Guido Herrmann

Incorporating Robustness Requirements Into Antiwindup Design

This paper treats the problem of synthesizing antiwindup compensators that are able to handle plant uncertainty in addition to controller saturation. The uncertainty considered is of the frequency-weighted additive type, often encountered in linear robust control theory, and representative of a wide variety of uncertainty encountered in practice. The main results show how existing linear matrix inequality based antiwindup synthesis algorithms can be modified to produce compensators that accommodate uncertainty better. Embedded within these results is the ever-present performance - robustness tradeoff. A remarkable feature is that the often criticized internal model control antiwindup solution emerges as an ldquooptimally robustrdquo solution. A simple example demonstrates the effectiveness of the modified algorithms.

Practical implementation of a novel anti-windup scheme in a HDD-dual-stage servo-system

Two novel discrete anti-windup (AW) techniques are applied to a dual-stage actuator of an experimental hard disk drive system. The techniques, one low order, the other full order, employ convex l/sub 2/-performance constraints in combination with linear-matrix-inequality-optimization methods. It is shown that the AW compensators can improve the performance of the nominal dual-stage servo-system when the secondary actuator control signal saturates at its allowable design limits. Also, stability is achieved despite saturation of both the secondary actuator and the voice-coil-motor actuator. Practical results show that the performance of each AW compensator is superior to another well-known ad-hoc AW technique, the internal model control AW scheme. The main contribution of the paper is the application of theoretically rigorous AW methods to an industrially relevant servo system.

Reinforcement learning and optimal adaptive control: An overview and implementation examples

Abstract This paper provides an overview of the reinforcement learning and optimal adaptive control literature and its application to robotics. Reinforcement learning is bridging the gap between traditional optimal control, adaptive control and bio-inspired learning techniques borrowed from animals. This work is highlighting some of the key techniques presented by well known researchers from the combined areas of reinforcement learning and optimal control theory. At the end, an example of an implementation of a novel model-free Q-learning based discrete optimal adaptive controller for a humanoid robot arm is presented. The controller uses a novel adaptive dynamic programming (ADP) reinforcement learning (RL) approach to develop an optimal policy on-line. The RL joint space tracking controller was implemented for two links (shoulder flexion and elbow flexion joints) of the arm of the humanoid Bristol-Elumotion-Robotic-Torso II (BERT II) torso. The constrained case (joint limits) of the RL scheme was tested for a single link (elbow flexion) of the BERT II arm by modifying the cost function to deal with the extra nonlinearity due to the joint constraints.

Robust adaptive finite-time parameter estimation and control of nonlinear systems

This paper exploits an alternative adaptive parameter estimation and control approach for nonlinear systems. An auxiliary filter is developed to derive a representation of the parameter estimation error, which is combined with an adaptive law to guarantee the exponential convergence of the control error as well as the estimation error. The proposed method is further improved via a sliding mode technique to achieve the finite-time (FT) error convergence. The traditional persistent excitation (PE) is simplified as an a priori verifiable sufficiently rich (SR) requirements on the demand signal. The robustness of the control schemes with bounded disturbances is also investigated. The developed methods are finally tested via simulations.

Online adaptive approximate optimal tracking control with simplified dual approximation structure for continuous-time unknown nonlinear systems

This paper proposes an online adaptive approximate solution for the infinite-horizon optimal tracking control problem of continuous-time nonlinear systems with unknown dynamics. The requirement of the complete knowledge of system dynamics is avoided by employing an adaptive identifier in conjunction with a novel adaptive law, such that the estimated identifier weights converge to a small neighborhood of their ideal values. An adaptive steady-state controller is developed to maintain the desired tracking performance at the steady-state, and an adaptive optimal controller is designed to stabilize the tracking error dynamics in an optimal manner. For this purpose, a critic neural network (NN) is utilized to approximate the optimal value function of the Hamilton-Jacobi-Bellman (HJB) equation, which is used in the construction of the optimal controller. The learning of two NNs, i.e., the identifier NN and the critic NN, is continuous and simultaneous by means of a novel adaptive law design methodology based on the parameter estimation error. Stability of the whole system consisting of the identifier NN, the critic NN and the optimal tracking control is guaranteed using Lyapunov theory; convergence to a near-optimal control law is proved. Simulation results exemplify the effectiveness of the proposed method.

A proximate-time-optimal-control design and its application to a hard disk drive dual-stage actuator system

We propose a compensator-based strategy for design of a track-seeking and track-following control system for a dual-stage servo actuator in hard disk drives. A well-known decoupling structure is employed to disconnect the control of the primary voice coil motor (VCM) actuator from the loop for a secondary high-bandwidth actuator. The compensator is placed in the secondary loop and suitably combined with a saturation nonlinearity in order to obtain actuator signal boundedness. The design procedure consists of four steps: 1) design of an established nonlinear seek-settle-track following controller for the VCM; 2) design of a linear track following controller for the secondary actuator; 3) observer design; and 4) design of a compensator to retain global stability and to improve performance. The proposed control system improves performance of both long-span seeking (proximate-time-optimal controller) and short-span seeking. In addition, it achieves high-bandwidth track following performance. The experimental results show good track-following performance, and short-span/long-span-seeking performance with fast settling time. The overshoot during track seeking can be made negligible for a suitably tuned VCM-actuator control loop.

Discrete-time and sampled-data anti-windup synthesis: stability and performance

The anti-windup (AW) problem is formulated in discrete time using a configuration which effectively decouples the nominal linear and nonlinear parts of a closed loop system with constrained plant inputs. Conditions are derived which ensure an upper bound on the induced l 2 norm of a certain mapping which is central to the anti-windup problem. Results are given for the full-order case, where a solution always exists, and for static and low-order cases, where a solution does not necessarily exist, but which is often more appealing from a practical point of view. The anti-windup problem is also framed and solved for continous-time systems under sampled-data control. It is proved that the stability of the anti-windup compensator loop is equivalent to a purely discrete-time problem, while a hybrid induced norm is used for performance recovery. The performance problem is solved using linear sampled-data lifting techniques to transpose the problem into the purely discrete domain. The results of the paper are demonstrated on a flight control example.

Practical implementation of a neural network controller in a hard disk drive

This brief gives a practical account of the application of an improved adaptive neural network (NN) controller to the voice-coil-motor (VCM)-actuator of a hard disk drive (HDD). Necessary practical modifications are presented which allow the implementation of the controller for a VCM-actuator with high-frequency resonances. For resonance compensation, notch filter compensators are augmented while parameter estimation errors are counteracted by employing robust parameter estimation techniques. It is shown practically that this controller is a good candidate for a track seek/following controller in HDDs.

Robust control applications

Abstract This paper (first presented as a plenary lecture at the Fifth IFAC Symposium on Robust Control Design, Toulouse, July 2006) demonstrates the practical importance of robust control theory by describing its application to two non-trivial practical control problems. Part 1 considers helicopter control and Part 2 addresses saturation problems in high-performance head-positioning servo systems in high-density hard-disk drives. In Part 1, we present the design and flight test of a new batch of H ∞ controllers for the Bell 205 helicopter. At the heart of each controller is an H ∞ loop-shaping controller, augmented with a hand-tuned reference filter to improve tracking performance and to reduce a perceived phase lag which pilots had complained of previously. Flight testing revealed that, with such an architecture, it was relatively easy to get Level 1 handling qualities ratings in low aggression manoeuvres. Further fine tuning resulted in Level 1 qualities for high aggression manoeuvres and one controller performed to Level 1 standard in all manoeuvres tested. In Part 2, we consider how robust control techniques can be used to design anti-windup compensators to counter performance and stability problems associated with saturating actuators in state-of-the-art hard-disk drive servo systems. A promising two-stage approach is given and illustrated with experimental results.

Adaptive Observer-Based Parameter Estimation With Application to Road Gradient and Vehicle Mass Estimation

A novel observer-based parameter estimation scheme with sliding mode term has been developed to estimate the road gradient and the vehicle weight using only the vehicles velocity and the driving torque. The estimation algorithm exploits all known terms in the system dynamics and a low-pass filtered representation of the dynamics to derive an explicit expression of the parameter estimation error without measuring the acceleration. The proposed parameter estimation scheme which features a sliding-mode term to ensure the fast and robust convergence of the estimation in the presence of persistent excitation is augmented to an adaptive observer and analyzed using Lyapunov Theory. The analytical results show that the algorithm is stable and ensures finite-time error convergence to a bounded error even in the presence of disturbances. In the absence of disturbances, convergence to the true values in finite time is guaranteed. A simple practical method for validating persistent excitation is provided using the new theoretical approach to estimation. This is validated by the practical implementation of the algorithm on a small-scaled vehicle, emulating a car system. The slope gradient as well as the vehicles mass/weight are estimated online. The algorithm shows a significant improvement over previous results.