Stability Of Digital Control Systems Research Articles

Stability of Digital Control System for Unmanned Aerial Vehicle with Numerical Analysis

The paper presents the analysis on stability of digital control system for unmanned vehicle with numerical analysis. The objective of this study is mainly emphasized on the fulfillment of the advanced control techniques according to the fundamental concepts of digital control system approaches for unmanned aerial vehicle system design. The targeted unmanned aerial vehicle system was designed based on the simple construction under the idea of fixed wing flight system approaches. The stability analyses on unmanned aerial vehicle are vital role to enhance the real world applications. The background concepts on digital control system for stability analysis on dynamic control system like unmanned aerial vehicle system. The appropriate controller design for dynamic control system of unmanned aerial vehicle is vital role to analyze the accurate stability condition for reality. The implementation of numerical analysis on compensator design has been developed by using MATLAB. The physical parameters in these analyses are based on the experimental outcomes from the recent research works in dynamical system implementations. The mathematical approaches are very helpful for numerical analysis on compensator design for the unmanned aerial vehicles schemes. The simulation results confirm that the high performance stability test on unmanned aerial vehicle system has been met with the theoretical works.

Formal Non-Fragile Stability Verification of Digital Control Systems with Uncertainty

A verification methodology is described and evaluated to formally determine uncertain linear systems stability in digital controllers with considerations to the implementation aspects. In particular, this methodology is combined with the digital-system verifier (DSVerifier), which is a verification tool that employs Bounded Model Checking based on Satisfiability Modulo Theories to check the stability of digital control systems with uncertainty. DSVerifier determines the control system stability, considering all the plant interval variation set, together with the Finite Word-length (FWL) effects in the digital controller implementation; DSVerifier checks the robust non-fragile stability of a given closed-loop system. The proposed methodology and respective tool are evaluated considering non-fragile control examples from literature. Experimental results show that the approach used in this study is able to foresee fragility problems in robust controllers, which could be overlooked by other existing approaches due to underestimating of FWL effects.

Stability of digital control systems implemented in error-recoverable computers

Safety-critical, real-time applications make use of fault-tolerant digital control systems to achieve their performance goals. Even though these digital control systems are fault-tolerant, they are susceptible to errors induced by common-mode faults, since these errors cannot be masked by standard redundancy provisions. Such errors can be handled by special error correction mechanisms, which could require stopping the control law computations while the errors are removed. Thus, the effect of these special error recovery mechanisms on digital control systems needs to be understood. This paper presents a comprehensive study of the effect of three error recovery mechanisms–rollback, reset and cold restart–on the stability of digital closed-loop control systems. The effect of the faults, detected and handled by these error recovery mechanisms, on the digital control system is modelled by a set of interference maps. It is assumed that the arrival and departure of common-mode faults can be represented by a Markov process. The overall system behaviour is then described by a Markov jump linear model, whose stability is explored using standard techniques from the literature. The result of this analysis is a new metric, the minimum average interarrival spacing (MAIS), which is useful for comparing the performance of different error recovery mechanisms and for designing new fault-tolerant controllers. The theoretical results are illustrated via Monte Carlo simulations that show the effects of common-mode faults on the closed-loop stability of the longitudinal dynamics of an AFTI/F-16 aircraft.

The PIL (Not PID?) Controller as Eigenvalue Assigner and Optimum Stabiliser

For reasons of saturation avoidance and limitation of high frequency noise, the classical PID controller is usually implemented with a lowpass filter on the derivative channel. As pointed out by the author some years ago, this has profound implications for the stability of digital control systems based on discretised analog designs. However, it then ceases to be a PID controller and might be better described as PIL, where L normally stands for phase “lead,” but might in exceptional circumstances be phase “lag.” Such controllers are investigated as eigenvalue assigners for an inherently unstable magnetic levitation (maglev) system and for a first order lag with pure time delay, where the time delay is approximated by a first order Padé approximation for design purposes and then simulated exactly for performance evaluation. Explicit controller designs are derived with all closed loop eigenvalues placed at the same location. It is demonstrated, using root locus arguments, that this gives an optimally stable system in the sense that as any single controller or process parameter is varied with respect to its nominal value, the rightmost eigenvalue, on passage through the nominal parameter setting, is as deep in the left half plane as possible.

Control of a PWM Convertor for Linear Generator as a Variable Impedance

We are developing a linear generator system as an onboard power source for Maglev vehicles. This linear generator system mainly consists of power collecting coils and has a Pulse Width Modulated convertor that functions as an impedance to compensate for reactive power in the generator circuit. The PWM convertor detects only instantaneous currents and realizes unity power factor control with excellent performance. Nevertheless, the measured impedance of the circuit differs from that estimated from the parameters of PWM convertor. The system becomes unstable when we set certain impedance values for the PWM convertor.We analyzed the control system as a closed loop digital control system and we derived impedance realized in the circuit We also obtained stable areas of impedance and currents from the conditions of stability of digital control system. The analyzed results of stability were in agreement with simulation results.

Integration of MRI/EEG/MEG/SPECT for source localisation

For reasons of saturation avoidance and limitation of high frequency noise, the classical PID controller is usually implemented with a lowpass filter on the derivative channel. As pointed out by the author some years ago, this has profound implications for the stability of digital control systems based on discretised analog designs. However, it then ceases to be a PID controller and might be better described as PIL, where L normally stands for phase “lead,” but might in exceptional circumstances be phase “lag.” Such controllers are investigated as eigenvalue assigners for an inherently unstable magnetic levitation (maglev) system and for a first order lag with pure time delay, where the time delay is approximated by a first order Padé approximation for design purposes and then simulated exactly for performance evaluation. Explicit controller designs are derived with all closed loop eigenvalues placed at the same location. It is demonstrated, using root locus arguments, that this gives an optimally stable system in the sense that as any single controller or process parameter is varied with respect to its nominal value, the rightmost eigenvalue, on passage through the nominal parameter setting, is as deep in the left half plane as possible.

The influence of finite word length on digital optimal control

This paper is concerned with the performance of linear discrete-time systems, controlled by a finite word length computer with floating-point arithmetic, and of which the state is directly measurable with an A/D converter of the same word length. The effect of using finite word length is twofold. First, roundings are made after addition or multiplication of two rounded numbers. Second, the control parameters are represented in the controller's memory, by rounded numbers. The first effect can be accounted for by considering the control parameters stochastic. The second effect is deterministic. After a description of the stochastlcs of the roundoff errors has been derived, the influence of both effects on the optimality and stability of digital control systems in the steady state in relation to a quadratic cost function is considered.