Donald J. Ballance

A nonlinear disturbance observer for robotic manipulators

A new nonlinear disturbance observer (NDO) for robotic manipulators is derived in this paper. The global exponential stability of the proposed disturbance observer (DO) is guaranteed by selecting design parameters, which depend on the maximum velocity and physical parameters of robotic manipulators. This new observer overcomes the disadvantages of existing DOs, which are designed or analyzed by linear system techniques. It can be applied in robotic manipulators for various purposes such as friction compensation, independent joint control, sensorless torque control and fault diagnosis. The performance of the proposed observer is demonstrated by the friction estimation and compensation for a two-link robotic manipulator. Both simulation and experimental results show the NDO works well.

Brief Optimal control of nonlinear systems: a predictive control approach

A new nonlinear predictive control law for a class of multivariable nonlinear systems is presented in this paper. It is shown that the closed-loop dynamics under this nonlinear predictive controller explicitly depend on design parameters (prediction time and control order). The main features of this result are that an explicitly analytical form of the optimal predictive controller is given, on-line optimisation is not required, stability of the closed-loop system is guaranteed, the whole design procedure is transparent to designers and the resultant controller is easy to implement. By establishing the relationship between the design parameters and time-domain transient, it is shown that the design of an optimal generalised predictive controller to achieve desired time-domain specifications for nonlinear systems can be performed by looking up tables. The design procedure is illustrated by designing an autopilot for a missile.

Genetic algorithm enabled computer-automated design of QFT control systems

This paper first reviews the existing quantitative feedback theory (QFT) based design techniques and difficulties that a designer encounters. Based on this analysis and taking into account the practical constraints, an evolutionary computation enabled automatic design procedure is developed. It can be employed to provide an initial controller quickly on which manual loop-shaping and refinements are based on, or be used to further tune existing controllers or start from scratch. A design example against a MATLAB QFT Toolbox benchmark problem shows that this methodology not only automates loop-shaping but also improves design quality and, most usefully, improves the quality with a reduced order controller. The entire design is targeted towards global optimisation, including the prefilter selection.

On a Switching Control Scheme for Nonlinear Systems with Ill-Defined Relative Degree

This paper discusses the applicability of a switching control scheme for a nonlinear system with ill-defined relative degree. The control scheme switches between exact and approximate input-output linearisation control laws. Unlike a linear system under a switching control scheme, the equilibria of a nonlinear system may change with the switching. It is pointed out that this is not sufficient to cause instability. When the region of the approximate linearisation control law is attractive to the exact zero dynamics, it is possible that the closed-loop system under the switching control scheme is still stable. The results in this paper shows that the switching control scheme proposed in Tomlin and Sastry (Systems Control Lett. 35(3) (1998) 145) is applicable for a wider class of nonlinear systems.

QFT design for uncertain non-minimum phase and unstable plants revisited

Design method for uncertain non-minimum phase and unstable plants in the quantitative feedback theory (QFT) developed by Horowitz and Sidi is revisited in this paper. It is illustrated that the existing method may not work since some design rules have not been clearly specified by several examples including non-minimum phase plants and unstable plants. Then stability of a new nominal plant is carefully examined and analysed, and an improved design method is presented. The result in this paper provides mathematical justification of the QFT design procedure for nonminimum phase and unstable plants in Horowitz and Sidi (1978) and Horowitz (1992).

Design and implementation of a bond-graph observer for robot control

Abstract In robotics, high-precision measurements of link positions are available for feedback control but tachometer measurements of link velocities are often severely contaminated by noise. This paper presents the use of a bond-graph model-based nonlinear observer to estimate the velocities in the control of an experimental two-link manipulator. A significant advantage of this approach is that the observer software may be written automatically from the bond-graph observer representation. Results are presented in simulation form, and for practical implementation on the experimental arm.

Plant template generation for uncertain plants in quantitative feedback Theory

The creation of templates for uncertain plants is an essential first step in Quantitative Feedback Theory (QFT) and other frequency domain methods. For the plants with general uncertain structure, a method to identify the critical interior points in an uncertain parameter set which map to the boundaries of plant templates is presented. It is shown that the boundaries of templates are only generated by the edges of an uncertain parameter set and those critical interior points. With the help of symbolic computation, a computational tractable procedure for generating the templates is developed. This general procedure is illustrated by a vehicle clutch systems and the longitudinal dynamics of a small aircraft where the underlying uncertain parameters perturb both plants nonlinearly.

Fishery management as a problem in feedback control

Abstract This paper arises out of a collaborative project to investigate fishery management, which poses problems of control in the presence of uncertainty, from the point of view of control engineering, which uses dynamic, but not necessarily optimal, feedback controllers to solve such problems. Management of one particular isolated population (the Western stock of mackerel) is considered in detail in order to show applicability of established techniques in control engineering. The control problem is seen to be nonlinear, as well as stochastic. A new single-state fishery model is presented. General results from the engineering analysis, in the form of strategies of constant catch and of constant effort and in the form of a warning about the instability of high exploitation, confirm what is well known in fishery management. Numerical data are obtained which could be used to design a controller minimising fluctuations about a chosen equilibrium state. It is concluded that control engineering provides a suitable scientific framework for further discussion of fishery management and of other problems of regulating harvested populations.

Bond graphs in model matching control

Bond graphs are primarily used in the network modeling of lumped parameter physical systems, but controller design with this graphical technique is relatively unexplored. It is shown that bond graphs can be used as a tool for certain model matching control designs. Some basic facts on the nonlinear model matching problem are recalled. The model matching problem is then associated with a particular disturbance decoupling problem, and it is demonstrated that bicausal assignment methods for bond graphs can be applied to solve the disturbance decoupling problem as to meet the model matching objective. The adopted bond graph approach is presented through a detailed example, which shows that the obtained controller induces port-Hamiltonian error dynamics. As a result, the closed loop system has an associated standard bond graph representation, thereby rendering energy shaping and damping injection possible from within a graphical context.

A comparison of methods for computing frequency response of uncertain plants

ABSTRACT The frequency response of an inverted pendulum with a flexible arm, which is perturbed by six uncertain parameters nonlinearly, is calculated by the analytic method in Chen and Ballance (1999). This approach is compared with the extreme point, the parameter gridding and the probabilistic approaches. It is shown that the analytic approach provides a powerful tool for computing the frequency response of a wide class of nonlinear dependence uncertain plants. It is pointed out that for a plant with hard bounds, it is better to combine the probabilistic approach with the extreme point technique.