System identification and control using genetic algorithms

An alternative method was proposed for identification of linear continuous time system with noisy output. Using Gaussian modulating filters, by numerical integration, a discrete equivalent identification model that was parametrized directly in continuous time model parameters was obtained, and the LS estimation algorithm was developed. The LS estimator is biased even with white measurement output noise, and the bias is determined by variance of output noise. On the basis of obtained output measurement noise variance, the bias was compensated and the consistent estimates of system parameters were given. Simulation which compares the standard LS with BCLS algorithm indicates that the proposed algorithm is an efficient method for noisy output continuous time system identification.

Identification of continuous-time nonlinear systems: The nonlinear difference equation with moving average noise (NDEMA) framework

A criterion is introduced for determining the optimum sampling interval for the identification of system parameters. It increases the accuracy and stability in identification procedures. This is done by employing a bilinear transformation from the z-plane to the w-plane. Some results of simulations are also included. These reveal the usefulness of the suggested algorithm even in the presence of measurement noise.

A third-order cumulants based adaptive recursive least-squares (CRLS) algorithm for the identification of time-invariant nonminimum phase systems, as well as time-variant nonminimum phase systems, has been successfully developed. As higher order cumulants preserve both the magnitude and the phase information of received signals, they have been considered as powerful signal processing tools for nonminimum phase systems. In this paper, the development of the CRLS algorithm is described and examined. A cost function based on the third-order cumulant and the third-order cross cumulant is defined for the development of the CRLS system identification algorithm. The CRLS algorithm is then applied to different moving average (MA) and autoregressive moving average (ARMA) models. In the case of identifying the parameters of an MA model, a direct application of the CRLS algorithm is adequate. When dealing with an ARMA model, the poles and the zeros are estimated separately. In estimating the zeros of the ARMA model, the construction of a residual time-series sequence for the MA part is required. Simulation results indicate that the CRLS algorithm is capable of identifying nonminimum phase and time-varying systems. In addition, because of the third-order cumulant properties, the CRLS algorithm can suppress Gaussian noise and is capable of providing an unbiased estimate in a noisy environment.

Subspace-based identification for continuous-time stochastic systems via distribution-theoretic approach

In this research, a new method for stabilizing non - minimum phase (NMP) system using Active Disturbance Rejection Control (ADRC) is proposed. The general ADRC maintains stability by determining the observer poles and the controller poles, but the non-minimum phase system is very delicate as the stable bandwidth is very limited. Most research using ADRC is the minimum phase system. Therefore, the proposed method is to easily obtain controller gain with a linear quadratic regulator (LQR) using an extended system including ADRC. This widens the range in which the system becomes stable, and can determine the responsiveness of the system with only the adjustment parameter. Further, by obtaining the condition for stabilizing, the system can be stabilized easily. After designing the system design method as the proposed method, the condition is shown for the system to stabilize. Finally, the effectiveness of the proposed method is verified through simulation experiments.

A simple control structure in servo system is occasionally needed for simple industrial application which precise and high control performance is not exessively important so that the cost production can be reduced efficiently. Simplified vector control, which has simple control structure, is utilized as the permanent magnet synchronous motor control algorithm and genetic algorithm is used to tune three PI controllers used in simplified vector control. The control performance is obtained from simulation and investigated to verify the feasibility of the algorithm to be applied in the real application. Simulation results show that the speed and torque responses of the system in both continuous time and discrete time can achieve good performances. Furthermore, simplified vector control combined with genetic algorithm has a similar performance with conventional field oriented control algorithm and possible to be realized into the real simple application in the future.

In our previous paper 4) -12), we have studied “Theory of Invariance” for nonlinear continuous-time systems with their inputs appearing linearly. The aim of this paper is to derive necessary and sufficient conditions that inputs never effect outputs (so called conditions of “Invariance”) for nonlinear discrete-time and continuous-time systems without the assumption of linearity in inputs. Applying these conditions to the decoupling problem, we obtained necessary and sufficient conditions which yield decoupling control laws for both the continuous-time systems and the discrete-time systems. The conditions of decoupling given by van der Schaft 13) and Grizzle 14) via geometric approach are different in forms from ours. But, it seems difficult to derive control laws from their conditions because the integration of partial deferential equations is needed there.

In this paper, sliding mode observer design principles based on the equivalent control approach are discussed for a linear time invariant system both in continuous and discrete time. For the continuous case, the observer is designed using a recursive procedure; however, the observer is eventually expressed as a replica of the original system with an additional auxiliary input with a certain nested structure. A direct discrete time counterpart of the sliding mode realization of a reduced order asymptotic observer using the discrete time equivalent control is also developed. Simulation of a linearized truck-trailer during a manoeuvre illustrates the approach. Results show the effectiveness and the finite time convergence characteristics of the proposed discrete and continuous time sliding mode observers.

System identification is a well known technique for developing mathematical models based on plant input and output data sequences. Models that describe the systems may be in various forms and one of the possibilities is a state space model formulation. The state space mathematical modelling involves vectors and matrices in a unique geometrical framework. It offers the key advantages on providing low parameter sensitivity with respect to perturbation for high order systems and also has shown its ability to present multi-input and multi-output systems with minimal state dimensions. We use a time domain subspace approach in conjunction with Laguerre filters and instrumental variables to develop a mathematical formulation of the state space model for identification of a continuous time system. The method aims at searching for accurate matrices of the state space model to ensure that the constructed model closely mimics the actual system as well as provide information for the purpose of control system design. The subspace identification algorithm provides state space models with better conditioning, improved quality and easily maintainable parametrisation. The algorithm is validated with identification of two systems: a simulated plant, and a magnetic bearing system. For both systems, the computer simulation results demonstrate that the obtained model describes the system closely.

This paper presents a novel interval observer design for uncertain locally Lipschitz continuous-time (CT) and discrete-time (DT) systems with noisy nonlinear observations that is input-to-state stable (ISS) and minimizes the L1-gain of the observer error system with respect to the uncertainties. Using mixed-monotone decompositions, the proposed observer is correct and positive by construction without the need for additional constraints/assumptions. This, in turn, allows us to directly leverage techniques for positive systems to design an ISS and L1-robust interval observer via mixed-integer (linear) programs instead of semi-definite programs with linear matrix inequalities. Further, our observer design offers additional degrees of freedom that may serve as a surrogate for coordinate transformations. Finally, we demonstrate the effectiveness of our proposed observer on some CT and DT systems.

In this paper, a decentralized controller is designed for cross coupled MIMO Twin rotor aerodynamic system (TRAS). The decentralized controller design is done by decoupling the MIMO system into two decoupled, a pitch and a yaw system. Then 2-DOF controller is designed using control technique in continuous and discrete time. The performance of these controllers are tested through extensive simulations in MatLAB and results are compared between discrete and continuous time systems.

This paper presents a novel methodology to design a discrete-time compensator for a high-order repetitive control system. An optimization-based approach is applied to design the compensator, which is required to be stable and causal. This methodology is applicable to both minimum and non-minimum phase systems, for which stability and tracking error convergence are ensured. The compensator is yielded in the form of a proper transfer function and can be implemented separately without being merged with a high-order internal model. The high-order internal model is used to provide robustness against period variations of the reference signal. Simulation and experimental results are provided to show the effectiveness of the compensator design methodology.

An adaptive constrained one-step-ahead controller is presented, which is appropriate for the case where the input steady-state value u/sub r/, corresponding to a desirable set-point y/sub r/, is known a priori. Specifically, it is the deterministic version of the generalized minimum variance controller, designed in such a way as to handle two kinds of constraints, namely, |u/sub r/(k)|/spl les/c and |u/sub r/(k)-u(k-1)|/spl les/w. It is shown that for a stable, discrete-time, either minimum or nonminimum phase system, this can be achieved by making a suitable online choice of the quantities l and Q(q/sup -1/). Apart from the well-known RLS and projection algorithms, any other recursive parameter estimation scheme can be applied, as far as it shares some of the basic properties of the above algorithms. The performance of the proposed controller is demonstrated by means of simulation. >

Sliding Mode Control in Discrete Time Linear Systems