Robust Model Reference Adaptive Control in the Presence of Parasitics

Partial-state feedback multivariable MRAC and reduced-order designs

The precise position control for electro-hydraulic servo system (EHSS) is a key technical problem for modern industry control. This paper presents a model reference adaptive control (MRAC) strategy combining fractional order calculus theory and neural network to solve the high nonlinearity and parameter uncertainties in the EHSS. The reference model in the MRAC strategy is a fractional second-order model and the controller with adaptive law is designed by a Wiener recurrent neural network (WRNN). Simulations indicate the validity and superiority of the proposed fractional MRAC strategy.

Recently, a class of adaptive control schemes called L1 Adaptive Control (L1-AC) has been proposed and widely advertised in aerospace control for achieving fast and robust adaptation and better performance than the existing Model Reference Adaptive Control (MRAC) Schemes. The L1-AC scheme is designed mainly for plants with full state measurement even though the name L1-AC has been used as an umbrella name for more general classes of plants. In this paper, we show that the L1-AC for plants with measured states is simply a standard MRAC with a low pass filter inserted in front of the control input. The analysis of the scheme is almost identical to that of MRAC as the same Lyapunov function is used to establish stability. The motivation for using the filter is the fact that for this class of adaptive schemes i.e. MRAC for plants with full state measurement the tracking error can be made arbitrarily small during transient by increasing the adaptive gain. A high adaptive gain however makes the differential equation of the adaptive law or estimator very stiff and leads to numerical problems that cause high oscillations in the estimated parameters leading to loss of adaptivity and deviations from what the theoretical properties dictate. The L1-AC approach mistook these numerical oscillations as properties of the adaptive scheme and inserted an input low pass filter in order to filter them out. While the filter helps reduce the frequency of these oscillations in the control law the price paid is high. First the numerical instability does not go away and the estimated parameters continue to oscillate without converging to the true parameters even in the presence of sufficiently rich signals. Second, due to the filter the tracking error is no longer guaranteed to converge to zero and the transient bounds for the tracking error also depend on the filter. As a result, the tracking properties of the L1-AC scheme are worse than what a simple MRAC scheme can generate with adaptive gains that could be high but away from the region of numerical instability. In addition, the presence of the filter reduces the robust stability margins in the presence of unmodeled dynamics and provides literally no advantage as simple robust MRAC techniques can solve the same problem achieving much better properties. The authors of L1-AC often compare the properties of a numerically unstable MRAC due to extremely high adaptive gains something that is prohibited by robust adaptive control with those of the filtered MRAC aka L1-AC to show that L1-AC performs better. Such comparisons are not only misleading but do not reveal what causes what giving the reader a false impression of a new theory that results to new performance and robustness improvements. The use of filters in adaptive control is not new and they are used to improve the performance and robustness of certain adaptive control schemes without destroying their ideal tracking properties. In this paper we present such a scheme that guarantees good transient performance and robustness and reveals the trade off between transient performance and robust stability.

Recently, variable structure design (VSD) has been intensively researched in the literature of model reference adaptive control (MRAC) for its well-behaved transient response and appealing tracking performance. In the recent work by Hsu [6], parameter switching mechanism has been introduced in the design of model reference controller to obtain better transient behavior. By taking a different viewpoint, we apply VSD to the control channel, and develop a new robust model reference adaptive controller for a class of uncertain plants with arbitrary relative degree. It is shown that in the presence of additive, multiplicative unmodeled dynamics, and bounded disturbance, the output tracking error can still be guaranteed to converge to zero with an exponential rate. Since the parameter update law is introduced in the synthesis of this new adaptive control law, the magnitude of the switching control forces can be reduced to a more realistic level for implementation. To highlight the improved performance, simulation results are conducted with an uncertain plant with relative degree two.

A Robust State Feedback Adaptive Controller with Improved Transient Tracking Error Bounds for Plants with Unknown Varying Control Gain

This paper investigates a robust model reference adaptive control (MRAC) method for a three-phase constant-voltage constant-frequency (CVCF) inverter with an output LC filter. The proposed MRAC method is designed to stabilize the error dynamics of the system by a feedback control term in the steady state and attenuate the parameter uncertainties of the system by an updated MRAC term. Unlike the conventional proportional-derivative control (PDC) scheme, the proposed MRAC scheme ensures the fast convergence of the output errors to the exponential trajectories predefined by the reference models. Furthermore, the adaptive state-feedback mechanism can guarantee the fast dynamic response in the transient state without using load current sensors or observers. The asymptotic stability is mathematically proven by a Lyapunov theory. The feasibility of the proposed controller is confirmed through extensive experimental studies on a prototype three-phase CVCF inverter with a TI TMS320LF28335 DSP. Finally, comparative experimental results of three control methods (i.e., conventional PDC, feedback linearization control, and proposed MRAC) are provided to validate the superior performance of the proposed method such as fast transient response, low total harmonic distortion, and robustness to parameter uncertainties under critical load conditions (i.e., abrupt load changes, unbalanced loads, and distorted nonlinear loads).

This paper presents a speed and position sensorless permanent magnet synchronous motor (PMSM) drive using simple and robust model reference adaptive control (MRAC) for light electric vehicle (LEV) application. The sensorless speed and position estimator consists the flux and torque based MRAC, which improves the performance during dynamic as well as steady state condition for wide range of speed operation. Mostly, PMSM drive uses field oriented control for the closed loop speed control operation. Generally, PI controller is used speed and current controller. However, the PI controller gain requirement often changes during various driving conditions of the vehicle. Therefore, this work is focused to eliminate fixed gain PI controller by utilizing online self-tuned PI speed controller and PMSM model based predictive current controller. The self-tuning approach of PI controller for the speed control loop uses the principle of adaptive interaction, which performs tuning by minimizing error objective function. The predictive current controller eliminates the need of modulator and incorporates the inverter nonlinearities. In addition to this, the sensorless approach reduces the complexity and cost of the drive. The combined system of improved controllers and sensorless estimator improves the drive performance for wide range of speed operation.

For a class of discrete-time systems with unmodeled dynamics and bounded disturbance, the design and analysis of robust indirect model reference adaptive control (MRAC) with normalized adaptive law are investigated. The main work includes three parts. Firstly, it is shown that the constructed parameter estimation algorithm not only possesses the same properties as those of traditional estimation algorithms, but also avoids the possibility of division by zero. Secondly, by establishing a relationship between the plant parameter estimate and the controller parameter estimate, some similar properties of the latter are also established. Thirdly, by using the relationship between the normalizing signal and all the signals of the closed-loop system, and some important mathematical tools on discrete-time systems, as in the continuous-time case, a systematic stability and robustness analysis approach to the discrete indirect robust MRAC scheme is developed rigorously.

Robust Adaptive Control

MODEL REFERENCE ADAPTIVE ESTIMATION AND CONTROL APPLIED TO A CONTINUOUS FLOW FERMENTATION PROCESS

Distributed model reference adaptive containment control of heterogeneous multi-agent systems with unknown uncertainties and directed topologies

Comments on a robust model reference adaptive control for non-minimum phase systems with unknown or time-varying delay

A recently introduced class of the well-posed error systems and the corresponding robust model reference adaptive control (MRAC) laws for systems represented by parabolic or hyperbolic partial differential equations (PDEs) with spatially varying parameters is extended to encompass the disturbance rejection capability. The disturbance is modeled as a space-time-varying signal generated by a parabolic PDE with known parameters or as a spatially-varying time-invariant signal.

The purpose of this chapter is to redesign the standard adaptive control schemes by using hybrid structure composed by Model Reference Adaptive Control (MRAC) or Adaptive Pole Placement Control (APPC) strategies, associated to Variable Structure (VS) schemes for achieving non-standard robust adaptive control strategies. The both control strategies is now on named VS-MRAC and VS-APPC. We start with the theoretical base of standard control strategies APPC and MRAC, discussing their structures, as how their parameters are identified by adaptive observers and their robustness properties for guaranteeing their stability. After that, we introduce the sliding mode control (variable structure) in each control scheme for simplifying their design procedure. These design procedure are based on stability analysis of each hybrid robust control scheme. With the definition of both hybrid control strategies, it is analyzed their behavior when controlling system plants with unmodeled disturbances and parameter variation. It is established how the adaptive laws compensates these unmodeled dynamics. Furthermore, by using simple systems examples it is realized a comparison study between the hybrid structures VS-APPC and VSMRAC and the standard schemes APPC and MRAC. As the hybrid structures use switching laws due to the sliding mode scheme, the effect of chattering is analyzed on the implementation and consequently effects on the digital control hardware where sampling times are limiting factor. For reducing these drawbacks it is also discussed possibilities which kind of modifications can employ. Finally, some practical considerations are discussed on an implementation on motor drive systems.

It is shown how to change the primary control structure of a model reference adaptive control (MRAC) scheme from the usual minimum settling time-type algorithm to a ripple-free response control (RFRC) scheme. RFRC does not try to compensate process zeros, avoiding ringing effects (like intersampling ripple). The main issue in the derivation of the RFRC-MRAC scheme is the establishment of a stable adaptive law which guarantees a ripple-free behavior if the error signal tends to zero. In the original MRAC scheme, the error signal consisted of the desired error plus a transient term which tends to zero when adaptation proceeds. In this MRAC scheme, the error consists of a filtered form of the desired RFRC error. Hence, if the error used in the adaption tends to zero, the RFRC behavior is achieved. The scheme avoids ringing effects and can control nonminimum-phase processes. The cost of these advantages is a slowing down of the process response by a number of samples equal to the order of the numerator polynomial. Simulations confirm the RFRC-like characteristics, and practical results on a water level system show the usability of the method.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>