Linear Time-invariant Continuous-time Plant Research Articles

Performance of periodically time-varying controllers for sampled data control

Analyzes performance of periodically time-varying sampled data controllers for L/sub p/ deterministic and uniform disturbance rejection. For a given linear periodic sampled data controller controlling a linear time-invariant continuous-time plant, it is shown that a linear time-invariant controller can be found to give better L/sub p/ sampled data control than the time-varying controller. The performance analysis is in time domain using convexity properties of the L/sub p/ signal space.

Indirect model reference adaptive control with dynamic adjustment of parameters

SUMMARY The paper discusses in detail a new method for indirect model reference adaptive control (MRAC) of linear time-invariant continuous-time plants with unknown parameters. The method involves not only dynamic adjustment of plant parameter estimates but also those of the controller parameters. Hence the overall system can be described by a set of non-linear differential equations as in the case of direct control. Many of the difficulties encountered in the conventional indirect approach, where an algebraic equation is solved to determine the control parameters, are consequently bypassed in this method. The proof of stability of the equilibrium state of the overall system is found to be different from that used in direct control. Using Lyapunov’s theory, it is first shown that the parameter errors between the parameter estimates of the identifier and the true parameters of the plant, as well as those between the actual parameters of the controller and their desired values, are bounded. Following this, using growth rates of signals in the adaptive loop as well as order arguments, it is shown that the error equations are globally uniformly stable and that the tracking (control) error tends to zero asymptotically. This in turn establishes the fact that both direct and indirect model reference adaptive schemes require the same amount of prior information to achieve stable adaptive control.

Performance study of multi-rate output controllers under noise disturbances

This paper presents a comparative study of the performance of a multi-rate output controller (MROC) with a linear quadratic gaussian (LQG) controller in the presence of noise disturbances and anti-aliasing filters. The basis of comparison is to apply an LQG law with a one-step-ahead prediction-type Kalman filter (hereafter called LQG law I) and an LQG law with a current estimation-type Kalman filter (hereafter called LQG law II) to a linear time-invariant continuous-time plant model with a white gaussian process and measurement noise and compute a linear quadratic performance index for the discretized plant. Equivalent noise matrices for using the MROC law are derived and the same quadratic performance index computed. In order to have a fair comparison, the cut-off frequency of the anti-aliasing filter used to remove high frequency noise components prior to sampling is also kept the same when applying both laws. Application of both laws in typical situations shows that the performance of the MROC law is worse than either that of LQG law I or LQG law II.

Robust Design of Model Reference Adaptive Control System Including Fixed Compensator

This paper presents a design method of model reference robust adaptive control systems (M RRACS) for a single-input single-output(SISO) linear time-invariant continuous-time plant in the presence of bounded unknown deterministic disturbances. The proposed adaptive control system consists of two feedback loops: one performs the model-matching adaptively, and the other includes a non-adaptive error feedback controller which can compensate the disturbances, uncertainty in initial condition of the system and unexactness in the plant model. This error feedback controller is designed based on H ∞ -optimal theory, so it is not necessary to know the structure of disturbances a prior . The aim of the proposed control structure is realization of harmonizing the adaptive control to the robust control.

Design of finite impulse response controllers by pole assignment in multirate sampled-data systems

Abstract The multirate sampled-data control of a linear time-invariant continuous-time plant is considered. It is shown that ‘gain variable’ multirate controllers can be viewed as finite impulse response (FIR) filters, and the pole assignment problem is studied from this viewpoint. Furthermore, it is shown how to evaluate the controller coefficients and how to improve the behaviour of the closed-loop system with respect to limit cycles and steady-state accuracy by introducing integral action.

Design of finite impulse response controllers by pole assignment in multirate sampled-data systems

Abstract The multirate sampled-data control of a linear time-invariant continuous-time plant is considered. It is shown that ‘gain variable’ multirate controllers can be viewed as finite impulse response (FIR) filters, and the pole assignment problem is studied from this viewpoint. Furthermore, it is shown how to evaluate the controller coefficients and how to improve the behaviour of the closed-loop system with respect to limit cycles and steady-state accuracy by introducing integral action.

Pole assignment by multirate sampled-data output feedback

Abstract Multirate sampled-data control of a linear time-invariant continuous-time plant is considered, It is shown that, if the plant is controllable and observable, a multirate sampled-data ‘gain‘ controller can always be constructed so that the poles of the closed-loop system become an arbitrarily-given symmetric set of complex numbers. It is also shown that the input sampling rate (JV,,[tdot],NJ can be chosen equal to the Kronecker invariants, or other locally minimum controllability indices. Here, ‘locally minimum controllability indices’ are defined as a set of integers (nlt[tdot], nm) such that ≪(+n2+[tdot]+ m, equals the dimension of the state vector and the matrix [b, [tdot] A‴∼1b1[tdot] bm[tdot] A″ m∼ 'b] is non-singular. This capability gives a new perspective to the application of multirate sampled-data controllers.