1,519 research outputs found
A Conformal Mapping Based Fractional Order Approach for Sub-optimal Tuning of PID Controllers with Guaranteed Dominant Pole Placement
A novel conformal mapping based Fractional Order (FO) methodology is
developed in this paper for tuning existing classical (Integer Order)
Proportional Integral Derivative (PID) controllers especially for sluggish and
oscillatory second order systems. The conventional pole placement tuning via
Linear Quadratic Regulator (LQR) method is extended for open loop oscillatory
systems as well. The locations of the open loop zeros of a fractional order PID
(FOPID or PI{\lambda}D{\mu}) controller have been approximated in this paper
vis-\`a-vis a LQR tuned conventional integer order PID controller, to achieve
equivalent integer order PID control system. This approach eases the
implementation of analog/digital realization of a FOPID controller with its
integer order counterpart along with the advantages of fractional order
controller preserved. It is shown here in the paper that decrease in the
integro-differential operators of the FOPID/PI{\lambda}D{\mu} controller pushes
the open loop zeros of the equivalent PID controller towards greater damping
regions which gives a trajectory of the controller zeros and dominant closed
loop poles. This trajectory is termed as "M-curve". This phenomena is used to
design a two-stage tuning algorithm which reduces the existing PID controller's
effort in a significant manner compared to that with a single stage LQR based
pole placement method at a desired closed loop damping and frequency.Comment: 23 pages, 7 figures, in press; Communications in Nonlinear Science
and Numerical Simulations, 201
Synthesis of Minimal Error Control Software
Software implementations of controllers for physical systems are at the core
of many embedded systems. The design of controllers uses the theory of
dynamical systems to construct a mathematical control law that ensures that the
controlled system has certain properties, such as asymptotic convergence to an
equilibrium point, while optimizing some performance criteria. However, owing
to quantization errors arising from the use of fixed-point arithmetic, the
implementation of this control law can only guarantee practical stability:
under the actions of the implementation, the trajectories of the controlled
system converge to a bounded set around the equilibrium point, and the size of
the bounded set is proportional to the error in the implementation. The problem
of verifying whether a controller implementation achieves practical stability
for a given bounded set has been studied before. In this paper, we change the
emphasis from verification to automatic synthesis. Using synthesis, the need
for formal verification can be considerably reduced thereby reducing the design
time as well as design cost of embedded control software.
We give a methodology and a tool to synthesize embedded control software that
is Pareto optimal w.r.t. both performance criteria and practical stability
regions. Our technique is a combination of static analysis to estimate
quantization errors for specific controller implementations and stochastic
local search over the space of possible controllers using particle swarm
optimization. The effectiveness of our technique is illustrated using examples
of various standard control systems: in most examples, we achieve controllers
with close LQR-LQG performance but with implementation errors, hence regions of
practical stability, several times as small.Comment: 18 pages, 2 figure
Stability of closed-loop fractional-order systems and definition of damping contours for the design of controllers
Fractional complex order integrator has been used since 1991 for the design of robust control-systems. In the CRONE control methodology, it permits the parameterization of open loop transfer function which is optimized in a robustness context. Sets of fractional order integrators that lead to a given damping factor have also been used to build iso-damping contours on the Nichols plane. These iso-damping contours can also be used to optimize the third CRONE generation open-loop transfer function. However, these contours have been built using non band-limited integrators, even if such integrators reveal to lead to unstable closed loop systems. One objective of this paper is to show how the band-limitation modifies the left half-plane dominant poles of the closed loop system and removes the right half-plane ones. It is also presented how to obtain a fractional order open loop transfer function with a high phase slope and a useful frequency response. It is presented how the damping contours can be used to design robust controllers, not only CRONE controllers but also PD and QFT controllers
Sound and Automated Synthesis of Digital Stabilizing Controllers for Continuous Plants
Modern control is implemented with digital microcontrollers, embedded within
a dynamical plant that represents physical components. We present a new
algorithm based on counter-example guided inductive synthesis that automates
the design of digital controllers that are correct by construction. The
synthesis result is sound with respect to the complete range of approximations,
including time discretization, quantization effects, and finite-precision
arithmetic and its rounding errors. We have implemented our new algorithm in a
tool called DSSynth, and are able to automatically generate stable controllers
for a set of intricate plant models taken from the literature within minutes.Comment: 10 page
- âŚ