Proportional-integral-plus (PIP) control of time delay systems

The paper shows that the digital proportional-integral-plus (PIP) controller formulated within the context of non-minimum state space (NMSS) control system design methodology is directly equivalent, under certain non-restrictive pole assignment conditions, to the equivalent digital Smith predictor (SP) control system for time delay systems. This allows SP controllers to be considered within the context of NMSS state variable feedback control, so that optimal design methods can be exploited to enhance the performance of the SP controller. Alternatively, since the PIP design strategy provides a more flexible approach, which subsumes the SP controller as one option, it provides a superior basis for general control system design. The paper also discusses the robustness and disturbance response characteristics of the two PIP control structures that emerge from the analysis and demonstrates the efficacy of the design methods through simulation examples and the design of a climate control system for a large horticultural glasshouse system

Store-and-forward based methods for the signal control problem in large-scale congested urban road networks

The problem of designing network-wide traffic signal control strategies for large-scale congested urban road networks is considered. One known and two novel methodologies, all based on the store-and-forward modeling paradigm, are presented and compared. The known methodology is a linear multivariable feedback regulator derived through the formulation of a linear-quadratic optimal control problem. An alternative, novel methodology consists of an open-loop constrained quadratic optimal control problem, whose numerical solution is achieved via quadratic programming. Yet a different formulation leads to an open-loop constrained nonlinear optimal control problem, whose numerical solution is achieved by use of a feasible-direction algorithm. A preliminary simulation-based investigation of the signal control problem for a large-scale urban road network using these methodologies demonstrates the comparative efficiency and real-time feasibility of the developed signal control methods

Optimal control of ankle joint moment: Toward unsupported standing in paraplegia

This paper considers part of the problem of how to provide unsupported standing for paraplegics by feedback control. In this work our overall objective is to stabilize the subject by stimulation only of his ankle joints while the other joints are braced, Here, we investigate the problem of ankle joint moment control. The ankle plantarflexion muscles are first identified with pseudorandom binary sequence (PRBS) signals, periodic sinusoidal signals, and twitches. The muscle is modeled in Hammerstein form as a static recruitment nonlinearity followed by a linear transfer function. A linear-quadratic-Gaussian (LQG)-optimal controller design procedure for ankle joint moment was proposed based on the polynomial equation formulation, The approach was verified by experiments in the special Wobbler apparatus with a neurologically intact subject, and these experimental results are reported. The controller structure is formulated in such a way that there are only two scalar design parameters, each of which has a clear physical interpretation. This facilitates fast controller synthesis and tuning in the laboratory environment. Experimental results show the effects of the controller tuning parameters: the control weighting and the observer response time, which determine closed-loop properties. Using these two parameters the tradeoff between disturbance rejection and measurement noise sensitivity can be straightforwardly balanced while maintaining a desired speed of tracking. The experimentally measured reference tracking, disturbance rejection, and noise sensitivity are good and agree with theoretical expectations

Adaptive Optimal Control The Thinking Man's GPC

Exploring connections between adaptive control theory and practice, this book treats the techniques of linear quadratic optimal control and estimation (Kalman filtering), recursive identification, linear systems theory and robust arguments

Continuous-time self-tuning algorithms

This thesis proposes some new self-tuning algorithms. In contrast to the conventional discrete-time approach to self-tuning control, the continuous-time approach is used here, that is continuous-time design but digital implementation is used. The proposed underlying control methods are combined with a continuous-time version of the well-known discrete recursive least squares algorithms. The continuous-time estimation scheme is chosen to maintain the continuous-time nature of the algorithms. The first new algorithm proposed is emulator-based relay control (which has already been described in a paper by the author). The algorithm is based on the idea of constructing the switching surface by emulators; that is, unrealisable output derivatives are replaced by their emulated values. In particular, the relay is forced to operate in the sliding mode. In this case, it is shown that emulator-based control and its proposed relay version become equivalent in the sense that both give the same control law. The second new algorithm proposed is a continuous-time version of the discrete-time generalized predictive control (GPC) of Clarke et al (which has already been described in a paper by the author). The algorithm, continuous-time generalized predictive control (CGPC), is based on similar ideas to the GPC, however the formulation is very different. For example, the output prediction is accomplished by using the Taylor series expansion of the output and emulating the output derivatives involved. A detailed closed-loop analysis of this algorithm is also given. It is shown that the CGPC control law only changes the closed-loop pole locations leaving the open-loop zeros untouched (except one special case). It is also shown that LQ control can be considered in the CGPC framework. Further, the CGPC is extended to include some design polynomials so that the model-following and pole-placement control can be considered in the same framework. A third new algorithm, a relay version of the CGPC, is described. The method is based on the ideas of the emulator-based relay control and again it is shown that the CGPC and its relay version become equivalent when the relay operates in the sliding mode. Finally, the CGPC ideas are extended to the multivariable systems and the resulting closed-loop system is analysed in some detail. It is shown that some special choice of design parameters result in a decoupled closed-loop system for certain systems. In addition, it is shown that if the system is decouplable, it is possible to obtain model-following control. It is also shown that LQ control, as in the scalar case, can be considered in the same framework. An illustrative simulation study is also provided for all of the above methods throughout the thesis

Robust Controller Synthesis Using the Maximum Entropy Design Equations

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/57847/1/MaxEntRobustControlTAC1986.pd

Controller Design for a Direct Coupled Motor

This thesis describes an effort to enhance the control capabilities of an electric motor. It is in the interest of TetraPak that the research on this motor is performed so that it, in the future, can be a part of their production systems. The thesis has been separated into three main parts, where in the first part we are trying to find a model that describes the process. The second part describes how the controllers were developed and the final part how they were implemented in real time. Our goal was to successfully identify the motor and control it within the, from TetraPak, specified demands. And if time allowed, do it all automatically

Stability and Performance Verification of Optimization-based Controllers

This paper presents a method to verify closed-loop properties of optimization-based controllers for deterministic and stochastic constrained polynomial discrete-time dynamical systems. The closed-loop properties amenable to the proposed technique include global and local stability, performance with respect to a given cost function (both in a deterministic and stochastic setting) and the $\mathcal{L}_2$ gain. The method applies to a wide range of practical control problems: For instance, a dynamical controller (e.g., a PID) plus input saturation, model predictive control with state estimation, inexact model and soft constraints, or a general optimization-based controller where the underlying problem is solved with a fixed number of iterations of a first-order method are all amenable to the proposed approach. The approach is based on the observation that the control input generated by an optimization-based controller satisfies the associated Karush-Kuhn-Tucker (KKT) conditions which, provided all data is polynomial, are a system of polynomial equalities and inequalities. The closed-loop properties can then be analyzed using sum-of-squares (SOS) programming

High-Order AFEM for the Laplace-Beltrami Operator: Convergence Rates

We present a new AFEM for the Laplace-Beltrami operator with arbitrary polynomial degree on parametric surfaces, which are globally $W^1_\infty$ and piecewise in a suitable Besov class embedded in $C^{1,\alpha}$ with $\alpha \in (0,1]$. The idea is to have the surface sufficiently well resolved in $W^1_\infty$ relative to the current resolution of the PDE in $H^1$. This gives rise to a conditional contraction property of the PDE module. We present a suitable approximation class and discuss its relation to Besov regularity of the surface, solution, and forcing. We prove optimal convergence rates for AFEM which are dictated by the worst decay rate of the surface error in $W^1_\infty$ and PDE error in $H^1$.Comment: 51 pages, the published version contains an additional glossar