Stability Analysis and Design of Digital Compensators for Networked Control Systems

Abstract

Networked Control Systems (NCSs) are distributed control systems where sensors, actuators, and controllers are interconnected by communication networks, e.g. LAN, WAN, CAN, Internet. Use of digital networks are advantageous due to less cost, ease in installation and/or ready availability. These are widely used in automobiles, manufacturing plants, aircrafts, spacecrafts, robotics and smart grids. Due to the involvement of network in such systems, the closed-loop system performance may degrade due to network delays and packet losses. Since delays are involved in NCS, predictor based compensators are useful to improve control performance of such systems. Moreover, the digital communication network demands implementation of digital compensators. First, the thesis studies stability analysis of NCSs with uncertain time-varying delays. For this configuration, both the controller and actuators are assumed as event-driven (i.e. the delays are fractional type). The NCS with uncertain delays and packet losses are represented
as systems in polytopic form as well as with norm-bounded uncertainties. The closed-loop system stability is guaranteed using quadratic Lyapunov function in terms of LMIs. For given controller gain the maximum tolerable delay calculated and the resultant stability regions of
the system is explored in the parameter plane of control gain and maximum tolerable delay. The stability region is found to be almost same for both the methods for the case of lower order systems (an integrator plant), whereas for higher order systems (second order example system), the obtained stability region is more for the case of polytopic approach than the norm-bounded one. This motivates to use the polytopic modeling approach in remaining of the thesis. Next, design of digital Smith Predictor (SP) to improve the performance of NCS with
bounded uncertain delays and packet losses in both the forward and feedback channels is con-sidered. For implementing a digital SP, it is essential that the controller is implemented with constant sampling interval so that predictor model is certain and therefore the controller is required to be time-driven one (sensor-to-controller channel uncertainties are integer type).
On the other hand, the actuator is considered to be event-driven since it introduces lesser delay compared to the time-driven case. Thereby, the controller-to-actuator channel delays are fractional type. The system with uncertain delay parameters (packet losses as uncertain
integer delays) are modeled in polytopic form. For this system, Lyapunov stability criterion has been presented in terms of LMIs to explore the closed-loop system stability. Finally, the proposed analysis is verified with numerical studies and using TrueTime simulation en-
vironment. It is observed that the digital SP improves the stability performance of the NCS considerably compared to without predictor. However, the choice of predictor delay affects the system performance considerably. Further, an additional filter is used along with conventional digital SP to improve the system response and disturbance rejection property of the controller. For this configurations, both the controller and actuators are assumed to be time-driven. The NCS with random but bounded delays and packet losses introduced by the network is modeled as a switched system and LMI based iterative algorithm is used for designing the controller.
A LAN-based experimental setup is developed to validate the above theoretical findings.The plant is an op-amp based emulated integrator plant.The plant is interfaced with a computer using data acquisition card. Another computer is used as the digital controller and the two computers are connected via LAN using UDP communication protocol. The effectiveness of the proposed controller design method is verified with this LAN-based experi-
mental setup. Three controller configurations (i.e. without and with digital SP as well as the digital SP with filter) are considered for comparison of their guaranteed cost performance. It is shown that the digital SP with filter improves the performance of NCS than with and without simple digital SP based NCS configurations.
Finally, design of digital predictor based robust H1 control for NCSs is made in such a way that the effect of randomness in network delays and packet losses on the closed-loop system dynamics is reduced. For the purpose, the predictor delay is chosen as a fixed one whereas variation of random delays in the system are modeled as disturbances. Then quadratic H1 design criterion in the form of LMIs is invoked so that the network jitter effect is minimized. The efficacy of the proposed configurations are validated with the developed LAN based NCS setup. It is seen that the designed controllers effectively regularize the system dynamics from random variations of the network delays and packet losses.