Dhafer Al-Makhles

Stability and Performance Analysis of Bit-Stream-Based Feedback Control Systems

Bit stream (BS)-based feedback control systems often use a delta-sigma modulator (ΔΣ-M) as a two-level dynamic quantizer to encode and decode feedback signals. The stability and performance of such systems are critically dependent on the selection of the quantizer step size. This paper derives the stability condition of a BS-based control system in terms of the quantizer step size using sliding mode analysis. It is proved that the quantized system is equivalent to the original system on the sliding manifold under ideal sliding. However, the presence of the quantizer in a ΔΣ-M introduces noise into the system that often degrades the performance of the overall system. This paper therefore determines the optimum quantizer gain, i.e., the upper and lower boundaries of the quantizer, which maintains the stability and reduces the quantization noise. BS-based proportional- integral-differential (BS-PID) controllers are designed using the proposed optimal dynamic quantizer and implemented using three different realizations. Simulation results show that the optimal quantizer significantly reduces the noise within the system bandwidth. The effectiveness of the BS-PID controller with the optimal quantizer is further demonstrated using the experimental prototype of a dc servomechanism by designing a BS-PID controller. The experimental results from a laboratory prototype illustrate that the BS-PID controller gives identical performance to a traditional PID controller and effectively controls the system while consuming less information rate (channel interfaces) and hardware resources.

An Adaptive Two-Level Quantizer for Networked Control Systems

This brief proposes a novel adaptive two-level quantizer, which generates 1-b per sample and can be used for a class of industrial networked control systems (NCSs). The adaptive quantizer is introduced to automatically estimate the input of the quantizer using equivalent control-based sliding mode control. The stability condition of the proposed quantizer is derived analytically with the help of a sliding-mode analysis. The effectiveness of the proposed quantized NCS is illustrated experimentally by designing a quantized feedback controller to control the position of a dc motor, where signals with 1-b per sample are utilized to interconnect the controller with the plant. Simulation results from a laboratory prototype illustrate that the proposed quantizer with the feedback controller controls the system effectively, introduces less quantization noise, and minimizes the data rate.

Adaptive quantizer for networked control system

This paper proposes a novel approach for data-compression using Delta-sigma modulator (ΔΣ-M) and applies it to design bit-stream based controllers. An adaptive scheme is introduced to automatically determine the upper and lower boundaries of the quantizer of the ΔΣ-M. The stability condition of the feedback control system with embedded ΔΣ-M is derived analytically based on sliding mode analysis. The effectiveness of the proposed controller is illustrated experimentally by designing hybrid bit-stream based feedback controller to control the position of a D.C. motor. Experimental results from a laboratory prototype illustrate that the adaptive ΔΣ-M with the feedback controller effectively controls the systems while consuming less significant channels interfaces between the measurement device and the controller.

Delta-Sigma based bit-stream controller for a D.C. motor

The present paper proposes a Delta Sigma (ΔΣ) modulator based control to control linear systems. This control method processes bit stream signals to control physical systems and offers various advantages compared to traditional methods of controller implementation, which uses multi-bit processing. To evaluate the performance of the bit-stream controller in real-life control applications, a digital controller based on a delta operator is used as a benchmark to which the controller utilizing bit-stream technique is compared. The effectiveness of the proposed bit-stream controller is experimentally validated considering an example of a DC motor. The results of the experiment show that the technique utilizing bit-stream signals are more attractive as an alternative to processing of multi-bit digital signal. Although both controllers display a comparable performance in simulation and experiment, the controller utilizing bit-stream uses approximately 400 logic elements (LE) on an Altera Cyclone FPGA comparing to the conventional controller which costs 600 (LE) and 17 9-bit multipliers.

The dynamic behaviour of data-driven Δ-M and ΔΣ-M in sliding mode control

ABSTRACT In recent years, delta (Δ-M) and delta-sigma modulators (ΔΣ-M) are increasingly being used as efficient data converters due to numerous advantages they offer. This paper investigates various dynamical features of these modulators/systems (both in continuous and discrete time domain) and derives their stability conditions using the theory of sliding mode. The upper bound of the hitting time (step) has been estimated. The equivalent mode conditions, i.e. where the outputs of the modulators are equivalent to the inputs, are established. The results of the analysis are validated through simulations considering a numerical example.

Passive actuator fault tolerant control for a class of MIMO nonlinear systems with uncertainties

ABSTRACT Fault tolerant control of affine class of multi-input multi-output (MIMO) nonlinear systems has not received considerable attention of researchers compared to other class of nonlinear systems. Therefore, this paper proposes an adaptive passive fault tolerant control method for actuator faults of affine class of MIMO nonlinear systems with uncertainties using sliding mode control . The actuator fault is represented by a multiplicative factor of the control signal which reflects the loss of actuator effectiveness. The design of the controller is based on the assumption that the maximum loss level of the actuator effectiveness is known. Furthermore, since the proposed controller is adaptive, it does not require any a-priori knowledge of the uncertainty bounds. The closed-loop stability conditions of the controller are derived based on Lyapunov theory. The effectiveness of the proposed controller is demonstrated considering two examples: a two degree of freedom helicopter and a two-link robot manipulator and has been found to be satisfactory.

Stabilisation of discrete-time polynomial fuzzy systems via a polynomial lyapunov approach

ABSTRACT This paper deals with the problem of designing a controller for a class of discrete-time nonlinear systems which is represented by discrete-time polynomial fuzzy model. Most of the existing control design methods for discrete-time fuzzy polynomial systems cannot guarantee their Lyapunov function to be a radially unbounded polynomial function, hence the global stability cannot be assured. The proposed control design in this paper guarantees a radially unbounded polynomial Lyapunov functions which ensures global stability. In the proposed design, state feedback structure is considered and non-convexity problem is solved by incorporating an integrator into the controller. Sufficient conditions of stability are derived in terms of polynomial matrix inequalities which are solved via SOSTOOLS in MATLAB. A numerical example is presented to illustrate the effectiveness of the proposed controller.

Two-level quantised control systems: sliding-mode approach

ABSTRACT Sliding mode quantisers (SMQs), where signals are converted to switching signals represented by the sequence of binary values s and s, are increasingly being used in various applications including control of power converters, networked control systems (NCSs), one-bit control processing, etc. This paper derives the stability conditions of nonlinear control system embedded with SMQ-based Δ-M. The equivalence conditions of the proposed SMQ, which assure that its binary outputs are equivalent to its inputs, are established. The results of theoretical analysis are validated through simulation considering an example of the underwater vehicle control system, where the transmission bit-rate is limited by . The results of the simulation demonstrates that the quantised feedback signals effectively control the system and achieves both the desired specifications and the bandwidth reduction.

Robust control of wireless power transfer system

In recent years, wireless power transfer systems have successfully been used in various industrial applications due to their contactless power transfer feature. However, these systems behave as higher order resonant networks and hence are highly sensitive to changes in system parameters. Traditional PID controllers often fail to maintain satisfactory power regulation in the presence of parametric uncertainties which include load and circuit parameter variations, variations in magnetic coupling between the primary and secondary coils. To overcome these problems, this paper designs a robust H∞ output feedback controller for a bi-directional inductive power transfer system. The control design is carried out following Ricatti approach. Simulations are conducted to verify the power regulation performance of the proposed controller and it is compared with a classical PID controller. The results show that the H∞ output feedback controller could successfully regulate the power in both directions in the presence of large uncertainties in various circuit parameters.

Single-bit modulator based controller for capacitive power transfer system

This paper proposes a single-bit ADC system based Proportional and Integral (PI) controller to regulate the output voltage of Capacitive Power Transfer (CPT) systems. A simple single-bit ADC system i.e., Single-Bit Modulator (SBM) is considered as an alternative to the commonly used multi-bit ADC systems. Unique features of employing SBM are 1) its ability to convert analog signals into single-bit signals and 2) its easy integrability in digital chips with linear variable differential transformers (LVDTs) such as FPGAs. A SBM based PI (SBM-PI) controller is designed which guarantees consumption of less hardware resources, latency and effectively regulates the output voltage to provide the desired power transfer efficiency. The performance of the proposed SBM-PI controller is compared to that of a conventional multi-bit PI controller and has been shown that both controllers give identical performance. However, the SBM-PI consumes significantly less hardware resources. The effectiveness of the proposed controller with SBM-PI is further demonstrated using the experimental prototype of CPT using 16 MHz ATmega8 microcontroller. The experimental results from a laboratory prototype illustrate that SBM-PI controller successfully regulates the output voltage of CPT to control the power flow.