Discrete Time Multivariable Adaptive Control for Non-Minimum Phase Plants with Unknown Dead Time

Robust Adaptive Control

Stable Discrete Time Multivariable Adaptive Control in the Presence of Unmodeled Dynamics

SummaryAt the present time, there is a great deal of interest in the adaptive control of systems with rapidly varying parameters. Such problems arise in different forms and in many disciplines including finance, sociology, biology, and engineering. In general, these problems are intractable mathematically and the time variations have to be classified in some form to obtain rigorous results. In this paper, we consider the adaptive identification and control of linear systems with periodically varying parameters (referred to as linear time‐varying periodic (LTP) systems). The class of systems with known periodic parameters has been investigated widely since the pioneering work of Floquet and lends itself to rigorous mathematical analysis. However, very little was known until the early years of the last decade concerning the adaptive control of such systems. The problem was introduced by Xu and explored in detail by Narendra and Zhiling in 2006 and 2009, respectively. In 2012, a new method was introduced in adaptive control by Han and Narendra and is referred to as second‐level adaptation. In this paper, the adaptive identification and control of LTP systems using second‐level adaptation is discussed.

Model Reference Adaptive Control (MRAC) of a wide repertoire of stable Linear Time Invariant (LTI) systems is addressed here. Even an upper bound on the order of the finite-dimensional system is unavailable. Further, the unknown plant is permitted to have both minimum phase and nonminimum phase zeros. Model following with reference to a completely specified reference model excited by a class of piecewise continuous bounded signals is the goal. The problem is approached by taking recourse to the time moments representation of an LTI system. The treatment here is confined to Single-Input Single-Output (SISO) systems. The adaptive controller is built upon an on-line scheme for time moment estimation of a system given no more than its input and output. As a first step, a cascade compensator is devised. The primary contribution lies in developing a unified framework to eventually address with more finesse the problem of adaptive control of a large family of plants allowed to be minimum or nonminimum phase. Thus, the scheme presented in this paper is confined to lay the basis for more refined compensators--cascade, feedback and both--initially for SISO systems and progressively for Multi-Input Multi-Output (MIMO) systems. Simulations are presented.

This study explores the integration of the adaptive control approach with the Model Reference Adaptive Control (MRAC) method, with a view to examining the impact of this integration on the performance of dynamic systems. Adaptive control is highlighted as a versatile and robust methodology that enables systems to cope with uncertainties and adapt to rapidly changing conditions in their operating environments. As a branch of adaptive control, the MRAC method focuses on efficiently achieving desired performance objectives by adjusting system parameters based on a predefined reference model. The primary focus is on investigating how these methods can be applied to optimize the functionality of systems characterized by dynamic and variable nature, such as unmanned aerial vehicles. By addressing challenges related to uncertainties, disturbances, and adaptability, the integration of adaptive control with the MRAC method demonstrates significant potential in improving the robustness, responsiveness, and reliability of such systems. This research investigates the performance of adaptive techniques in enhancing the capabilities of modern control systems. The objective of the research is to assess the effectiveness of MRAC in terms of reference signal tracking. Simulation results demonstrate the ability of MRAC to maintain accurate tracking of the desired reference for key vehicle dynamics, including roll, pitch and yaw. The results demonstrate the robustness of the MRAC algorithm in attitude control, which may lead to support for sustainability issues such as energy consumption.

Adaptive traffic control systems continuously monitor traffic conditions on an arterial and adjust traffic signal timings to accommodate variation in traffic volume and minimize stops and delays. This paper describes currently practical adaptive control systems which have been used in the United States and worldwide, which include Adaptive Control System-Lite (ACS-Lite), Optimization Policies for Adaptive Control (OPAC), Real-Time Hierarchical Optimized Distributed and Effective System (RHODES), Sydney Coordinated Adaptive Traffic System (SCATS) and Split Cycle Offset Optimization (SCOOT). The comparisons of the benefits from past experiences, cost and hardware requirements will help the traffic engineers and decision makers a guideline to select the optimized adaptive control system based on research objectives.

SummaryIn this study, we present a reinforcement learning (RL)‐based flight control system design method to improve the transient response performance of a closed‐loop reference model (CRM) adaptive control system. The methodology, known as RL‐CRM, relies on the generation of a dynamic adaption strategy by implementing RL on the variable factor in the feedback path gain matrix of the reference model. An actor‐critic RL agent is designed using the performance‐driven reward functions and tracking error observations from the environment. In the training phase, a deep deterministic policy gradient algorithm is utilized to learn the time‐varying adaptation strategy of the design parameter in the reference model feedback gain matrix. The proposed control structure provides the possibility to learn numerous adaptation strategies across a wide range of flight and vehicle conditions instead of being driven by high‐fidelity simulators or flight testing and real flight operations. The performance of the proposed system was evaluated on an identified and verified mathematical model of an agile quadrotor platform. Monte‐Carlo simulations and worst case analysis were also performed over a benchmark helicopter example model. In comparison to the classical model reference adaptive control and CRM‐adaptive control system designs, the proposed RL‐CRM adaptive flight control system design improves the transient response performance on all associated metrics and provides the capability to operate over a wide range of parametric uncertainties.

In this research, the positioning control of a water hydraulic servo cylinder system with the simple adaptive control (SAC) is discussed. Conventional model reference adaptive control (MRAC) also achieves good tracking performance for cylinder control, but the controller structure is much more complicated and has less robustness for disturbance in real application. Compared with MRAC, SAC has simpler and lower order structure, i.e. higher feasibility. In this paper, we examined and evaluated the control performance of SAC on a water hydraulic servo cylinder system. With the recent increased concerns over global environmental problems, the water hydraulic technique using pure tap water as a pressure medium has become a new drive source comparable to electric, oil hydraulic and pneumatic drive systems. This technique is also preferred due to its high power density, high safety against fire hazard in production plants, and easy availability. However, the main problems for precise control in a water hydraulic system are steady state errors and overshoot due to its large friction torque and considerable leakage flow. To compensate these effects, MRAC had been already applied and the better control performances were obtained. However, no result has been reported on SAC application for water hydraulics. To make clear the merits of SAC, tracking control performance and robustness were discussed via experimental results. It was confirmed that SAC gives (1) better tracking performance compared with PI control, and (2) comparable control precision with MRAC within 70 micrometers to the reference position and higher robustness for parameter change despite simple controller. These results ensure wider application of simple adaptive control in real mechanical system.

An Adaptive Feedforward Control Algorithm for Computer Control of Wastewater Neutralization

This paper presents a new on-line procedure for identifying MIMO time-varying stochastic dynamic systems. It is based on a decomposition model derived from the state-space representation. This scheme gives an estimated model with a minimal number of parameters. The parameters of the MIMO system are identified from short records with unknown dead times. Extended recursive least-squares and fixed-lag smoothing identification algorithms are applied to identify the validity of the model structure. Artificial and hydrological records are used to illustrate the efficiency of the proposed procedure.

Important class of adaptive control systems with non-stochastic description of the uncertainty and disturbances is considered. New approach to the design of the non-stochastic adaptive dual control algorithms is suggested. The elaborated approach is based on the introducing of two new cost functions for optimisation of the control signal and exiting signal added to the control signal. The ellipsoid bounded estimation of the plant parameters is used for the plant parameter estimation and indirect adaptation. This estimation method was also named set-membership estimation. The approach is introduced and described comprehensive using simple controller of self-tuning type. The designed controller, which is used as an example to demonstrate the new suggested method, can be applied to control of nonminimumphase plants. The method can be extended to adaptive controllers of various other types. The violent contrast is attributed to the suggested design method as compared with other dual control approaches for non-stochastic systems with set-membership estimation. The method allows designing of non-stochastic dual adaptive controllers that are very simple computational and consist of the cautious controller with the optimal excitations. Non-stochastic adaptive dual controllers, which are designed using suggested approach, have superiorities over the similar controllers based on the certainty equivalence approach because of the properties of caution and optimal excitation.

Properties and control of the quadruple-tank process with multivariable dead-times

This paper presents the analysis of two control methods used to increase the kinematic performance of two-axle bogie when the rail vehicle travels on curved track with constant speed. A holistic model for the bogie and wheelsets is developed using the multibody system approach. The mathematical model is implemented in MATLAB environment using Simulink toolbox. Then the bogie model is included in a closed loop and PID controller tuning is performed using Control Systems toolbox from MATLAB environment. The simulated values for lateral and yaw angular displacement of wheelsets are compared with those obtained by applying the Model Reference Adaptive Control (MRAC) method. The results of the sensitivity analysis for rise time, peak overshoot and settling time with respect to travel speed for rail vehicle show that MRAC method improves the time domain closed-loop performance. The proposed MRAC method applied to the bogie system within the rail vehicle multibody model represents an important contribution to the development of rail transportation systems where rolling stock is equipped with motion control systems with superior efficiency and reduced energy consumption.

This paper is concerned with a new discrete-time adaptive control scheme for pneumatic servo systems. In order to reduce the number of unknown parameters, a nonminimum phase discrete-time model of the control object is used to construct the proposed adaptive control system. Since the usual model reference adaptive control scheme cannot be applied to nonminimum phase plants, we propose a quasi-model-reference adaptive control system which includes an adaptive precompensator. The asymptotical stability of the control system is proven under a certain condition. The validity of the control system is confirmed experimentally.

An algorithm for providing adaptive control and dead time compensation of single input-single output systems with unknown or varying dead time is presented. The algorithm is designed by pole-zero placement and is unique in that an explicit estimate of the dead time is not required, thus avoiding a difficult estimation problem. Parameter estimation for the adaptive controller/dead time compensator is performed with a recursive least squares algorithm. Simulation studies and experimental application on a heat exchange loop on a pilot scale distillation column verify the performance of the algorithm. In each example, the performance of the adaptive controller/dead time compensator is compared to that of a proportional plus integral controller, illustrating the improvement in performance obtainable with the adaptive algortihm.