Other Control Structures

Besides open- and closed-control, many other control structures are used in practice, but they can be seen as a combination, or perhaps a repeated combination of these two basic concepts.

Two Degrees-of-Freedom (2DoF) Control

The stability properties of a controlled system are determined by the control loop(s). When stability is of concern, and there are also disturbances acting on the system, and/or there are tracking requirements, a single loop control strategy does not provide enough design freedom to achieve all objectives. Because signals can be shaped by systems, the tracking performance clearly depends not only on the loop but also on any system in cascade. This reasoning leads to the very common control structure with two degrees of freedom, called two degrees-of-freedom

(2DoF) control [89]. This is a standard technique in linear control theory that

separates a controller into a feedforward compensator and a feedback compensator. The feedforward compensator generates the nominal input required to track a given reference trajectory. The feedback compensator corrects for errors between the desired and actual trajectories.

Cascade Control

Full system state information may be unavailable, or difficult to use at once. In cascade control, successive control loops are used, each using a single measurement and a single actuated variable. The output of the primary controller is an input to the secondary and so on. A judicious choice of how to pair variables and the ordering of the multiple loops can lead to a very efficient control implementation without the need for a full state feedback control.

Adaptive Control

In an adaptive control structure [140], the controller must adapt to a controlled

system where parameters may vary over time, or are initially uncertain. The way the parameter estimation law, that is the adaptation law), is combined with the

control law gives rise to different approaches to adaptive control. In general one should distinguish between two approaches:

• Direct methods, where the estimated parameters are those directly used in the adaptive controller. In this approach, the plant model is parameterized in terms of the desired controller parameters, which are then estimated directly without intermediate calculations involving plant parameter estimates. This approach has also been referred to as implicit adaptive control because the design is based on the estimation of an implicit plant model.

• Indirect methods, where the estimated parameters are used to calculated required controller parameters. In this approach, the plant parameters are estimated online and used to calculate the controller parameters. In other words, at each control time, the estimated plant is formed and treated as if it is the true plant in calculating the controller parameters (i.e., the so called certainty equivalence principle). This approach has also been referred to as explicit adaptive control, because the controller design is based on an explicit plant model.

In literature, several adaptation schemes have been proposed. The most widely used adaption schemes are: gain scheduling, self-tuning regulation, and model reference adaptive control.

Gain scheduling. In some situation it is known how system dynamics change

with the operating conditions. It is then possible to change the parameters of the controller by monitoring the operating conditions of the system. This idea is called gain scheduling. Essentially, the gain scheduler consists of a lookup table and the appropriate logic for detecting the operating point and choosing the corresponding value of other controller gain from the lookup table. With this approach, plant parameter variations can be compensated by changing the controller gains as functions of the input, output, and auxiliary measurements. The advantage of gain scheduling is that the controller gains can be changed as quickly as the auxiliary measurements respond to parameter changes. Frequent and rapid

changes of the controller gains, however, may lead to instability [153]; therefore,

Figure 5.3: Adaptive control – The MIAC structure.

of the disadvantages of gain scheduling is that the adjustment mechanism of the controller gains is precomputed offline and, therefore, provides no feedback to compensate for incorrect schedules.

Self-Tuning Regulation (STR). The Self-Tuning Regulation (STR) adaptation

scheme, also known as Model Identification Adaptive Control (MIAC), is based on the idea of separating the estimation of unknown parameters from the design

of the controller (as shown in Fig.5.4). Specifically, target system parameters are

estimated on-line and controller parameters are obtained from the solution of a control design problem using such estimated parameters as if they were correct (as stated by certainty equivalence principle) The STR scheme is composed of two control loops: (1) the inner loop, which contains the target system (i.e., the “target system” box) and an ordinary feedback controller (i.e., the “controller”

box), acts on the controlled system in order to track the reference signal, while (2) the outer loop, which is composed by a recursive parameter estimator (i.e., the “estimation” box) and design calculations (i.e., the “controller design” box), adjusts

the parameters of the inner controller.

Model Reference Adaptive Control (MRAC). The Model Reference Adaptive

Control (MRAC) adaptation scheme, also known as Model Reference Adaptive

System(MRAS), is an adaptive control technique where the performance specifi-

cations are given in terms of a model, which represents the ideal response of the

process to a reference signal (see Fig.5.4). The basic idea of MRAC, is to create a

Figure 5.4: Adaptive control – The MRAC structure.

of the system. First, the output of the system is compared to a desired response from a reference model, and then control parameters are update based on this error. The goal is for the parameters to converge to ideal values that cause the system response to match the response of the reference model.

Optimal Control

In an optimal control structure [122], the objective of the controller is to “determine

the control signals that will cause a process to satisfy the physical constraints and,

at the same time, minimize (or maximize) some performance criterion” [99]. Put

in another way, optimal control deals with the problem of finding a control law for a given system such that a certain optimality criterion is achieved.

If the information which the control system must use is uncertain or if the dynamic system is subjected to random disturbances, it may not be possible to satisfy this criterion with certainty; in this case, the best one can hope is to minimize (or maximize) its expected value. This leads to the concept of stochastic optimal control.

An optimal control problem includes (1) a mathematical representation of the controlled system, (2) a cost functional (or performance index) which is a function of state and control variables, and (3) a statement of boundary conditions and physical constraints on states and/or controls.

A special case of optimal control structure is the Linear Quadratic Regulator

(LQR) optimal control [107], a feedback controller where the optimal control

problem (in this case, called the LQ problem) comprises a set of linear difference equations and the performance index is described by a quadratic functional. More

details about the LQR, will be provided below, in Section5.4.2.

Decentralized and Hierarchical Control

Decentralized control structures [150] present a practical and efficient way for

designing control algorithms that utilize just the state of each subsystem, possibly without any information from other subsystems, to achieve a specific control objective (e.g., the regulation of each subsystem state to zero)..

A special case of decentralized control structure is the hierarchical control structure, where a coordinating (centralized) control is introduced to ensure that the local controls are properly modified according to a common global objective. Specifically, a hierarchical control system is a control system in which a set of devices and governing software is arranged in a hierarchical tree. Each element of the hierarchy is a linked node in the tree. Commands, tasks and goals to be achieved flow down the tree from superior nodes to subordinate nodes, whereas command results flow up the tree from subordinate to superior nodes. Nodes may also exchange messages with their siblings. The two distinguishing features of a

hierarchical control system are [64]:

• each higher layer of the tree operates with a longer interval of planning and execution time than its immediately lower layer;

• the lower layers have local tasks and goals, and their activities are planned and coordinated by higher layers which do not generally override their decisions.