The paper presents a new method for model reference adaptive control for nonminimum phase discrete-time systems using approximate inverse systems obtained from the least-squares approximation. We show how unstable pole-zero cancellations can be avoided and how the effect of the disturbances can be decoupled from the plant output. Finally, the results of computer simulation are presented to illustrate the effectiveness of the proposed method.
Sufficient conditions are obtained for absolute stability of systems that are described by Lurie-type functional differential equations. It is assumed that the uncontrolled systems are unstable. The problem of Lurie consists of finding conditions for the feedback coefficients, and characterising the feedback function which make the trivial solutions of the functional differential equation stable. We assume that the system is completely controllable. The method is based on the use of Lyapunov functionals. A set of 'easily verifiable' sufficient conditions on the roots of certain 'quasi-polynomial' have been obtained. Systems of this kind are used for modelling a variety of control processes, including processes in biological systems.
A simple and noniterative procedure for the computation of the exact value of the infimum in the singular Hinfinity -optimisation problem is presented, as a continuation of earlier work (Chen. Saberi, and Ly, 1992). The authors' problem formulation is general and they do not place any restrictions in the finite and infinite zero structures of the system, and the direct feedthrough terms between the control input and the controlled output variables, and between the disturbance input and the measurement output variables. The method is applicable to a class of singular Hinfinity -optimisation problems for which the transfer functions from the control input to the controlled output and from the disturbance input to the measurement output satisfy certain geometric conditions. In particular, the paper extends the result of earlier work by allowing these two transfer functions to have invariant zeros on the j omega -axis.
A simple recursive method for the computation of Gramians for stable linear continuous systems is proposed. The method is based on an extension of Astrom-Jury-Agniel algorithm. The algorithms for the computation of controllability, observability, and cross Gramians for both SISO and MIMO systems are presented. The proposed method is illustrated by numerical examples and is also compared with the Lyapunov equation method of computing the Gramians.
An algorithm for self-tuning control of discrete-time linear plant is proposed. The algorithm uses a stochastic right-matrix-fraction innovation description as the system representation, a recursive-prediction-error algorithm for online estimation of the system parameters and the costates, and pole placement plus moving-average control via costate and innovation feedback.
The problems of controller windup and directional change in controls, in controllers for multiinput multioutput processes with input saturation, is considered. To avoid the windup problem, a generalisation is proposed for the conditioning technique based antiwindup compensator, by introducing a filtered setpoint. This provides a parameterisation to deal with situations where the original conditioning technique was not suitable. To reduce the effect of directional change in controls due to the multiple saturation, further modifications to the conditioning technique are proposed. An interesting outcome is that the generalised antiwindup compensator due to Astrom and Wittenmark is interpreted in terms of the conditioning technique; moreover, these interpretations are used to introduce modifications to their scheme in order to deal with the problem of directional change in controls.
The LQG optimal continuous-time control philosophy is extended so that use may be made of future setpoint or reference signal information. The tracking error is defined in terms of an ideal response model so that a model following capability may also be introduced. A dual criterion cost function is employed that enables the feedback and reference input controllers to be designed independently. The solution of the problem is obtained in the s-domain following a polynomial-based optimisation procedure. This type of controller should be useful for continuous-time adaptive systems which require a predictive capability.
The paper is concerned with the application of reinforcement learning techniques to the stochastic control problem, and in particular presents a method based on learning automata for designing controllers for the control of unknown complex dynamic systems. The work is focused on the design of a learning automaton using subsets of control actions to reduce the number of actions during a learning procedure. The subsets of actions can be expanded or contracted according to action probabilities which are reset from time to time so as to achieve a global selection over the action set. Two reinforcement schemes have been investigated alongside the variable subsets of control actions. A reference performance index and an approach to quantification and normalisation of the performance index are proposed in association with the two schemes to evaluate environment responases during the learning procedure. The method has been used to achieve learning control for an unknown nonlinear turbo-generator system.
The paper details the design and experimental implementation of a practical discrete-time version of a sliding-mode controller. The controller is derived and proven robustly stable to bounded plant modelling errors and exogenous disturbances. Sliding-surface design is treated as an energy minimisation problem where state energy during sliding on the surface is minimised according to a linear quadratic measure. Analysis of the properties of the control system lead to static and dynamic optimal switching gains. Application of the controller to simulated and experimental versions of a coupled-drives apparatus provide evidence of the robust performance and stability of the controller with classical linear quadratic optimal control. Also demonstrated is the compared effectiveness of the dynamic optimal switching gain.
In the paper, the authors present a method for the numerical solution of modified algebraic Riccati equations, A(T)Q + QA - Q(SIGMA)Q + V + F(Q) = 0, where the perturbation term F is low rank. They use a continuous homotopy approach with discrete corrections at each homotopy step. Their algorithm requires the solution of several perturbed Lyapunov equations during each iteration; thus they also address the rapid solution of sets of perturbed Lyapunov equations.
In this paper two types of intelligence supervised controllers are proposed with the aim to achieve an overall performance beyond the limit of linear controllers. In each case, the overall controller has a hierarchical structure with two conventional linear controllers in the bottom layer to perform accurate control action under the supervision of a reasoning process in the top layer. The reasoning process consists of heuristic rules drawn from our physical insight, and can easily be implemented either by fuzzy logics or by IF ... THEN statements. Both intelligence supervised controllers achieve a performance beyond the limit of linear control laws, and are superior to both a fuzzy controller and a neural controller at least in the sense that their performances are independent of the type of command.
The H(infinity) filtering problem of state estimation for LTI systems is considered. The LTI system is driven at its input and corrupted at its output by processes with known energy bounds (but unknown spectral densities), and state estimates are sought such that the energy of the estimation error is minimised. The H(infinity) filtering problem is formulated as a model-matching problem and is solved using a state-space based algebraic approach. A characterisation for a family of H(infinity) filters is obtained in the form of a linear fractional transformation. It is shown that the H(infinity) filter generalises the Kalman filter and a condition is given under which the H(infinity) filter reduces to the Kalman filter. A derivation for minimum-entropy H(infinity) filters is given.
The linear-quadratic-Gaussian (LQG) embedding approach for solving the H(infinity) control problem is much simplified by the introduction of a special Youla parameterisation and auxiliary LQG problem. The approach has the advantage over previous solutions that most of the analysis concerns an auxiliary LQG problem. The influence of the weighting function which changes the controller from a usual LQG design to an H(infinity)-norm minimisation device is transparent in this new problem formalism. The cost functions minimised in both H-2 and H(infinity) problems include cross-product terms for greater generality. The conditions under which a simplified design procedure may be used are established and related to the solution of a 1-block Nehari problem.
A simple and noniterative procedure for the computation of the exact value of the infimum in the singular H∞-optimisation problem is presented, as a continuation of our earlier work. Our problem formulation is general and we do not place any restrictions in the finite and infinite zero structures of the system, and the direct feed-through terms between the control input and the controlled output variables, and between the disturbance input and the measurement output variables. Our method is applicable to a class of singular H∞-optimisation problems for which the transfer functions from the control input to the controlled output and from the disturbance input to the measurement output satisfy certain geometric conditions. In particular, the paper extends the result of earlier work by allowing these two transfer functions to have invariant zeros on the jω-axis.
The robust stability of a class of uncertain systems involving internal delays while being regulated by a sliding mode controller (SMC) is studied. The method for designing a SMC is proposed for the generation of a sliding motion in the system. The robustness property and asymptotic stability of the system are discussed and conditions for the design of the switching hyperplane are given. Further generalisation results, which lead to a simple design and implementation, are made for the case when the system is in companion form. A method is proposed for the elimination of limit cycles in systems being regulated by a relay SMC while allowing the generation of sliding motion and thus ensuring the closed-loop asymptotic stability.
In the paper, a unifying approach is presented for the solution of the following five major observer design problems, for both regular and singular systems: the necessary and sufficient conditions for the problem to have a solution, the order of the minimal observer, the general analytical expressions for the observer matrices, the properties of the closed-loop system, and the full order observer.
This paper presents a simple and non-iterative procedure for the computation of the exact value of the infimum in the singular H∞ optimization problem and is a continuation of our earlier work [1]-[3]. Our problem formulation in general and we do not place any restrictions on the finite and infinite zero structures of the system, and the direct feedthrough terms between the control input and the controlled output variables, and between the disturbance input and the measurement output variables. Our method is applicable to a class of singular H∞-optimization problem for which the transfer functions from the control input to the controlled output and from the disturbance input to the measurement output satisfy certain geometric conditions. In particular this paper extends the result of [3] by allowing these two transfer functions to have invariant zeros on the jw axis.
New insights on the role of the innovations system representation in the context of the optimal LQG (H-2) 'standard' problem are provided. The optimal controller is derived by using polynomial matrix techniques based on an innovations representation of the system. This can be obtained from the physical description by solving an appropriate minimum mean-square error filtering problem. The key result is that both the descriptions share the same optimal controller. A quite general cascade control structure is revisited in the present setting and the appropriate filtering problem is solved. The optimal controller is further obtained and the overall design procedure is compared with the one based on the physical system description. As a result, both a generalisation of the solution for the proposed cascade control problem and a better understanding of the role of the innovations system representation are provided.
Compensators can be designed to give zero steady-state error in tracking arbitrary periodic or repetitive reference signals. The previously presented technique for design of the compensator has a limited convergence rate for the decay of tracking errors and a limited region of stability. Several alternative design approaches are presented which yield improvements in high-frequency convergence rate while some designs also improve stability. The design approaches are in two classes, designs based on adding periodic correction to an existing controller and total designs for transient and periodic performance. The approaches include FIR and IIR filter design by pole placement and linear quadratic control design.
The paper presents a hybrid state-space self-tuner using a new dual-rate sampling scheme for digital adaptive control of continuous-time uncertain linear systems. A state-space-based recursive least-squares algorithm, together with a variable forgetting factor, is used for direct estimations of both the equivalent discrete-time uncertain linear system parameters and the associated discrete-time state of a continuous-time uncertain linear system from the sampled input and Output data. An analogue optimal regional pole-placement design method is used for designing an optimal observer-based analogue controller. A suboptimal observer-based digital controller is then designed from the designed analogue controller using digital redesign technique. To enhance the robustness of parameter identification and state estimation algorithms, a dynamic bound for a class of uncertain bilinear parameters and a fast-rate digital controller are developed at each fast-sampling period. Also, to accommodate computation loads and computation delay for developing the advanced hybrid self-tuner, the designed analogue controller and observer gains are both updated at each slow-sampling period. This control technique has been successfully applied to benchmark control problems.
