D.-W. Gu

Robust control of an unknown plant—the IFAC 93 benchmark

Many control design specifications, such as the IFAC 1993 benchmark, include stringent closed-loop performance requirements, which are required to be met in the face of uncertainties. Such problems can be effectively designed by a combination of the method of inequalities, which designs for explicit closed-loop performance, and analytical optimization techniques, from which robustness is obtained. This paper describes how to combine the method of inequalities with a variety of analytical optimization methods. An introduction to μ synthesis is also included. The design of robust controllers for the benchmark problem using these methods is described, and a simple adaptive gain scheme to improve the performance is suggested.

A Robust Design Approach to Integrated Controls and Diagnostics

Abstract This paper considers the design problem of integrated controls and diagnostics. The foundation for such an integrated approach was presented in (Nett et al., 1988), where the approach made use of the so-called four degrees-of-freedom (4-DOF) controller. This controller has 2-inputs and 2-outputs (rather than one). The additional controller output was viewed as a diagnostic output which is monitored to detect and isolate sensor and actuator failures. It will be shown that the 4-DOF controller is a simple case of the standard regulator framework. The design of the integrated controls and diagnostics can thus be done in the framework of robust control theory. This gives the advantage of synthesizing the 4-DOF controller in a single step approach. The effect of model uncertainty is directly incorporated in the synthesis so that when uncertain plants are used, the diagnostic performance should remain reasonable. An example will be presented to demonstrate the proposed design approach.

Low-order stabilizing controllers

A method for designing low-order stabilizing controllers is described. It is shown that for some plants the order of stabilizing controllers may be less than or equal to l (respectively m), where l (respectively m) is the number of plant outputs (respectively inputs). An explicit characterization of a set of low-order stabilizing controllers is given and numerical examples are provided to illustrate the results of the note. >

State-space approach to discrete-time super-optimal H ∞ control problems

Abstract An algorithm is presented for solving the strengthened discrete-time 1-block model-matching problem. All the steps of the algorithm are performed using state-space models and each step has a closed-form solution. The uniqueness of the super- optimal solution follows from the constructions in the algorithm. Although the problem is analogous to the continuous-time case and the strategy used is the same, there are some intricate differences in detail which make the derivation of one from the other non-trivial. By working completely in discrete-time, the super-optimal controller can be analysed explicitly in the z-domain and implemented directly on a digital computer.

Optimal Eigenstructure Assignment of Linear Systems

Abstract A versatile eigenstructure assignment method which utilizes the freedom in the modal matrix of the closed-loop system matrix and may be used in the solution of wide range optimisation problems arising in the design of multi-input continuous-time and discrete-time systems is presented. The method is applied to the pole assignment with H 2 and H ∞ optimisation, to the robust pole assignment and pole assignment with maximum stability radius and to the design of dynamic output compensators.

A Comprehensive Study on Current Source Circuits

A current source is one of the key components in an EIT system, particularly in EIT based breast imaging which is called electrical impedance mammography (EIM). It is also a critical source of systematic errors due to limited output impedance and associated frequency bandwidth. One method for increasing the output impedance is a Generalised Impedance Converter (GIC). This paper investigates two Howland-based, voltage-to-current conversion (V/I) circuits; one is a simple, optimized current source developed by the Leicester Group while the other includes a GIC. This investigation evaluates both circuits using PSpice, measuring output impedances at 1KΩ loading along with -3dB and -1dB bandwidths; these are of clinical interest, as EIT needs to cover a wide range of frequencies. It was expected that the GIC would increase the output impedance with required frequency bandwidth. The results show that, the GIC has improved the output impedance, reaching 120MOhm. However, the high output impedance was only for a limited bandwidth.

Improved perturbation bounds for general quadratic matrix equations

Perturbation analysis of general algebraic quadratic matrix equations is presented, which include as particular cases the standard and descriptor algebraic matrix Riccati equations, arising in the optimal control and filtering of continuous, time-invariant, linear systems. The perturbation bounds derived are superior to the bounds, already available in the literature. They are applicable to the error analysis of general quadratic matrix equations. The results are based on the use of Lyapunov majorants, fixed point principles and detailed estimates of the norms of tensor products of matrices.

Robust control of a high purity distillation column using mu -K iteration

The authors address the theme problem described by D.J.N. Limebeer (1991). This problem concerns the robust control of a high-purity distillation column. The authors formulate the design as a mu -synthesis and solve it using a novel algorithm called mu -K iteration (Lin et al., 1991). Some preliminary results are presented for a controller designed for the LV configuration.<<ETX>>

Low-Order H∞ Sub-Optimal Controllers

Abstract This paper presents a methodology for the problem of reducing the order of H ∞ sub-optimal controllers. It is shown that the order of H ∞ sub-optimal controllers may be reduced to n - p 2 and that for some plants the order may be less than n - p 2 , where n is the size of the system matrix of the generalized plant and p 2 is the number of process outputs. A characterization of a set of ( n - p 2 )th-order H ∞ sub-optimal controllers is given. A numerical example is given to illustrate the results.

MILP AND ITS APPLICATION IN FLIGHT PATH PLANNING

Abstract A finite receding horizon approach for path planning of uninhabited air vehicles (UAVs) is presented. The approach is based on mixed integer linear programming (MILP) techniques. Various constraints are formulated to avoid radar zones and collisions, etc. These constraints are extended to be both hard and soft so as to alleviate the infeasibility problem usually encountered. The finite receding horizon approach is numerically stable and can be applied to the path planning of a fleet of UAVs. Further improvements are possible for use in real time planning. The MILP is solved using commercially available software AMPL/CPLEX.