Fouad M. AL-Sunni

Guaranteed Cost Control of a Markov Jump Linear Uncertain System Using a Time-Multiplied Cost Function

This paper addresses the guaranteed cost control problem of jump linear systems with norm-bounded uncertain parameters. A time-multiplied performance index is considered. The performance is calculated first and an LMI-based algorithm is developed to design a state feedback control law with constant gain matrices which robustly stabilizes the system in the mean-square quadratically stable sense.

Approximation of time-delay systems

We propose a new method for approximating time-delays in dynamical systems. A weighted H/sup /spl infin// norm criterion is minimized to obtain rational approximation of e/sup -sd/. We report the approximation in a diagram relating both the amount of time delay and the bandwidth to the order of the approximating rational function for a given level of infinity norm. The obtained approximations are compared to the widely used Pades approximation. Examples are used for illustrations.

Optimal output tracker using a time‐weighted performance index

In this paper we develop necessary conditions for the optimality of discrete system feedback controllers using a performance index imposed of (1) time weighting of the states, (2) steady-state error weighting and (3) weighting of the control gain. The controller performance is demonstrated using an F-14 digital pitch rate controller.

A Smith predictor FL-based controller for processes with long dead time

Abstract A Smith predictor ( SP) fuzzy logic ( FL) based controller for processes with long dead time is proposed. The basic concept is to combine the Smith predictor scheme with FL. The FL, in this scheme, is going to be used to auto-tune the PI controller while the SP is going to compensate for the long dead time that is commonly associated with different processes. The new scheme has been tested on several simulated plant models and demonstrated marked improvements in the performance. The simulation results demonstrated the ability of the new scheme to accommodate uncertainties in the plant model.

A Fuzzy Logic Based PID Self-Tuning Scheme For Process Control

Abstract A new fuzzy logic based PID self-tuning regulator is proposed in this paper. The basic concept behind the new scheme is to combine the classical PID control with the knowledge based Fuzzy Logic (FL) technology. The PID is going to regulate the process as usual, and the FL part is going to adjust the PID. The FL adaptation scheme will evaluate the process output at specified time instances and generate appropriate PID tuning parameters instantaneously based on number of fuzzy control rules derived from studying the general performance of the process under PID control. The performance of the new scheme is compared to the PID controller tuned by the Z-N technique through a series of simulations of different plant models.

Design Based on Transfer Function

Tackling a control design problem is always a challenge even for more experienced control engineers. The system for which the controller must be designed, may be an existing one with some poor performances and that we would like to improve, or a new system that we are building. In both cases, the design procedure starts, after getting the mathematical model for the system, by defining the desired performances that will allow us to determine the structure of the controller and its parameters.

Optimal tracker for unreliable manufacturing systems

This paper deals with the inventory-production control problem where the produced items are assumed to deteriorate at a rate that depends on the demand rate of the production system. The state of this production system is assumed to be described by a continuous-time Markov process taking values in a finite discrete space. The inventory production control problem is formulated as a stochastic optimal control problem. The optimal policy that solves the optimal control problem is obtained in terms of a set of coupled Riccati equations. The guaranteed cost problem is also treated. A numerical example is provided to show the usefulness of the proposed model.

Digital tracker with output feedback: Application to aircraft controls

A linear-quadratic output-feedback approach is given for designing digital servo-control systems of specified structure. The result is digital controllers that have a sensible-structure based on classical control theory, in contrast to standard LQR design using state feedback plus an observer. The correct initial conditions for determining the LQ tracker output-feedback gains are not uniformly distributed as is traditionally assumed, but are shown to be explicitly given in terms of the step command magnitude. Both pole and zero placement are used to optimize the performance index. Arbitrary systems are treated, not only those with integrators in the forward paths, by adding a term to the performance index that weights the steady-state error. The approach works even if the system is non-minimum-phase. Necessary conditions are derived that may be used in a gradient-based routine to determine the optimal digital control gains. The approach does not rely on redesign of a continuous control system using techniques like the bilinear transformation, but uses direct discrete-time design. An aircraft digital command augmentation system is included as a sample design.

Analysis Based on Transfer Function

Nowadays the microcontrollers are more powerful and their prices are affordable which makes their use attractive. In mechatronic systems they are used either for On/Off or continuous-time controls. In both cases, the microcontroller is the hearth of the mechatronic system. In the On/Off case, it is used for security and control purposes. The algorithm in this case is easy and doesn’t take time in general to compute the action to be taken. While for the continuous-time case, the microcontroller receives the data at each sampling period and compute the desired action according to a chosen algorithm. The computation in this case may take more time and more care should be taken to prevent surprises. In both cases interrupts are used. The microcontrollers we will use in this book must have a quite high processing speed.

Guaranteed Cost Control Problem

In the previous chapter, we presented different results that can be used to deal with nominal and uncertain systems and also with systems that are subject to external disturbances. LMI conditions were developed to design controller to achieve the desired goal. In this chapter we consider uncertain discrete-time with norm bounded uncertainties and try to present results that can be used to design a controller such that the resulting closed-loop system is asymptotically stable while an upper bound on the closed-loop value of the associated linear quadratic cost function is guaranteed.