Two-Level Dynamic Quantizers for Feedback Control Systems

Abstract

The two-level quantized control systems which inherently involve switching signals (i.e., two-level discrete set f0;1g or ON/OFF), are one of the actively studied topics in control system. Switching signals are extensively being used in various types of control systems, such as on-off control systems, sliding mode control systems, hybrid systems, etc. This is due in part to the simple switching functions (SFs) that are embedded in these systems, such as relay, pulse-width-modulator (PWM), switch mode power supply (SMPS), delta modulators (D-M), delta-sigma modulators (DS-M) and sliding mode modulators. As a result, switching signals can be used to drive power convertor or ON/OFF actuators, analog-todigital converter (ADC) and switches (multiplexers) in single-bit signal processing and single-bit control system. These switching signals are also being used as triggers for the event-triggered control systems. To partially overcome the limitations of the communication constraint, packets of single-bit replace packets of multi-bits as the transmitted information through communication-channels in networked control systems (NCSs). This thesis proposes a novel approach of designing switching functions using hybrid delta modulator (DH-M) and investigates the stability and performance of switch-based control systems (SBCS) which are embedded with D-M, DS-M and the proposed DH-M. The central component in switched based control systems are either D-M, DS-M or the proposed DHM, which are often regarded as dynamic quantizers. Therefore, before designing controllers for SBCS, the stability and performance analysis of SFs based on these three different modulators are investigated using the theory of sliding mode. It has been shown that the stability and hitting time of these SFs are critically dependent on the choice of the quantizer gain. Next, the stability and performance of a single-bit control system, which is embedded with a DS- M, are investigated. The DS-M essentially acts as a two-level dynamic quantizer. It is proved that under ideal sliding condition, the quantized feedback control system is equivalent to the original control system on the sliding manifold. The optimum gain of the quantizer, which ensures stability and gives better performance, is derived. The effectiveness of the single-bit control system with the optimal quantizer is demonstrated using the experimental prototype of a dc servomechanism by designing single-bit PID controller. The experimental results illustrate that the single-bit controller gives identical performance to a traditional controller and effectively controls the system while consuming less information rate (channel interfaces) and hardware resources. Since the SFs can be used as single-bit encoders/decoders, they can be embedded in the NCS to relax communication constraints. The stability and performance of control systems using all the three modulators ( i.e., D-M, DS-M and DH-M) are derived analytically and their performance is investigated from the perspective of NCS both through simulations and experiments. It has been shown that, for a given sampling interval, the proposed hybrid DH-M effectively attenuates the chattering compared to the conventional D-M and DS-M. Finally, this thesis investigates the use of SF based sliding mode modulator in general SBCS where signals can be converted to their equivalent switching signals. The condition which guarantees the stability of SBCS is established in both continuous-time and discrete-time domains. The standard assumption of infinite sampling of the switch component in stable continuous-time SF (CT-SF) guarantees the equivalence condition between the converted signals and switching signals. However, the inherited delay in the discrete-time SF (DT-SF), which is induced by the finite sampling frequency, adds more constraint to the convergence rate and adversely affects the equivalence condition. Thus, unlike CT-SF, the existence of quasi-sliding mode in DT-SF does not necessarily guarantee the equivalence condition between the converted signals (inputs) and switching outputs. We show that only DT-SF with zero convergence rate can be used for the mapping purpose in discrete-time SBCS (DT-SBCS). The feasibility and effectiveness of the DT-SBCS is demonstrated experimentally using an example of servomechanism with GPI controller. The simulation and results of experiments reported in the thesis use Matlab/Simulink and Quartus II. The synthesized VHDL codes are used to program FPGA (Altera DE2-115). The performance of all the controllers and SFs are demonstrated using an experimental prototype of DC servomechanism. Both simulation and experimental results are used to analyze the effects of using such SFs on control system stability, performances, information rate (channel interfaces) and hardware resources.