sedative under a wide range of transport delay and pharmacological profiles. The results suggest that adaptation of transport delay and pharmacological characteristics may be beneficial in achieving consistent and robust regulation of medication-elicited clinical effects.

Comparative Controlling of the Lorenz Chaotic System Using the SMC and APP Methods

The Lorenz chaotic system is based on a nonlinear behavior and this causes the system to be unstable. Therefore, two different controller models were developed and named as the adaptive pole placement and sliding mode control (SMC) methods for the establishment of continuous time nonlinear Lorenz chaotic system. In order to achieve this, an improved controller structure was developed first theoretically for both the controller methods and then tested practically using the numerical samples. During the establishment of adaptive pole placement method for the Lorenz chaotic system, various stages were applied. The nonlinear chaotic system was also linearized by means of Taylor Series expansion processes. In addition, the feedback matrix of the adaptive pole placement method was determined using linear Jacobian matrix. The chaotic system reached an equilibrium point by using both the SMC and adaptive pole placement methods; however the simulation results of the SMC had better success than adaptive pole placement control technique.

Classical pole placement adaptive control revisited: linear-like convolution bounds and exponential stability

While the original classical parameter adaptive controllers do not handle noise or unmodelled dynamics well, redesigned versions have been proven to have some tolerance; however, exponential stabilization and a bounded gain on the noise are rarely proven. Here we consider a classical pole placement adaptive controller using the original projection algorithm rather than the commonly modified version; we impose the assumption that the plant parameters lie in a convex, compact set, although some progress has been made at weakening the convexity requirement. We demonstrate that the closed-loop system exhibits a very desirable property: there are linear-like convolution bounds on the closed-loop behaviour, which confers exponential stability and a bounded noise gain, and which can be leveraged to prove tolerance to unmodelled dynamics and plant parameter variation. We emphasize that there is no persistent excitation requirement of any sort; the improved performance arises from the vigilant nature of the parameter estimator.

Using Adaptive Pole Placement Control Strategy for Active Steering Safety System

Using Adaptive Pole Placement Control Strategy for Active Steering Safety System

Adaptive pole placement pitch angle control of a flapping-wing flying robot

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Observer backstepping control of DFIG-Generators for wind turbines variable-speed: FPGA-based implementation

In this paper, we present a new contribution for the control of Wind-turbine energy systems, a nonlinear robust control of active and reactive power by the use of the Adaptative Backstepping approach based in double-fed asynchronous generator (DFIG-Generator).Initially, a control strategy of the MPPT for extraction of maximum power of the turbine generator is presented. Thereafter, a new control technique for wind systems is presented. This control system is based on an adaptive pole placement control approach integrated to a Backstepping control system. The stability of the system is shown using Lyapunov technique. Using the FPGA to implement the order gives us a better rapidity. A Benchmark was realized by a prototyping platform based on DFIG-generator, FPGA and wind-turbine; the experimental results obtained show the effectiveness and the benefit of our contribution.

Active power control design for supporting grid frequency regulation in wind farms

Among renewable energy sources, wind power is expected to contribute a larger and rapidly growing portion of the world's energy portfolio. However, the increased penetration of wind power into the power grid has challenged the reliable and stable operation of the grid. This motivates new opportunities in the design and development of novel control schemes capable of actively maintaining the necessary balance between power generation and load, which in turn regulates the grid frequency when plenty of winds are available. This paper presents two active power control schemes that are developed based on adaptive pole placement control and fuzzy gain-scheduled proportional-integral control approaches. The active power control is conducted collectively across a wind farm to provide rapid power response while maintaining safe structural loading on turbines’ components. The proposed active power control schemes are evaluated and compared by a series of simulations on an advanced wind farm benchmark model in the presence of wind turbulences, measurement noises, and grid load variations. It is further demonstrated that the mentioned schemes are able to tolerate probable occurrence of sudden imbalance between generation and load due to relevant faults/failures in the wind farm or electric grid.

Multivariable adaptive control: A survey

Adaptive control is a control methodology capable of dealing with uncertain systems to ensure desired control performance. This paper provides an overview of some fundamental theoretical aspects and technical issues of multivariable adaptive control, and a thorough presentation of various adaptive control schemes for multi-input–multi-output systems, literature reviews on adaptive control foundations and multivariable adaptive control methods, and related technical problems. It covers some basic concepts and issues such as certainty equivalence, stability, tracking, robustness, and parameter convergence. It discusses some of the most important topics of adaptive control: plant uncertainty parametrization, stable controller adaptation, and design conditions for different adaptive control schemes. The paper also presents a detailed study of well-developed multivariable model reference adaptive control theory and design techniques. It provides an introduction to multivariable adaptive pole placement and adaptive nonlinear control, and it concludes by identifying some open research problems.

Backstepping Adaptive Control of DFIG-Generators for Variable-Speed Wind Turbines

In this paper, we present a nonlinear robust control of active and reactive power by the use of the technique Backstepping a double-fed asynchronous generator (DFIG) system incorporated in a wind. The power transfer between the stator and the network is carried out by acting on the rotor via a bidirectional signal converter.Initially, a control strategy of the MPPT asynchronous double fed generator is presented. Thereafter, a new control technique for wind systems is presented. This control scheme is based on an adaptive pole placement control strategy integrated to a Backstepping control scheme. The overall stability of the system is shown using Lyapunov technique. The performance and robustness are analyzed and compared by simulation based Matlab / Simulink software.

Design of a Pole Placement Active Power Control System for Supporting Grid Frequency Regulation and Fault Tolerance in Wind Farms

Among renewable energy sources, wind power is expected to contribute a larger and rapidly growing portion of the world's energy portfolio. However, the increased penetration of wind power into the power grid has challenged the reliable and stable operation of the grid. This motivates new opportunities in design and development of novel control schemes capable of actively maintaining the necessary balance between power generation and load, which in turn regulates the grid frequency when plenty of wind is available. This paper presents a novel Active Power Control (APC) strategy based on an adaptive pole placement control approach. The proposed APC strategy is evaluated by a series of simulations on an advanced wind farm benchmark model in the presence of wind turbulences and grid load variations. It is also demonstrated that the APC strategy is able to tolerate against probable occurrence of sudden changes in the generated power which can be caused by torque offset faults in generator/converter actuators of wind turbines in a wind farm.

Pole placement adaptive control with persistent jumps in the plant parameters

In this paper we consider the control objective of step tracking and pole placement in the context of significant plant uncertainty and occasional, but persistent, jumps in the plant parameters. Here we have a compact set of admissible single-input single-output, controllable and observable plant models of a fixed order. The controller incorporates an integrator, and its action emulates the behaviour of a pole placement state feedback compensator. We demonstrate that this controller has the facility to tolerate occasional (but persistent) switches between these models without an undue effect on the performance.

Adaptive pole placement control for vibration control of a smart cantilevered beam in thermal environment

Piezoelectric actuators used in vibration control and high precision control have been widely used in recent years. In aeronautics and MEMS systems especially, their applications are spread from vibration suppression to position control. In this paper, a finite element model (FEM) of a piezoelectric actuator and cantilever in a thermal environment is presented to suppress vibration effectively. In other words, the FEM is namely a thermal-electrical-mechanical coupled FEM. Based on an eight-node plane finite element, the harmonic analysis and the free vibration analysis have been obtained in the current work. Therefore a transfer function model will be attained through the harmonic analysis by an identification method. In addition, a controller is designed with the adaptive pole placement control (APPC). Finally, through simulation, the thermal influence is considerable for natural frequencies, harmonic response and free vibration. Moreover, the APPC is a significant plan to vibration control in the paper.